Finite Density Black Holes in a Quantum Gravity Framework

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We investigate whether photon ring observations in black hole imaging are able to distinguish between the Kerr black hole in general relativity and alternative black holes that deviate from Kerr. Certain aspects of photon rings have been argued to be robust observables in very-long-baseline interferometry black hole observations which carry imprints of the underlying spacetime. The photon ring shape, as well as its Lyapunov exponent (which encodes the narrowing of successive photon subrings), are detailed probes of the underlying geometry; measurements thereof have been argued to provide a strong null test of general relativity and the Kerr metric. However, a more complicated question is whether such observations of the photon ring properties can distinguish between Kerr and alternative black holes. We provide a first answer to this question by calculating photon rings of the Johannsen, Rasheed-Larsen, and Manko-Novikov black holes. We find that large deviations from Kerr and large observer inclinations are needed to obtain measurable differences in the photon ring shape. In other words, the Kerr photon ring shape appears to be the universal shape even for deviating black holes at low inclinations. On the other hand, the Lyapunov exponent shows more marked variations for deviations from the Kerr metric. Our analysis lays out the groundwork to determine deviations from the Kerr spacetime in photon rings that are potentially detectable by future observing missions.

We study the gravitational lensing by a Kerr–Sen Black Hole arising in heterotic string theory. A closed form expression for the bending angle of light in equatorial plane of Kerr–Sen Black Hole is derived as a function of impact parameter, spin and charge of the Black Hole. Results obtained are also compared with the corresponding cases of Kerr Black Hole in general relativity. It is observed that charge parameter behaves qualitatively similar as the spin parameter for photons travelling in direct orbits while behaves differently for photons in retrograde orbits around Black Hole. As the numerical value of the Black Hole charge increases, bending angle becomes larger in strong field limit. Further it is observed that this effect is more pronounced in case of direct orbits in comparison to the retro orbits. For both the direct and retro motion, the bending angle exceeds 2π, which in turn results in multiple loops and formation of relativistic images.

We find a black hole solution with non-Abelian field in Brans-Dicke theory.\nIt is an extension of non-Abelian black hole in general relativity. We discuss\ntwo non-Abelian fields: "SU(2)" Yang-Mills field with a mass (Proca field) and\nthe SU(2)$\\times$SU(2) Skyrme field. In both cases, as in general relativity,\nthere are two branches of solutions, i.e., two black hole solutions with the\nsame horizon radius. Masses of both black holes are always smaller than those\nin general relativity. A cusp structure in the mass-horizon radius\n($M_{g}$-$r_{h}$) diagram, which is a typical symptom of stability change in\ncatastrophe theory, does not appear in the Brans-Dicke frame but is found in\nthe Einstein conformal frame. This suggests that catastrophe theory may be\nsimply applied for a stability analysis as it is if we use the variables in the\nEinstein frame. We also discuss the effects of the Brans-Dicke scalar field on\nblack hole structure.\n

The event horizon of a black hole in general relativity absorbs all infalling radiation. Any observation of the contrary would immediately challenge the expectation that astrophysical black holes are described by the vacuum Kerr geometry. If a putative black hole does reflect part of the ingoing radiation, its quasinormal mode structure is drastically altered. Low frequency modes can be introduced that are resonantly excited during the inspiral of a binary system. We study the resulting phase shift of the gravitational wave signal. Building on neutron star results, we obtain a model-independent expression for the phase shift that depends only on quasinormal modes and Love numbers of the compact object. We find that the phase shift might be detectable with Einstein Telescope for asymmetric binaries in high signal-to-noise events ($\ensuremath{\sim}{10}^{3}$), but by far cannot explore the Planck scale.

One of the most fundamental features of a black hole in general relativity is its event horizon: a boundary from which nothing can escape. There has been a recent surge of interest in the nature of these event horizons and their local neighbourhoods. In an attempt to resolve black hole information paradox(es), and more generally, to better understand the path towards quantum gravity, ‘firewalls’ have been proposed as an alternative to black hole event horizons. In this paper, we explore the phenomenological implications of black holes possessing a surface or ‘firewall’, and predict a potentially detectable signature of these firewalls in the form of a high energy astrophysical neutrino flux. We compute the spectrum of this neutrino flux in different models and show that it is a possible candidate for the source of the PeV neutrinos recently detected by IceCube. This opens up a new area of research, bridging the non-perturbative physics of quantum gravity with the observational black hole and high energy astrophysics.

