Classical and Quantum Gravity

The theory of general relativity predicts the existence of closed time-like curves (CTCs), which theoretically would allow an observer to travel back in time and interact with their past self. This raises the question of whether this could create a grandfather paradox, in which the observer interacts in such a way to prevent their own time travel. Previous research has proposed a framework for deterministic, reversible, dynamics compatible with non-trivial time travel, where observers in distinct regions of spacetime can perform arbitrary local operations with no contradiction arising. However, only scenarios with up to three regions have been fully characterised, revealing only one type of process where the observers can verify to both be in the past and future of each other. Here we extend this characterisation to an arbitrary number of regions and find that there exist several inequivalent processes that can only arise due to non-trivial time travel. This supports the view that complex dynamics is possible in the presence of CTCs, compatible with free choice of local operations and free of inconsistencies.

Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by somebody nearby. For this, our team at Double Negative Visual Effects, in collaboration with physicist Kip Thorne, developed a code called Double Negative Gravitational Renderer (DNGR) to solve the equations for ray-bundle (light-beam) propagation through the curved spacetime of a spinning (Kerr) black hole, and to render IMAX-quality, rapidly changing images. Our ray-bundle techniques were crucial for achieving IMAX-quality smoothness without flickering; and they differ from physicists’ image-generation techniques (which generally rely on individual light rays rather than ray bundles), and also differ from techniques previously used in the film industry’s CGI community. This paper has four purposes: (i) to describe DNGR for physicists and CGI practitioners, who may find interesting and useful some of our unconventional techniques. (ii) To present the equations we use, when the camera is in arbitrary motion at an arbitrary location near a Kerr black hole, for mapping light sources to camera images via elliptical ray bundles. (iii) To describe new insights, from DNGR, into gravitational lensing when the camera is near the spinning black hole, rather than far away as in almost all prior studies; we focus on the shapes, sizes and influence of caustics and critical curves, the creation and annihilation of stellar images, the pattern of multiple images, and the influence of almost-trapped light rays, and we find similar results to the more familiar case of a camera far from the hole. (iv) To describe how the images of the black hole Gargantua and its accretion disk, in the movie Interstellar, were generated with DNGR—including, especially, the influences of (a) colour changes due to doppler and gravitational frequency shifts, (b) intensity changes due to the frequency shifts, (c) simulated camera lens flare, and (d) decisions that the film makers made about these influences and about the Gargantua’s spin, with the goal of producing images understandable for a mass audience. There are no new astrophysical insights in this accretion-disk section of the paper, but disk novices may find it pedagogically interesting, and movie buffs may find its discussions of Interstellar interesting.

The LIGO Scientific Collaboration and the Virgo Collaboration have cataloged eleven confidently detected gravitational-wave events during the first two observing runs of the advanced detector era. All eleven events were consistent with being from well-modeled mergers between compact stellar-mass objects: black holes or neutron stars. The data around the time of each of these events have been made publicly available through the gravitational-wave open science center. The entirety of the gravitational-wave strain data from the first and second observing runs have also now been made publicly available. There is considerable interest among the broad scientific community in understanding the data and methods used in the analyses. In this paper, we provide an overview of the detector noise properties and the data analysis techniques used to detect gravitational-wave signals and infer the source properties. We describe some of the checks that are performed to validate the analyses and results from the observations of gravitational-wave events. We also address concerns that have been raised about various properties of LIGO–Virgo detector noise and the correctness of our analyses as applied to the resulting data.

 The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4 σ to 6 σ disagreement between predictions of the Hubble constant, H ₀, made by the early time probes in concert with the ‘vanilla’ ΛCDM cosmological model, and a number of late time, model-independent determinations of H ₀ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations—whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1–2 σ between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J. 908 L6) measurement of the Hubble constant ( H ₀ = 73.2 ± 1.3 km s ⁻¹ Mpc ⁻¹ at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3 σ disagreement level. In many cases, reduced tension comes not simply from a change in the value of H ₀ but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations.

