Displacement memory and BMS symmetries

<p><strong>The future of theoretical physics is unclear. Two large areas that fall under the umbrella of theoretical physics are cosmology and quantum gravity. Modern cosmology is relatively a much younger field than quantum gravity, and both of these fields require further developments of general relativity. In this thesis we do not hope to resolve the problems facing modern cosmology or theories of quantum gravity. Rather, we will conduct original research into aspects of general relativity that may be used in the future to aid the development and testing of theories of cosmology and quantum gravity.</strong></p><p>It is our view that the largest problem facing astrophysics and cosmology stem from the existence of the dark sector of the Universe. The implication here being that more than ninety percent of the energy density of the Universe is “missing in action” and seemingly consists of dark energy and dark matter. Furthermore, it is apparent that there exist conceptual flaws in our understanding of observational concepts such as expansion versus motion and observer biases. To this end, we investigate the standard spacetime metric used in cosmology, the Friedmann–Lemaˆıtre-Roberston–Walker (FLRW) metric in a peculiar coordinate system — the Painlev´e–Gullstrand coordinates. In this coordinate system (slicing), space is no longer expanding, rather, the galaxies are receding from each other. We hope this will aid in the understanding of expansion, motion, curvature, and observer bias with future work. We further investigate the possibility of black holes in cosmology being directly coupled to the accelerated expansion of the Universe — in other words, black holes as a source for dark energy. However, we show that this is highly implausible.</p><p>Relatively recently it has been postulated that the near black hole horizon limit may be a regime where quantum gravity effects become relevant i.e., quantum gravity may not be restricted to near the Planck scale. We investigate a curious model of black and white holes that shows how one may transition into the other over a finite period of time. This is research conducted in the near horizon limit of the Schwarzschild black hole. We introduce a time dependent function into the usual Schwarzschild black hole spacetime (leaving this new spacetime not a simple coordinate transformed version of the original). This function allows the black hole to transition into a white hole. Importantly, the action for this transition can be shown to be zero, meaning it can be added to the Feynman path integral at no cost.</p><p>Finally, we move to investigating the black hole memory effect. During the last decade, there has been an interesting connection made between the Bondi– Metzner–Sachs (BMS) group — an infinite dimensional group of symmetries found at null infinity — and the gravitational memory effect. In particular, it was shown that the passage of a gravitational wave that alters a Schwarzschild black hole is seen as a supertranslation of the spacetime at null infinity. We extend these calculations to the Kerr and Kerr–Newman black holes. Hence, showing that there may be a way to verify the abstract mathematical ideas predicated on the BMS group by detection of the memory effect in future observations.</p><p>It is our hope that when future gravitational wave detectors such as the laser-interferometer-space-antenna (LISA) are launched, research conducted in this thesis may shed light on how the memory may relate to black holes in their asymptotic & near horizon limits to aid our understanding of the nature of quantum gravity.</p>

One of the most important geodesics in a black hole spacetime is the marginally bound spherical orbit. This critical geodesic represents the innermost spherical orbit which is bound to the central black hole. The radii ${r}_{\mathrm{mb}}(\overline{a})$ of the marginally bound equatorial circular geodesics of rotating Kerr black holes were found analytically by Bardeen et al. more than four decades ago (here $\overline{a}\ensuremath{\equiv}J/{M}^{2}$ is the dimensionless angular momentum of the black hole). On the other hand, no closed-form formula exists in the literature for the radii of generic (nonequatorial) marginally bound geodesics of the rotating Kerr spacetime. In the present study, we analyze the critical (marginally bound) orbits of rapidly rotating Kerr black holes. In particular, we derive a simple analytical formula for the radii ${r}_{\mathrm{mb}}(\overline{a}\ensuremath{\simeq}1;\mathrm{cos}i)$ of the marginally bound spherical orbits, where $\mathrm{cos}i$ is an effective inclination angle (with respect to the black hole equatorial plane) of the geodesic. We find that the marginally bound spherical orbits of rapidly rotating black holes are characterized by a critical inclination angle, $\mathrm{cos}i=\sqrt{2/3}$, above which the coordinate radii of the geodesics approach the black hole radius in the extremal $\overline{a}\ensuremath{\rightarrow}1$ limit. It is shown that this critical inclination angle signals a transition in the physical properties of the orbits: in particular, it separates marginally bound spherical geodesics which lie a finite proper distance from the black hole horizon from marginally bound geodesics which lie an infinite proper distance from the horizon.

