Table of contents

We present a novel public package 'EFTofPNG' for high precision computation in the effective field theory of post-Newtonian (PN) gravity, including spins. We created this package in view of the timely need to publicly share automated computation tools, which integrate the various types of physics manifested in the expected increasing influx of gravitational wave (GW) data. Hence, we created a free and open source package, which is self-contained, modular, all-inclusive, and accessible to the classical gravity community. The 'EFTofPNG' Mathematica package also uses the power of the 'xTensor' package, suited for complicated tensor computation, where our coding also strategically approaches the generic generation of Feynman contractions, which is universal to all perturbation theories in physics, by efficiently treating n-point functions as tensors of rank n. The package currently contains four independent units, which serve as subsidiaries to the main one. Its final unit serves as a pipeline chain for the obtainment of the final GW templates, and provides the full computation of derivatives and physical observables of interest. The upcoming 'EFTofPNG' package version 1.0 should cover the point mass sector, and all the spin sectors, up to the fourth PN order, and the two-loop level. We expect and strongly encourage public development of the package to improve its efficiency, and to extend it to further PN sectors, and observables useful for the waveform modelling.

The Laser Interferometer Space Antenna (LISA) will explore the source-rich milli-Hertz band of the gravitational wave spectrum. In contrast to ground based detectors, where typical signals are short-lived and discrete, LISA signals are typically long-lived and over-lapping, thus requiring a global data analysis solution that is very different to the source-by-source analysis that has been developed for ground based gravitational wave astronomy. Across the LISA band, gravitational waves are both signals and noise. The dominant contribution to this so-called confusion noise (better termed unresolved signal noise) is expected to come from short period galactic white dwarf binaries, but all sources, including massive black hole binaries and extreme mass ratio captures will also contribute. Previous estimates for the galactic confusion noise have assumed perfect signal subtraction. Here we provide analytic estimates for the signal subtraction residuals and the impact they have on parameter estimation while for the first time incorporating the effects of noise modeling. The analytic estimates are found using a maximum likelihood approximation to the full global Bayesian analysis. We find that while the confusion noise is lowered in the global analysis, the waveform errors for individual sources are increased relative to estimates for isolated signals. We provide estimates for how parameter estimation errors are inflated from various parts of a global analysis.

We investigate whether a spontaneously-broken gauge theory of the group $SU(2, 2)$ may be a viable alternative to general relativity. The basic ingredients of the theory are an $SU(2, 2)$ gauge field $\newcommand{\m}[1]{\mathcal{#1}} A_{\mu}$ and a Higgs field W in the adjoint representation of the group with the Higgs field producing the symmetry breaking $SU(2, 2)\rightarrow SO(1, 3)\times SO(1, 1)$. The action for gravity is polynomial in $\newcommand{\m}[1]{\mathcal{#1}} \{A_{\mu}, W\}$ and the field equations are first-order in derivatives of these fields. The new $SO(1, 1)$ symmetry in the gravitational sector is interpreted in terms of an emergent local scale symmetry and the existence of 'conformalized' general relativity and fourth-order Weyl conformal gravity as limits of the theory is demonstrated. Maximally symmetric spacetime solutions to the full theory are found and stability of the theory around these solutions is investigated; it is shown that regions of the theory's parameter space describe perturbations identical to that of general relativity coupled to a massive scalar field and a massless one-form field. The coupling of gravity to matter is considered and it is shown that Lagrangians for all fields are naturally gauge-invariant, polynomial in fields and yield first-order field equations; no auxiliary fields are introduced. Familiar Yang–Mills and Klein–Gordon type Lagrangians are recovered on-shell in the general-relativistic limit of the theory. In this formalism, the general-relativistic limit coincides with a spontaneous breaking of scale invariance and it is shown that this generates mass terms for Higgs and spinor fields.

Using algebraic techniques we obtain quasinormal modes and frequencies associated to generalized forms of the scattering Pöschl–Teller potential. This approach is based on the association of the corresponding equations of motion with Casimir invariants of differential representations of the Lie algebra $\mathfrak{sl}(2)$. In the presented development, highest weight representations are constructed and fundamental states are calculated. An infinite tower of quasinormal mode solutions is obtained by the action of a lowering operator. The algebraic results are used in the analysis of the Cauchy initial value problem associated to the generalized Pöschl–Teller potentials. For the scattering potentials considered, there are no late-time tails and the dynamics is always stable.

Gravitational waves from merging neutron stars are expected to be observed in the next five years. We explore the potential impact of matter effects on gravitational waves from merging double neutron-star binaries. If neutron star binaries exist with chirp masses less than roughly one solar mass and typical neutron-star radii are larger than roughly 14 km, or if neutron-star radii are larger than 15–16 km for the chirp masses of galactic neutron-star binaries, then matter will have a significant impact on the effectiveness of a point-particle-based search at Advanced LIGO design sensitivity (roughly 5% additional loss of signals). In a configuration typical of LIGO's first observing run, extreme matter effects lead to up to 10% potential loss in the most extreme cases.