We report on the development and extensive characterization of co-sputtered tantala–zirconia (Ta ₂O ₅-ZrO ₂) thin films, with the goal to decrease coating Brownian noise in present and future gravitational-wave detectors. We tested a variety of sputtering processes of different energies and deposition rates, and we considered the effect of different values of cation ratio η = Zr/(Zr + Ta) and of post-deposition heat treatment temperature T _a on the optical and mechanical properties of the films. Co-sputtered zirconia proved to be an efficient way to frustrate crystallization in tantala thin films, allowing for a substantial increase of the maximum annealing temperature and hence for a decrease of coating mechanical loss φ _c. The lowest average coating loss was observed for an ion-beam sputtered sample with η = 0.485 ± 0.004 annealed at 800 °C, yielding rad. All coating samples showed cracks after annealing. Although in principle our measurements are sensitive to such defects, we found no evidence that our results were affected. The issue could be solved, at least for ion-beam sputtered coatings, by decreasing heating and cooling rates down to 7 °C h ⁻¹. While we observed as little optical absorption as in the coatings of current gravitational-wave interferometers (0.5 parts per million), further development will be needed to decrease light scattering and avoid the formation of defects upon annealing.

There are several common conventions in use by the gravitational-wave community to describe the amplitude of sources and the sensitivity of detectors. These are frequently confused. We outline the merits of and differences between the various quantities used for parameterizing noise curves and characterizing gravitational-wave amplitudes. We conclude by producing plots that consistently compare different detectors. Similar figures can be generated on-line for general use at http://rhcole.com/apps/GWplotter.

GW170817 is the very first observation of gravitational waves originating from the coalescence of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to directly probe the internal structure of neutron stars. We perform Bayesian model selection on a wide range of theoretical predictions for the neutron star equation of state. For the binary neutron star hypothesis, we find that we cannot rule out the majority of theoretical models considered. In addition, the gravitational-wave data alone does not rule out the possibility that one or both objects were low-mass black holes. We discuss the possible outcomes in the case of a binary neutron star merger, finding that all scenarios from prompt collapse to long-lived or even stable remnants are possible. For long-lived remnants, we place an upper limit of 1.9 kHz on the rotation rate. If a black hole was formed any time after merger and the coalescing stars were slowly rotating, then the maximum baryonic mass of non-rotating neutron stars is at most , and three equations of state considered here can be ruled out. We obtain a tighter limit of for the case that the merger results in a hypermassive neutron star.

The Einstein–Cartan equations in first-order action of torsion are considered. From Belinfante–Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion is given by the spin which leads to an extended Oppenhaimer–Volkov equation. Outside matter a second solution is found besides the torsion-free Schwarzschild one with the torsion completely determined by the metric and vice versa. This solution is shown to be of non-spherical origin and its uniqueness with respect to the consistence is demonstrated. Unusual properties are discussed in different coordinate systems where the cosmological constant assumes the role of the Friedman parameter in Friedman–Lamaître–Robertson–Walker cosmoses. Parameters are specified where wormholes are possible. Transformations are presented to explore and map regions of expanding and contracting universes to the form of static metrics. The autoparallel equations are solved exactly and compared with geodesic motion. The Weyl tensor reveals that the here found solution is of Petrov-D type.

The Advanced LIGO gravitational wave detectors are second-generation instruments designed and built for the two LIGO observatories in Hanford, WA and Livingston, LA, USA. The two instruments are identical in design, and are specialized versions of a Michelson interferometer with 4 km long arms. As in Initial LIGO, Fabry–Perot cavities are used in the arms to increase the interaction time with a gravitational wave, and power recycling is used to increase the effective laser power. Signal recycling has been added in Advanced LIGO to improve the frequency response. In the most sensitive frequency region around 100 Hz, the design strain sensitivity is a factor of 10 better than Initial LIGO. In addition, the low frequency end of the sensitivity band is moved from 40 Hz down to 10 Hz. All interferometer components have been replaced with improved technologies to achieve this sensitivity gain. Much better seismic isolation and test mass suspensions are responsible for the gains at lower frequencies. Higher laser power, larger test masses and improved mirror coatings lead to the improved sensitivity at mid and high frequencies. Data collecting runs with these new instruments are planned to begin in mid-2015.

This topical review gives a comprehensive overview and assessment of recent results in causal dynamical triangulations, a modern formulation of lattice gravity, whose aim is to obtain a theory of quantum gravity nonperturbatively from a scaling limit of the lattice-regularized theory. In this manifestly diffeomorphism-invariant approach one has direct, computational access to a Planckian spacetime regime, which is explored with the help of invariant quantum observables. During the last few years, there have been numerous new and important developments and insights concerning the theory’s phase structure, the roles of time, causality, diffeomorphisms and global topology, the application of renormalization group methods and new observables. We will focus on these new results, primarily in four spacetime dimensions, and discuss some of their geometric and physical implications.