We show that charges associated with the internal Lorentz symmetries of general relativity, with higher derivative boundary terms included in the action, capture observable gravitational wave effects. In particular, the Gauss-Bonnet charge measures the precession rate of a freely-falling gyroscope, while the Pontryagin charge encodes the relative radial acceleration of freely-falling test masses. This relation highlights the importance of the tetrad formalism and the physical significance of asymptotic internal Lorentz symmetries.

We present an introduction to dynamical trapping horizons as quasi-local models for black hole horizons, from the perspective of an Initial Value Problem approach to the construction of generic black hole spacetimes. We focus on the geometric and structural properties of these horizons aiming, as a main application, at the numerical evolution and analysis of black hole spacetimes in astrophysical scenarios. In this setting, we discuss their dual role as an a priori ingredient in certain formulations of Einstein equations and as an a posteriori tool for the diagnosis of dynamical black hole spacetimes. Complementary to the first-principles discussion of quasi-local horizon physics, we place an emphasis on the rigidity properties of these hypersurfaces and their role as privileged geometric probes into near-horizon strong-field spacetime dynamics.

In this paper, we study a proposal put forward recently by Bodendorfer, Mele and Münch and García-Quismondo and Marugán, in which the two polymerization parameters of spherically symmetric black hole spacetimes are the Dirac observables of the four-dimensional Ashtekar’s variables. In this model, black and white hole horizons in general exist and naturally divide the spacetime into the external and internal regions. In the external region, the spacetime can be made asymptotically flat by properly choosing the dependence of the two polymerization parameters on the Ashtekar variables. Then, we find that the asymptotical behavior of the spacetime is universal, and, to the leading order, the curvature invariants are independent of the mass parameter m. For example, the Kretschmann scalar approaches zero as K≃A0r−4 asymptotically, where A0 is generally a non-zero constant and independent of m, and r the geometric radius of the two-spheres. In the internal region, all the physical quantities are finite, and the Schwarzschild black hole singularity is replaced by a transition surface whose radius is always finite and non-zero. The quantum gravitational effects are negligible near the black hole horizon for very massive black holes. However, the behavior of the spacetime across the transition surface is significantly different from all loop quantum black holes studied so far. In particular, the location of the maximum amplitude of the curvature scalars is displaced from the transition surface and depends on m; so does the maximum amplitude. In addition, the radius of the white hole is much smaller than that of the black hole, and its exact value sensitively depends on m, too.

Analyses of astrophysical observations, such as quasiperiodic oscillations (QPOs), combined with theoretical studies, help to understand the deeper properties of black hole spacetime and obtain parameters of black holes and alternative gravity theories. In this study, we investigate the dynamics of charged particles orbiting magnetized black holes within the Bertotti–Robinson (BR) geometry, also known as the electromagnetic universe (EU). We study the circular motion and oscillations of charged particles around a black hole in the presence of a magnetic field, focusing on their applications to QPOs. First, we obtain solutions for the Maxwell equations for orthonormal components of magnetic fields around the black holes in radial and angular directions and analyze the dependence on the EU field and magnetic interactions. The effective potential, specific angular momentum, energy, and innermost stable circular orbits (ISCOs) of charged particles are analyzed to demonstrate how the black hole spacetime, in conjunction with magnetic interaction and EU parameters, affects particle dynamics. Then, we calculate the Keplerian, radial, and vertical epicyclic frequencies, providing insight into the orbital and oscillatory behavior of particles near the black holes. Furthermore, we investigate twin-peak QPOs using the relativistic precession (RP) model and compare the main results with those of the standard Schwarzschild limit. Finally, we employ Monte Carlo Markov Chain (MCMC) simulations to obtain constraint values for black hole mass, the EU, and magnetic interaction parameters, using QPO frequency data observed in microquasars (as an example, XTE J1550-564, GRO J1655-40, GRS 1915+105) and galactic centers (in cases of M82 and Milky Way). Our findings may provide valuable insights into understanding the combined effects of RB spacetime and electromagnetic interactions around black holes on astrophysical observations of QPOs and testing gravity theories in a strong gravity regime.

