Table of contents

We formulate a Hamiltonian description of the orbital motion of a point particle in Kerr spacetime for generic (eccentric, inclined) orbits, which accounts for the effects of the conservative part of the gravitational self-force. This formulation relies on a description of the particle's motion as geodesic in a certain smooth effective spacetime, in terms of (generalized) action-angle variables. Clarifying the role played by the gauge freedom in the Hamiltonian dynamics, we extract the gauge-invariant information contained in the conservative self-force. We also propose a possible gauge choice for which the orbital dynamics can be described by an effective Hamiltonian, written solely in terms of the action variables. As an application of our Hamiltonian formulation in this gauge, we derive the conservative self-force correction to the orbital frequencies of Kerr innermost stable spherical (inclined or circular) orbits. This gauge choice also allows us to establish a 'first law of mechanics' for black-hole-particle binary systems, at leading order beyond the test-mass approximation.

Three-mode parametric instability is a threat to attaining design power levels in advanced gravitational wave detectors. The first observation of three-mode parametric instability in a long optical cavity revealed that instabilities could be suppressed by time variation of the mirror radius of curvature. In this paper, we present three dimensional finite element analysis of this thermo-acousto-optics system to determine whether thermal modulation could provide sufficient instability suppression without degrading time averaged optical performance. It is shown that deformations due to the time averaged heating profile on the mirror surface can be compensated by rear surface heating of the test mass. Results show that a heating source with a modulation amplitude of 1 W at 0.01 Hz is sufficient to stabilize an acoustic mode with parametric gain up to 3. The parametric gain suppression factor is linearly proportional to the peak modulation power.

Newtonian noise is likely to be a future challenge at low frequencies for Advanced LIGO and other second generation gravitational wave detectors. We present the TorPeDO system: a dual torsion pendulum sensor designed to measure local gravitational forces to high precision. Gravitational forces induce a differential rotation between the two torsion beams, which is measured with an optical read-out. Both torsion pendulums have a common suspension point, tunable centre of mass, and resonant frequency. This produces a high level of mechanical common mode noise cancellation. We report on a controls prototype of the TorPeDO system, presenting the frequency response and tuning range of both pendulums. A noise budget and mechanical cross-coupling model for this system are also presented. We demonstrate frequency tuning of the two torsion pendulums to a difference of 4.3 μHz.

We explore the constraints boundary causality places on the allowable Gauss–Bonnet gravitational couplings in asymptotically AdS spaces, specifically considering spherical black hole solutions. We additionally consider the hyperbolicity properties of these solutions, positing that hyperbolicity-violating solutions are sick solutions whose causality properties provide no information about the theory they reside in. For both signs of the Gauss–Bonnet coupling, spherical black holes violate boundary causality at smaller absolute values of the coupling than planar black holes do. For negative coupling, as we tune the Gauss–Bonnet coupling away from zero, both spherical and planar black holes violate hyperbolicity before they violate boundary causality. For positive coupling, the only hyperbolicity-respecting spherical black holes which violate boundary causality do not do so appreciably far from the planar bound. Consequently, eliminating hyperbolicity-violating solutions means the bound on Gauss–Bonnet couplings from the boundary causality of spherical black holes is no tighter than that from planar black holes.

Since the late1950s, almost all discussions of asymptotically flat (Einstein–Maxwell) space-times have taken place in the context of Penrose's null infinity, $\mathcal{I}^{+}.$ In addition, almost all calculations have used the Bondi coordinate and tetrad systems. Beginning with a known asymptotically flat solution to the Einstein–Maxwell equations, we show first, that there are other natural coordinate systems, near $\mathcal{I}^{+},$ (analogous to light-cones in flat-space) that are based on (asymptotically) shear-free null geodesic congruences (analogous to the flat-space case). Using these new coordinates and their associated tetrad, we define the complex dipole moment, (the mass dipole plus i times angular momentum), from the l  =  1 harmonic coefficient of a component of the asymptotic Weyl tensor. Second, from this definition, from the Bianchi identities and from the Bondi–Sachs mass and linear momentum, we show that there exists a large number of results—identifications and dynamics—identical to those of classical mechanics and electrodynamics. They include, among many others, ${\bf P}={\rm M}{\bf v}\!+..., {\bf L}= {\bf r} \times {\bf P}$, spin, Newton's second law with the rocket force term ($\dot{\rm M}$v) and radiation reaction, angular momentum conservation and others. All these relations take place in the rather mysterious H-space rather than in space-time.

This leads to the enigma: 'why do these well known relations of classical mechanics take place in H-space?' and 'What is the physical meaning of H-space?'