GW170817 is the very first observation of gravitational waves originating from the coalescence of two compact objects in the mass range of neutron stars, accompanied by electromagnetic counterparts, and offers an opportunity to directly probe the internal structure of neutron stars. We perform Bayesian model selection on a wide range of theoretical predictions for the neutron star equation of state. For the binary neutron star hypothesis, we find that we cannot rule out the majority of theoretical models considered. In addition, the gravitational-wave data alone does not rule out the possibility that one or both objects were low-mass black holes. We discuss the possible outcomes in the case of a binary neutron star merger, finding that all scenarios from prompt collapse to long-lived or even stable remnants are possible. For long-lived remnants, we place an upper limit of 1.9 kHz on the rotation rate. If a black hole was formed any time after merger and the coalescing stars were slowly rotating, then the maximum baryonic mass of non-rotating neutron stars is at most , and three equations of state considered here can be ruled out. We obtain a tighter limit of for the case that the merger results in a hypermassive neutron star.

The LIGO Scientific Collaboration and the Virgo Collaboration have cataloged eleven confidently detected gravitational-wave events during the first two observing runs of the advanced detector era. All eleven events were consistent with being from well-modeled mergers between compact stellar-mass objects: black holes or neutron stars. The data around the time of each of these events have been made publicly available through the gravitational-wave open science center. The entirety of the gravitational-wave strain data from the first and second observing runs have also now been made publicly available. There is considerable interest among the broad scientific community in understanding the data and methods used in the analyses. In this paper, we provide an overview of the detector noise properties and the data analysis techniques used to detect gravitational-wave signals and infer the source properties. We describe some of the checks that are performed to validate the analyses and results from the observations of gravitational-wave events. We also address concerns that have been raised about various properties of LIGO–Virgo detector noise and the correctness of our analyses as applied to the resulting data.

Investigations of shadows of astrophysical entities constitute a major source of insight into the evolution of compact objects. Such effects depend on the nature of the compact object and arise on account of the strong gravitational lensing that casts a shadow on the bright background. We consider the Kerr-like wormhole spacetime (Bueno et al 2018 Phys. Rev. D 97 024040), which is a modification of the Kerr black hole that degenerates into wormholes for nonzero values of the deviation parameter . The results suggest that the Kerr spacetime can reproduce far away from the throat of the wormhole. We obtain the shapes of the shadow for the Kerr-like wormholes and discuss the effect of the spin a, the inclination angle , and the deviation parameter on the size and nature of the shadow. As a consequence, it is discovered that the shadow is distorted due to the spin as well as the deviation parameter and the radius of the shadow decreases with if the ADM mass of the Kerr-like wormholes is considered.

We construct rotating black holes in Einstein-scalar-Gauss–Bonnet theory with a quadratic coupling function. We map the domain of existence of the rotating fundamental solutions, we construct radially excited rotating black holes (including their existence lines), and we show that there are angularly excited rotating black holes. The bifurcation points of the radially and angularly excited solutions branching out of the Schwarzschild solution follow a regular pattern.

We use Dirac's method for the quantization of constrained systems in order to quantize a spatially flat Friedmann–Lemaître–Robertson–Walker spacetime in the context of f(Q) cosmology. When the coincident gauge is considered, the resulting minisuperspace system possesses second class constraints. This distinguishes the quantization process from the typical Wheeler–DeWitt quantization, which is applied for cosmological models where only first class constraints are present (e.g. for models in general relativity or in f(R) gravity). We introduce the Dirac brackets, find appropriate canonical coordinates and then apply the canonical quantization procedure. We perform this method both in vacuum and in the presence of matter: a minimally coupled scalar field and a perfect fluid with a linear equation of state. We demonstrate that the matter content changes significantly the quantization procedure, with the perfect fluid even requiring to put in use the theory of fractional quantum mechanics in which the power of the momentum in the Hamiltonian is associated with the fractal dimension of a Lévy flight. The results of this analysis can be applied in f(T) teleparallel cosmology, since f(Q) and f(T) theories have the same degrees of freedom and same dynamical constraints in cosmological studies.