We consider the effects of a cosmological constant on the dynamics of constant angular momentum discs orbiting Schwarzschild-de Sitter black holes. The motivation behind this study is to investigate whether the presence of a radial force contrasting the black hole's gravitational attraction can influence the occurrence of the runaway instability, a robust feature of the dynamics of constant angular momentum tori in Schwarzschild and Kerr spacetimes. In addition to the inner cusp near the black hole horizon through which matter can accrete onto the black hole, in fact, a positive cosmological constant introduces also an outer cusp through which matter can leave the torus without accreting onto the black hole. To assess the impact of this outflow on the development of the instability we have performed time-dependent and axisymmetric hydrodynamical simulations of equilibrium initial configurations in a sequence of background spacetimes of Schwarzschild-de Sitter black holes with increasing masses. The simulations have been performed with an unrealistic value for the cosmological constant which, however, yields sufficiently small discs to be resolved accurately on numerical grids and thus provides a first qualitative picture of the dynamics. The calculations, carried out for a wide range of initial conditions, show that the mass-loss from the outer cusp can have a considerable impact on the instability, with the latter being rapidly suppressed if the outflow is large enough.

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

We propose an upgrade to Advanced LIGO (aLIGO), named LIGO-LF, that focuses on improving the sensitivity in the 5-30Hz low-frequency band, and we explore the upgrade's astrophysical applications. We present a comprehensive study of the detector's technical noises and show that with technologies currently under development, such as interferometrically sensed seismometers and balanced-homodyne readout, LIGO-LF can reach the fundamental limits set by quantum and thermal noises down to 5Hz. These technologies are also directly applicable to the future generation of detectors. We go on to consider this upgrade's implications for the astrophysical output of an aLIGO-like detector. A single LIGO-LF can detect mergers of stellar-mass black holes (BHs) out to a redshift of z≃6 and would be sensitive to intermediate-mass black holes up to 2000 M_{⊙}. The detection rate of merging BHs will increase by a factor of 18 compared to aLIGO. Additionally, for a given source the chirp mass and total mass can be constrained 2 times better than aLIGO and the effective spin 3-5 times better than aLIGO. Furthermore, LIGO-LF enables the localization of coalescing binary neutron stars with an uncertainty solid angle 10 times smaller than that of aLIGO at 30Hz and 4 times smaller when the entire signal is used. LIGO-LF also significantly enhances the probability of detecting other astrophysical phenomena including the tidal excitation of neutron star r modes and the gravitational memory effects.

Three-dimensional spacetime with a negative cosmological constant has proven to be a remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees of freedom, the asymptotic symmetries become all the more crucial. For pure (2+1) gravity they consist of two copies of the Virasoro algebra. There exists a black hole which may be endowed with all the corresponding charges. The pure (2+1) gravity theory may be reformulated in terms of two Chern-Simons connections for sl(2,R). An immediate generalization containing gravity and a finite number of higher spin fields may be achieved by replacing sl(2,R) by sl(3,R) or, more generally, by sl(N,R). The asymptotic symmetries are then two copies of the so-called W_N algebra, which contains the Virasoro algebra as a subalgebra. The question then arises as to whether there exists a generalization of the standard pure gravity (2+1) black hole which would be endowed with all the W_N charges. The original pioneering proposal of a black hole along this line for N=3 turns out, as shown in this paper, to actually belong to the so called "diagonal embedding" of sl(2,R) in sl(3,R), and it is therefore endowed with charges of lower rather than higher spins. In contradistinction, we exhibit herein the most general black hole which belongs to the "principal embedding". It is endowed with higher spin charges, and possesses two copies of W_3 as its asymptotic symmetries. The most general diagonal embedding black hole is studied in detail as well, in a way in which its lower spin charges are clearly displayed. The extension to N>3 is also discussed. A general formula for the entropy of a generalized black hole is obtained in terms of the on-shell holonomies.