We derive a class of non-static inhomogeneous dust solutions in $f(R)$ gravity described by the Lemaître–Tolman–Bondi (LTB) metric. The field equations are fully integrated for all parameter subcases and compared with analogous subcases of LTB dust solutions of GR. Since the solutions do not admit regular symmetry centres, we have two possibilities: (i) a spherical dust cloud with angle deficit acting as the source of a vacuum Schwarzschild-like solution associated with a global monopole, or (ii) fully regular dust wormholes without angle deficit, whose rest frames are homeomorphic to the Schwarzschild–Kruskal manifold or to a 3d torus. The compatibility between the LTB metric and generic $f(R)$ ansatzes furnishes an 'inverse procedure' to generate LTB solutions whose sources are found from the $f(R)$ geometry. While the resulting fluids may have an elusive physical interpretation, they can be used as exact non-perturbative toy models in theoretical and cosmological applications of $f(R)$ theories.

We extend the foliation-based quantization scheme of Park (2015 Eur. Phys. J. C 75 459) to arbitrary asymptotically flat backgrounds including those that are time- and position- dependent. One of the ingredients to accomplishing the extension is imposition of a Neumann-type boundary condition. The quantization procedure, especially the gauge-fixing-induced reduction, provides a new insight into the black hole information paradox. The hypersurface degrees of freedom in the asymptotic region—whose dynamics should be responsible for part of the 'hair'—as well as transitions among various excitations play a central role in the global formulation of the information and proposed solution of the information paradox. In retrospect, the quantization scheme reveals the origin of the difficulty of the information problem: the problem's ties with the quantization of gravity and subtle boundary dynamics as well as the multilayered techniques required for its setup and study. We also comment on the implications of the asymptotic symmetries for the present quantization framework.

A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr–Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which a photon orbit is stable on an asymptotically flat extremal Kerr–Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas an electrical charge tends to stabilize it. We investigated the effect of a negative cosmological constant on this observation, and found the same behavior in the case of extremal asymptotically Kerr–Newman–AdS black holes in $(3+1)$-dimensions. In $(2+1)$-dimensions, in the presence of an electrical charge, the angular momentum never becomes large enough to destabilize the photon orbit. We comment on the instabilities of black hole spacetimes with a stable photon orbit.

Employing a Mathematica symbolic computer algebra package called xTensor, we present $(1+3)$-covariant special case proofs of the shear-free perfect fluid conjecture in general relativity. We first present the case where the pressure is constant, and where the acceleration is parallel to the vorticity vector. These cases were first presented in their covariant form by Senovilla et al. We then provide a covariant proof for the case where the acceleration and vorticity vectors are orthogonal, which leads to the existence of a Killing vector along the vorticity. This Killing vector satisfies the new constraint equations resulting from the vanishing of the shear. Furthermore, it is shown that in order for the conjecture to be true, this Killing vector must have a vanishing spatially projected directional covariant derivative along the velocity vector field. This in turn implies the existence of another basic vector field along the direction of the vorticity for the conjecture to hold. Finally, we show that in general, there exists a basic vector field parallel to the acceleration for which the conjecture is true.

Lunar laser ranging provides a number of leading experimental tests of gravitation—important in our quest to unify general relativity and the standard model of physics. The apache point observatory lunar laser-ranging operation (APOLLO) has for years achieved median range precision at the  ∼2 mm level. Yet residuals in model-measurement comparisons are an order-of-magnitude larger, raising the question of whether the ranging data are not nearly as accurate as they are precise, or if the models are incomplete or ill-conditioned. This paper describes a new absolute calibration system (ACS) intended both as a tool for exposing and eliminating sources of systematic error, and also as a means to directly calibrate ranging data in situ. The system consists of a high-repetition-rate (80 MHz) laser emitting short ($<$10 ps) pulses that are locked to a cesium clock. In essence, the ACS delivers photons to the APOLLO detector at exquisitely well-defined time intervals as a ‘truth’ input against which APOLLO’s timing performance may be judged and corrected. Preliminary analysis indicates no inaccuracies in APOLLO data beyond the  ∼3 mm level, suggesting that historical APOLLO data are of high quality and motivating continued work on model capabilities. The ACS provides the means to deliver APOLLO data both accurate and precise below the 2 mm level.

The Apache point observatory lunar laser-ranging operation (APOLLO) has produced a large volume of high-quality lunar laser ranging (LLR) data since it began operating in 2006. For most of this period, APOLLO has relied on a GPS-disciplined, high-stability quartz oscillator as its frequency and time standard. The recent addition of a cesium clock as part of a timing calibration system initiated a comparison campaign between the two clocks. This has allowed correction of APOLLO range measurements—called normal points—during the overlap period, but also revealed a mechanism to correct for systematic range offsets due to clock errors in historical APOLLO data. Drift of the GPS clock on  ∼1000 s timescales contributed typically 2.5 mm of range error to APOLLO measurements, and we find that this may be reduced to  ∼1.6 mm on average. We present here a characterization of APOLLO clock errors, the method by which we correct historical data, and the resulting statistics.