In this paper we explore the idea that black holes can persist in a universe that collapses to a big crunch and then bounces into a new phase of expansion. We use a scalar field to model the matter content of such a universe near the time of the bounce, and look for solutions that represent a network of black holes within a dynamical cosmology. We find exact solutions to Einstein's constraint equations that provide the geometry of space at the minimum of expansion and that can be used as initial data for the evolution of hyperspherical cosmologies. These solutions illustrate that there exist models in which multiple distinct black holes can persist through a bounce, and allow for concrete computations of quantities such as the black hole filling factor. We then consider solutions in flat cosmologies, as well as in higher-dimensional spaces (with up to nine spatial dimensions). We derive conditions for the black holes to remain distinct (i.e. avoid merging) and hence persist into the new expansion phase. Some potentially interesting consequences of these models are also discussed.

A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck information density in invariant proper time determined by the world line of an observer. It describes macroscopic spacelike correlations that appear as observable timelike correlations in phase differences of light propagating on paths that begin and end on the same world line. The model allows an exact prediction for the autocorrelation of any interferometer time signal from the shape of the light paths. Specific examples computed for configurations that approximate realistic experiments show that the model can be rigorously tested, allowing a direct experimental probe of Planck scale degrees of freedom.

Continuous gravitational waves signals, emitted by asymmetric spinning neutron stars, are among the main targets of current detectors like Advanced LIGO and Virgo. In the case of sources, like pulsars, whose rotational parameters are measured through electromagnetic observations, typical searches assume that the gravitational wave frequency is at a given known fixed ratio with respect to the star rotational frequency. For instance, for a neutron star rotating around one of its principal axis of inertia the gravitational signal frequency would be exactly two times the rotational frequency of the star. It is possible, however, that this assumption is wrong. This is why search algorithms able to take into account a possible small mismatch between the gravitational waves frequency and the frequency inferred from electromagnetic observations have been developed. In this paper we present an improved pipeline to perform such narrow-band searches for continuous gravitational waves from neutron stars, about three orders of magnitude faster than previous implementations. The algorithm that we have developed is based on the 5-vectors framework and is able to perform a fully coherent search over a frequency band of width $\mathcal{O}$(Hertz) and for hundreds of spin-down values running a few hours on a standard workstation. This new algorithm opens the possibility of long coherence time searches for objects whose rotational parameters are highly uncertain as shown in the case study of the central compact object in the supernova remnant G353.6–0.7.

We start with the Hamiltonian formulation of the first order action of pure gravity with a full $\mathfrak{sl}(2, \mathbb C)$ internal gauge symmetry. We make a partial gauge-fixing which reduces $\mathfrak{sl}(2, \mathbb C)$ to its sub-algebra $\mathfrak{su}(1, 1)$. This case corresponds to a splitting of the space-time ${\mathcal M}=\Sigma \times \mathbb R$ where $\Sigma$ inherits an arbitrary Lorentzian metric of signature (−, +, +). Then, we find a parametrization of the phase space in terms of an $\mathfrak{su}(1, 1)$ commutative connection and its associated conjugate electric field. Following the techniques of loop quantum gravity, we start the quantization of the theory and we consider the kinematical Hilbert space on a given fixed graph $\Gamma$ whose edges are colored with unitary representations of $\mathfrak{su}(1, 1)$. We compute the spectrum of area operators acting on the kinematical Hilbert space: we show that space-like areas have discrete spectra, in agreement with usual $\mathfrak{su}(2)$ loop quantum gravity, whereas time-like areas have continuous spectra. We conclude on the possibility to make use of this formulation of gravity to construct a holographic description of black holes in the framework of loop quantum gravity.

The recent direct detection of gravitational waves reported by Advanced LIGO has inspired the current article. In this context, a particular Lorentz-violating framework for classical, massive particles is the focus. The latter is characterized by a preferred direction in spacetime comprised of CPT-odd components with mass dimension 1. Curvature effects in spacetime, which are caused by a propagating gravitational wave, are assumed to deform the otherwise constant background field. In accordance with spontaneous Lorentz violation, a particular choice for the vector field is taken, which was proposed elsewhere. The geodesic equations for a particle that is subject to this type of Lorentz violation are obtained. Subsequently, their numerical solutions are computed and discussed. The particular model considered leads to changes in the particle trajectory whose impact on interferometric gravitational-wave experiments such as LIGO will be studied.

The maximally gyrotropic configurations of the hypermagnetic field at the electroweak epoch can induce a stochastic background of relic gravitational waves with comoving frequencies ranging from the μHz to the kHz. Using two complementary approaches we construct a physical template family for the emission of the gravitational radiation produced by the hypermagnetic knots. The current constraints and the presumed sensitivities of the advanced wide-band interferometers (both terrestrial and space-borne) are combined to infer that the lack of observations at intermediate frequencies may invalidate the premise of baryogenesis models based (directly or indirectly) on the presence of gyrotropic configurations of the hypermagnetic field at the electroweak epoch. Over the intermediate frequency range the spectral energy density of the gravitational waves emitted by the hypermagnetic knots at the electroweak scale can exceed the inflationary signal even by nine orders of magnitude without affecting the standard bounds applicable on the stochastic backgrounds of gravitational radiation. The signal of hypermagnetic knots can be disambiguated, at least in principle, since the the produced gravitational waves are polarized.