Test the growth models of black hole by jointing LIGO and Insight-HXMT observations

We have investigated the strong gravitational lensing in a rotating squashed Kaluza-Klein (KK) black hole spacetime. Our result show that the strong gravitational lensings in the rotating squashed KK black hole spacetime have some distinct behaviors from those in the backgrounds of the four-dimensional Kerr black hole and of the squashed KK Gödel black hole. In the rotating squashed KK black hole spacetime, the marginally circular photon radius ρ ps , the coefficient $ \overline{a} $ , $ \overline{b} $ , the deflection angle α(θ) in the ϕ direction and the corresponding observational variables are independent of whether the photon goes with or against the rotation of the background, which is different with those in the usual four-dimensional Kerr black hole spacetime. Moreover, we also find that with the increase of the scale of extra dimension ρ0, the marginally circular photon radius ρ ps and the angular position of the relativistic images θ ∞ first decreases and then increases in the rotating squashed KK black hole for fixed rotation parameter b, but in the squashed KK Gödel black hole they increase for the smaller global rotation parameter j and decrease for the larger one. In the extremely squashed case ρ 0 = 0, the coefficient a in the rotating squashed KK black hole increases monotonously with the rotation parameter, but in the squashed KK Gödel black hole it is a constant and independent of the global rotation of the Gödel Universe. These information could help us to understand further the effects of the rotation parameter and the scale of extra dimension on the strong gravitational lensing in the black hole spacetimes.

`Gravitational memory' refers to the possibility that, in cosmologies with a\ntime-varying gravitational `constant', objects such as black holes may retain a\nmemory of conditions at the time of their birth. We consider this phenomenon in\na different physical scenario, where the objects under consideration are boson\nstars. We construct boson star solutions in scalar-tensor gravity theories, and\nconsider their dependence on the asymptotic value of the gravitational\nstrength. We then discuss several possible physical interpretations, including\nthe concept of pure gravitational stellar evolution.\n

We show that rotating black holes do not experience any tidal deformation when they are perturbed by a weak and adiabatic gravitational field. The tidal deformability of an object is quantified by the so-called "Love numbers", which describe the object's linear response to its external tidal field. In this work, we compute the Love numbers of Kerr black holes and find that they vanish identically. We also compute the dissipative part of the black hole's tidal response, which is non-vanishing due to the absorptive nature of the event horizon. Our results hold for arbitrary values of black hole spin, for both the electric-type and magnetic-type perturbations, and to all orders in the multipole expansion of the tidal field. The boundary conditions at the event horizon and at asymptotic infinity are incorporated in our study, as they are crucial for understanding the way in which these tidal effects are mapped onto gravitational-wave observables. In closing, we address the ambiguity issue of Love numbers in General Relativity, which we argue is resolved when those boundary conditions are taken into account. Our findings provide essential inputs for current efforts to probe the nature of compact objects through the gravitational waves emitted by binary systems.

The standard Black Holes (BHs) in General Relativity, as well as other ultra-compact objects (with or without an event horizon) admit planar circular photon orbits. These light rings (LRs) determine several spacetime properties. For instance, stable LRs trigger instabilities and, in spherical symmetry, (unstable) LRs completely determine BH shadows. In generic stationary, axi-symmetric spacetimes, non-planar bound photon orbits may also exist, regardless of the integrability properties of the photon motion. We suggest a classification of these fundamental photon orbits (FPOs) and, using Poincar\'e maps, determine a criterion for their stability. For the Kerr BH, all FPOs are unstable (similarly to its LRs) and completely determine the Kerr shadow. But in non-Kerr spacetimes, stable FPOs may also exist, even when all LRs are unstable, triggering new instabilities. We illustrate this for the case of Kerr BHs with Proca hair, wherein, moreover, qualitatively novel shadows with a cuspy edge exist, a feature that can be understood from the interplay between stable and unstable FPOs. FPOs are the natural generalisation of LRs beyond spherical symmetry and should generalise the LRs key role in different spacetime properties.