An immense class of physical counterexamples to the four dimensional strong cosmic censor conjecture—in its usual broad formulation—is exhibited. More precisely, out of any closed and simply connected 4-manifold an open Ricci-flat Lorentzian 4-manifold is constructed which is not globally hyperbolic, and no perturbation of which, in any sense, can be globally hyperbolic. This very stable non-global-hyperbolicity is the consequence of our open spaces having a ‘creased end’—i.e. an end diffeomorphic to an exotic $\newcommand{\R}{{{\mathbb R}}} \R^4$. Open manifolds having an end like this is a typical phenomenon in four dimensions.

The construction is based on a collection of results of Gompf and Taubes on exotic and self-dual spaces, respectively, as well as applying Penrose' non-linear graviton construction (i.e. twistor theory) to solve the Riemannian Einstein's equation. These solutions then are converted into stably non-globally-hyperbolic Lorentzian vacuum solutions. It follows that the plethora of vacuum solutions we found cannot be obtained via the initial value formulation of the Einstein's equation because they are 'too long' in a certain sense (explained in the text). This different (i.e. not based on the initial value formulation, but twistorial) technical background might partially explain why the existence of vacuum solutions of this kind have not been realized so far in spite of the fact that, apparently, their superabundance compared to the well-known globally hyperbolic vacuum solutions is overwhelming.

The evolution of heat-conducting fluid described by a pair of Maxwell-like equations is used to construct thermal-fluid helicity and thermal-helicity currents. These currents are found to be dissipative. It is shown that the magnetic part of the particle vorticity two-form is a thermal-fluid vorticity flux vector field composed of a linear combination of the fluid's vorticity and a spacelike twist of heat flow lines. Heat flow lines are non-geodesic because of the interplay between gravitation and the entropy entrainment in a system composed of a heat-conducting fluid which is in state of rapid differential rotation and far from equilibrium. In general, alignment of the heat flux vector with that of the fluid's vorticity leads to non-conservation of thermal-fluid vorticity flux in both a thermal-fluid flux tube and a stream tube. It is demonstrated that the twist of the fluid's vortex lines is caused by the heat flow along the fluid's vorticity vector in the case of an axisymmetric stationary differentially rotating heat-conducting fluid configuration. In this case, dissipation of thermal-fluid vorticity flux along the flux tube is caused by coupled effects of the fluid's vorticity magnitude, thermal resistivity and entropy entrainment.

In this paper, we study constant-roll inflation in $F(R)$ gravity. We take two different approaches, one that relates $F(R)$ gravity to well-known scalar models of constant-roll and a second that examines the constant-roll condition in $F(R)$ gravity directly. With regard to the first approach, by using well-known techniques, we find the $F(R)$ gravity that realizes a given constant-roll evolution in the scalar–tensor theory. We also perform a conformal transformation in the resulting $F(R)$ gravity and find the Einstein frame counterpart theory. As we demonstrate, the resulting scalar potential is different in comparison to the original scalar constant-roll case, and the same applies for the corresponding observational indices. Moreover, we discuss how cosmological evolutions that can realize constant-roll to constant-roll era transitions in the scalar-tensor description can be realized by vacuum $F(R)$ gravity. With regard to the second approach, we examine the effects of the constant-roll condition on the inflationary dynamics of vacuum $F(R)$ gravity directly. We present in detail the formalism of constant-roll $F(R)$ gravity inflationary dynamics and we discuss the inflationary indices for this case. We use two well-known $F(R)$ gravities in order to illustrate our findings: the R² model and a power-law $F(R)$ gravity in vacuum. As we demonstrate, in both cases the parameter space is enlarged in comparison to the slow-roll counterparts of the models and, in effect, the models can also be compatible with the observational data. Finally, we briefly address the graceful exit issue.

We consider a free p-form gauge theory on a d-dimensional sphere of radius R and calculate its free energy. We perform the calculation for generic values of p and obtain the free energy as a function of $d, p$ and R. The result contains a $\renewcommand{\r}{\rho} \renewcommand{\l}{\lambda} \log R$ term with a coefficient proportional to $\renewcommand{\r}{\rho} \renewcommand{\l}{\lambda} (2p+2-d)$, which is consistent with lack of conformal invariance for p form theories in dimensions other than $2p+2$. We also compare the result for p-form and $(d-p-2)$-form theory which are classically Hodge dual to each other in d dimensions and find that they agree for odd values of d. Also, for even d, we find that the results disagree by an amount that is consistent with the reported values in the literature.