Exact solutions describing rotating black holes can offer important tests for alternative theories of gravity, motivated by the dark energy and dark matter problems. We present an analytic rotating black hole solution for a class of vector-tensor theories of modified gravity, valid for arbitrary values of the rotation parameter. The new configuration is characterised by parametrically large deviations from the Kerr-Newman geometry, controlled by non-minimal couplings between vectors and gravity. It has an oblate horizon in Boyer-Lindquist coordinates, and it can rotate more rapidly and have a larger ergosphere than black holes in General Relativity (GR) with the same asymptotic properties. We analytically investigate the features of the innermost stable circular orbits for massive objects on the equatorial plane, and show that stable orbits lie further away from the black hole horizon with respect to rotating black holes in GR. We also comment on possible applications of our findings for the extraction of rotational energy from the black hole.

The \\textit{axial} electromagnetic (EM) perturbations of the black hole (BH)\nsolutions in general relativity coupled to nonlinear electrodynamics (NED) were\nstudied for both electrically and magnetically charged BHs, assuming that the\nEM perturbations do not alter the spacetime geometry in our preceding paper\n[Phys. Rev. D 97, 084058 (2018)]. Here, as a continuation of that work, the\nformalism for the \\textit{polar} EM perturbations of the BHs in general\nrelativity coupled to the NED is presented. We show that the quasinormal modes\n(QNMs) spectra of polar EM perturbations of the electrically and magnetically\ncharged BHs in the NED are not isospectral, contrary to the case of the\nstandard Reissner-Nordstr\\"{o}m BHs in the classical linear electrodynamics. It\nis shown by the detailed study of QNMs properties in the eikonal approximation\nthat the EM perturbations can be a powerful tool to confirm that in the NED\nlight ray does not follow the null geodesics of the spacetime. By specifying\nthe NED model and comparing axial and polar EM perturbations of the\nelectrically and magnetically charged BHs, it is shown that QNM spectra of the\naxial EM perturbations of magnetically (electrically) charged BH and polar EM\nperturbations of the electrically (magnetically) charged BH are isospectral,\ni.e., $\\omega_{mag}^{ax}\\approx\\omega_{el}^{pol}$\n($\\omega_{mag}^{pol}\\approx\\omega_{el}^{ax}$).\n

We use black holes with a negative cosmological constant to investigate aspects of the freeze-out temperature for hadron production in high energy heavy-ion collisions. The two black hole solutions present in the anti-de Sitter geometry have different mass and are compared to the data showing that the small black hole solution is in good agreement. This is a new feature in the literature since the small black hole in general relativity has different thermodynamic behavior from that of the large black hole solution. We find that the inclusion of the cosmological constant (which can be interpreted as the plasma pressure) leads to a lowering of the temperature of the freeze-out curve as a function of the baryochemical potential, improving the description previously suggested by Castorina, Kharzeev, and Satz.

We discuss corrections to the mainstream theory of black holes in general relativity. We discuss the Schwarzschild point-mass and extended-mass solutions of the Einstein Field Equations, concluding that many of the features traditionally associated with black hole theory are absurd and incorrect. The picture of a point singularity surrounded by a surface singularity at the Schwarzschild radius does not hold water. As an afterthought, we suggest how to solve the Kerr problem (rotating black hole): by numerical methods/machine computation.

In the framework of the AdS/CFT correspondence, we define and compute the spherical analogue of the shear viscosity for QFTs dual to five-dimensional charged AdS black holes in general relativity (GR) and Gauss-Bonnet (GB) gravity. We show that the ratio between this quantity and the entropy density, ῆ/s exhibits a temperature-dependent hysteresis.

We study the quasi-normal modes (QNM) of scalar, electromagnetic and gravitational perturbations of black holes in general relativity whose horizons have toroidal, cylindrical or planar topology in an asymptotically anti-de Sitter (AdS) spacetime. The associated QNM frequencies describe the decay in time of the corresponding test field in the vicinities of the black hole. In terms of the AdS/CFT conjecture, the inverse of the frequency is a measure of the dynamical timescale of approach to thermal equilibrium of the corresponding conformal field theory.

Area-entropy relation for spherical symmetric black holes

<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>

Most no-hair theorems involve the assumption that the scalar field is independent of time. Recently in [Phys. Rev. D90 (2014) 041501(R)] the existence of time-dependent scalar hair outside a stationary black hole in general relativity was ruled out. We generalize this work to modified gravities and non-minimally coupled scalar field with an additional assumption that the spacetime is axisymmetric. It is shown that in higher-order gravity such as metric $f(R)$ gravity the time-dependent scalar hair doesn't exist. While in Palatini $f(R)$ gravity and non-minimally coupled case the time-dependent scalar hair may exist.