The ESA/JAXA BepiColombo mission, launched on 20 October 2018, is currently in cruise toward Mercury. The Mercury Orbiter Radio-science Experiment (MORE), one of the 16 experiments of the mission, will exploit range and range-rate measurements collected during superior solar conjunctions to better constrain the post-Newtonian parameter γ. The MORE radio tracking system is capable of establishing a 5-leg link in X- and Ka-band to obtain 2-way range-rate measurements with an accuracy of 0.01 mm s⁻¹ @ 60 s sampling time and 2-way range measurements at centimeter level after a few seconds of integration time, at almost all solar elongation angles. In this paper, we investigate if the light-time formulation derived by Moyer, implemented in JPL's orbit determination code MONTE, is still a valid approximation, in light of the recent advancements in radiometric measurement performance. Several formulations of the gravitational time delay, expressed as an expansion in powers of GM/c²r, are considered in this work. We quantified the contribution of each term of the light-time expansion for the first superior solar conjunction experiment of BepiColombo. The maximum 2-way error caused by Moyer approximation with respect to a complete second order expansion amounts to 17 mm. This is at the level of accuracy of the novel pseudo-noise (PN) ranging system at 24 Mcps used by MORE. A complete second order expansion is then recommended for present and future superior solar conjunction experiments. The perturbation caused by the planets in the Solar System is considered as well, resulting in significant effects due to the Jupiter, the Earth and the Saturn systems. For these bodies the classical Shapiro time delay is sufficient. The corrections due to the Sun oblateness and angular momentum are negligible. The aforementioned considerations are valid for all superior conjunction experiments involving state-of-the-art radio-tracking measurements.

We use zero angular momentum null geodesics in the Kerr–de Sitter spacetime to transform the metric in a generalised Bondi coordinate system. We write the metric components explicitly. Next, we choose the radial coordinate to be the areal coordinate and write the asymptotic metric in the Bondi–Sachs gauge.

This article derives and presents the Feynman rules for (effective) quantum general relativity coupled to the standard model for any vertex valence and with general gauge parameter ζ. The results are worked out for the metric decomposition g_μν = η_μν + ϰh_μν, a linearized de Donder gauge fixing and four dimensions of spacetime. To this end, we calculate the Feynman rules for gravitons, graviton-ghosts and for the couplings of gravitons to scalars, spinors, gauge bosons and gauge ghosts.

We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a suitable boundary value problem. This puts on solid ground previous approximate calculations. We find consistency with previous results obtained from eikonal expansions at the level of accuracy accessible to current gravitational wave detectors.

Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified form the long-term evolution of small initial data. Topics covered include turbulent and regular motion, dynamical recurrences analogous to the Fermi–Pasta–Ulam phenomena in oscillator chains, and relations between AdS dynamics and nonrelativistic nonlinear Schrödinger equations in harmonic potentials. Special mention is given to the way the classical dynamics of weakly nonlinear strongly resonant systems is illuminated by perturbative considerations within the corresponding quantum theories, in particular, in relation to quantum chaos theory.

 The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4 σ to 6 σ disagreement between predictions of the Hubble constant, H ₀, made by the early time probes in concert with the ‘vanilla’ ΛCDM cosmological model, and a number of late time, model-independent determinations of H ₀ from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations—whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1–2 σ between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J. 908 L6) measurement of the Hubble constant ( H ₀ = 73.2 ± 1.3 km s ⁻¹ Mpc ⁻¹ at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3 σ disagreement level. In many cases, reduced tension comes not simply from a change in the value of H ₀ but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.

This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations and discussions. We pay special attention to the role of the equations of motion and to the relation between classical and quantum theories. Pointwise energy conditions were first introduced as physically reasonable restrictions on matter in the context of general relativity. They aim to express e.g. the positivity of mass or the attractiveness of gravity. Perhaps more importantly, they have been used as assumptions in mathematical relativity to prove singularity theorems and the non-existence of wormholes and similar exotic phenomena. However, the delicate balance between conceptual simplicity, general validity and strong results has faced serious challenges, because all pointwise energy conditions are systematically violated by quantum fields and also by some rather simple classical fields. In response to these challenges, weaker statements were introduced, such as quantum energy inequalities and averaged energy conditions. These have a larger range of validity and may still suffice to prove at least some of the earlier results. One of these conditions, the achronal averaged null energy condition, has recently received increased attention. It is expected to be a universal property of the dynamics of all gravitating physical matter, even in the context of semiclassical or quantum gravity.