The detection of GW150914 by ground based gravitational wave observatories has brought about a new era in astrophysics. At optimal sensitivity, these observatories are expected to detect several events each year, with one or two of these occurring with non-negligible eccentricity. Such eccentric binaries will emit bursts of gravitational radiation during every pericenter passage, where orbital velocities can reach greater than ten percent the speed of light. As a result, such binaries may prove to be powerful probes of extreme gravitational physics and astrophysics. A promising method of achieving detection of such binaries is through power stacking, where the power in each burst is added up in time-frequency space. This detection strategy requires a theoretical prior of where the bursts will occur in time and frequency so that one knows where to search for successive bursts. We here present a generic post-Newtonian formalism for constructing such time-frequency model priors at generic post-Newtonian order. We apply our formalism to generate a burst model at third post-Newtonian order, making it potentially the most accurate, fully analytic model to date.

In calculations of gravitational collapse to form black holes, trapping horizons (foliated by marginally trapped surfaces) make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Those which then move outwards with respect to the matter have been proposed for use in defining black holes, replacing the global concept of an 'event horizon' which has some serious drawbacks for practical applications. We here present results from a study of the properties of both outgoing and ingoing trapping horizons, assuming strict spherical symmetry throughout. We have investigated their causal nature (i.e. whether they are spacelike, timelike or null), making contact with the Misner–Sharp–Hernandez formalism, which has often been used for numerical calculations of spherical collapse. We follow two different approaches, one using a geometrical quantity related to expansions of null geodesic congruences, and the other using the horizon velocity measured with respect to the collapsing matter. After an introduction to these concepts, we then implement them within numerical simulations of stellar collapse, revisiting pioneering calculations from the 1960s where some features of the emergence and subsequent behaviour of trapping horizons could already be seen. Our presentation here is aimed firmly at 'real world' applications of interest to astrophysicists and includes the effects of pressure, which may be important for the asymptotic behaviour of the ingoing horizon.

Working within the recent formalism of Poisson–Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order $O(\lambda)$. Here λ is the deformation parameter, plausibly the Planck scale. We find that $r, t, {\rm d} r, {\rm d} t$ are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order $\lambda^2$. We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace–Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson–Riemannian geometry we show that it deforms to

$$\begin{align*} \square f+{\lambda\over 2}\omega^{\alpha\beta}({\rm Ric}^\gamma{\hspace{0pt}}_\alpha-S^\gamma{\hspace{0pt}}_{;\alpha})(\widehat\nabla_\beta{\rm d} f)_\gamma + O(\lambda^2) \nonumber \end{align*}$$

$\widehat\nabla$

$[x, t]=\lambda x$

We analyze propagation equations for the polar modes of gravitational waves in cosmological space-times. We prove that polar gravitational waves must perturb the density and non-azimuthal components of the velocity of material medium of the Friedman–Lemaitre–Robertson–Walker spacetimes. Axial gravitational waves can influence only the azimuthal velocity, leading to local cosmological rotation. The whole gravitational dynamics reduces to the single 'master equation' that has the same form for polar and axial modes. That allows us to conclude that the status of the Huygens principle is the same for axial and polar gravitational waves. In particular, this principle is valid exactly in radiation spacetimes with the vanishing cosmological constant, and it is broken otherwise.

For Gauss–Bonnet gravity and in the context of holography we show how the thermal DC conductivity can be obtained by solving a generalised system of Stokes equations for an auxiliary fluid on a curved black hole horizon. For more general higher derivative theories of gravity coupled to gauge-fields, we also analyse the linearised thermal and electric currents that are produced by DC thermal and electric sources. We show how suitably defined DC transport current fluxes of the dual field theory are given by current fluxes defined at the black horizon.

Bridging between descriptions involving few large and many small quantum numbers is the main open problem in loop quantum gravity. In other words, one would like to be able to represent the same physical system in terms of a few 'coarse' quantum numbers, while the effective dynamics at the coarse level should agree with the one induced by a description involving many small quantum numbers. Efforts to understand this relationship face the problem of the enormous computational complexity involved in evolving a generic state containing many quanta. In a cosmological context however, certain symmetry assumptions on the quantum states allow one to simplify the problem. In this paper, we will show how quantum states describing a spatially flat homogeneous and isotropic universe can be refined and coarse grained. Invariance of the dynamics of the coarse observables is shown to require a certain scaling property (familiar from loop quantum cosmology) of the quantum states if no running of parameters is taken into account. The involved states are solutions to the Hamiltonian constraint when terms coming from spatial derivatives are neglected, i.e. one works in the approximation of non-interacting FRW patches. The technical means to arrive at this result are a version of loop quantum gravity based on variables inspired by loop quantum cosmology, as well as an exact solution to the quantum dynamics of loop quantum cosmology which extends to the full theory in the chosen approximation.

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math. 70 21–48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.

The results reported in (2010 Class. Quantum Grav. 27 025002) are special cases of a general treatment of canonical variables for dilaton gravity models published in (2009 Class. Quantum Grav. 26 035018).