In this introductory review, we argue that a quantum structure of space-time naturally entails a higher-spin theory, to avoid significant Lorentz violation. A suitable framework is provided by Yang–Mills matrix models, which allow to consider space-time as a physical system, which is treated on the same footing as the fields that live on it. We discuss a specific quantum space-time solution, whose internal structure leads to a consistent and ghost-free higher-spin gauge theory. The spin 2 modes give rise to metric perturbations, which include the standard gravitons as well as the linearized Schwarzschild solution.

With the arrival of the era of gravitational wave astronomy, the strong gravitational field regime will be explored soon in various aspects. In this article, we provide a general review over cylindrical systems in Einstein’s theory of general relativity. In particular, we first review the general properties, both local and global, of several important solutions of Einstein’s field equations, including the Levi-Civita and Lewis solutions and their extensions to include the cosmological constant and matter fields, and pay particular attention to properties that represent the generic features of the theory, such as the formation of the observed extragalactic jets and gravitational Faraday rotation. We also review studies of cylindrical wormholes, gravitational collapse and hoop conjecture, and polarizations of gravitational waves. In addition, by rigorously defining cylindrically symmetric spacetimes, we clarify various (incorrect) claims existing in the literature, regarding to the generality of such spacetimes.

This article derives and presents the Feynman rules for (effective) quantum general relativity coupled to the standard model for any vertex valence and with general gauge parameter ζ. The results are worked out for the metric decomposition g _μν = η _μν + ϰ h _μν , a linearized de Donder gauge fixing and four dimensions of spacetime. To this end, we calculate the Feynman rules for gravitons, graviton-ghosts and for the couplings of gravitons to scalars, spinors, gauge bosons and gauge ghosts.

We analyse the response of laser interferometric gravitational wave detectors using the full Maxwell equations in curved spacetime in the presence of weak gravitational waves. Existence and uniqueness of solutions is ensured by setting up a suitable boundary value problem. This puts on solid ground previous approximate calculations. We find consistency with previous results obtained from eikonal expansions at the level of accuracy accessible to current gravitational wave detectors.

The Galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future large scale structure surveys. The precision demanded by these stage IV surveys requires the use of second order cosmological perturbation theory. Based on the independent calculation published previously, we present the result of the comparison with the results of three other groups at leading order. Overall we find that the differences between the different approaches lie mostly on the definition of certain quantities, where the ambiguity of signs results in the addition of extra terms at second order in perturbation theory.

The Einstein–Cartan equations in first-order action of torsion are considered. From Belinfante–Rosenfeld equation special consistence conditions are derived for the torsion parameters relating them to the metric. Inside matter the torsion is given by the spin which leads to an extended Oppenhaimer–Volkov equation. Outside matter a second solution is found besides the torsion-free Schwarzschild one with the torsion completely determined by the metric and vice versa. This solution is shown to be of non-spherical origin and its uniqueness with respect to the consistence is demonstrated. Unusual properties are discussed in different coordinate systems where the cosmological constant assumes the role of the Friedman parameter in Friedman–Lamaître–Robertson–Walker cosmoses. Parameters are specified where wormholes are possible. Transformations are presented to explore and map regions of expanding and contracting universes to the form of static metrics. The autoparallel equations are solved exactly and compared with geodesic motion. The Weyl tensor reveals that the here found solution is of Petrov-D type.

The polarisation Sagnac speedmeter interferometer has the potential to replace the Michelson interferometer as the instrumental basis for future generations of ground-based gravitational wave detectors. The quantum noise benefit of this speedmeter is dependent on high-quality polarisation optics, the polarisation beam-splitter (PBS) and quarter-waveplate (QWP) optics that are key to this detector configuration and careful consideration of the effect of birefringence in the arm cavities of the interferometer. A PBS with an extinction ratio of better than 4000 in transmission and 700 in reflection for a 41° angle of incidence was characterised along with a QWP of birefringence of . The cavity mirror optics of a 10 m prototype polarisation Sagnac speedmeter were measured to have birefringence in the range 1 × 10 ⁻³ to 2 × 10 ⁻⁵ radians. This level of birefringence, along with the QWP imperfections, can be cancelled out by careful adjustment of the QWP angle, to the extent that the extinction ratio of the PBS is the leading limitation for the polarisation Sagnac speedmeter in terms of polarisation effects.

We present a systematic construction of the Penrose coordinates and plane wave limits of spacetimes for which both the null Hamilton–Jacobi and geodesic equations separate. The method is applied to Kerr-NUT-(A)dS four-dimensional black holes. The plane wave limits of the near horizon geometry of the extreme Kerr black hole are also explored. All near horizon geometries of extreme black holes with a regular Killing horizon admit Minkowski spacetime as a plane wave limit.

We report on the development and extensive characterization of co-sputtered tantala–zirconia (Ta ₂O ₅-ZrO ₂) thin films, with the goal to decrease coating Brownian noise in present and future gravitational-wave detectors. We tested a variety of sputtering processes of different energies and deposition rates, and we considered the effect of different values of cation ratio η = Zr/(Zr + Ta) and of post-deposition heat treatment temperature T _a on the optical and mechanical properties of the films. Co-sputtered zirconia proved to be an efficient way to frustrate crystallization in tantala thin films, allowing for a substantial increase of the maximum annealing temperature and hence for a decrease of coating mechanical loss φ _c. The lowest average coating loss was observed for an ion-beam sputtered sample with η = 0.485 ± 0.004 annealed at 800 °C, yielding rad. All coating samples showed cracks after annealing. Although in principle our measurements are sensitive to such defects, we found no evidence that our results were affected. The issue could be solved, at least for ion-beam sputtered coatings, by decreasing heating and cooling rates down to 7 °C h ⁻¹. While we observed as little optical absorption as in the coatings of current gravitational-wave interferometers (0.5 parts per million), further development will be needed to decrease light scattering and avoid the formation of defects upon annealing.

We study some properties of the Rovelli–Smolin–DePietri volume operator in loop quantum gravity, which significantly simplify the diagonalization problem and shed some light on the pattern of degeneracy of the eigenstates. The operator is defined by its action in the spaces of tensor products of the irreducible SU(2) representation spaces , labelled with spins . We restrict to spaces of SU(2) invariant tensors (intertwiners) with all spins equal j ₁ =⋯= j _N = j. We call them spin j monochromatic intertwiners. Such spaces are important in the study of SU(2) gauge invariant states that are isotropic and can be applied to extract the cosmological sector of the theory. In the case of spin 1/2 we solve the eigenvalue problem completely: we show that the volume operator is proportional to identity and calculate the proportionality factor.

Many states of linear real scalar quantum fields (in particular Reeh–Schlieder states) on flat as well as curved spacetime are entangled on spacelike separated local algebras of observables. It has been argued that this entanglement can be ‘harvested’ by a pair of so-called particle detectors, for example singularly or non-locally coupled quantum mechanical harmonic oscillator Unruh detectors. In an attempt to avoid such imperfect coupling, we analyse a model-independent local and covariant entanglement harvesting protocol based on the local probes of a recently proposed measurement theory of quantum fields. We then introduce the notion of a local particle detector concretely given by a local mode of a linear real scalar probe field on possibly curved spacetime and possibly under the influence of external fields. In a non-perturbative analysis we find that local particle detectors cannot harvest entanglement below a critical coupling strength when the corresponding probe fields are initially prepared in quasi-free Reeh–Schlieder states and are coupled to a system field prepared in a quasi-free state. This is a consequence of the fact that Reeh–Schlieder states restrict to truly mixed states on any local mode.

A typical geometry extracted from the path integral of a quantum theory of gravity may be quite complicated in the UV region. Even if a single configuration is not physical, its properties may be of interest to understand the details of its nature, since some universal features can be important for the physics of the model. If the formalism describing the geometry is coordinate independent, which is the case in the model studied here, such understanding may be facilitated by the use of suitable coordinate systems. In this article we use scalar fields that solve Laplace’s equation to introduce coordinates on geometries with a toroidal topology. Using these coordinates we observe what we identify as the cosmic voids and filaments structure, even if matter is only a tool to visualize the geometry. We also show that if the scalar fields we used as coordinates are dynamically coupled to geometry, they can change it in a dramatic way, leading to a modification of the spatial topology.