General Theory of Black Holes

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

We propose a theoretical framework to address the singularity problem in black holes by introducing the concept of finite-density cores composed of ultra-dense crystalline matter formed under extreme pressure. By modifying the Einstein field equations to incorporate a scalar field representing quantum corrections and defining an anisotropic equation of state (EoS) for this exotic matter, we aim to unify classical and quantum descriptions without introducing singularities. Our model explores the possibility that subatomic particles, when subjected to pressures beyond those in neutron stars, form a crystalline lattice at scales approaching the Planck length. We present the modified field equations, the proposed EoS, and discuss the implications for black hole physics, quantum gravity, and potential observational signatures. The EoS is contained in a separate file in this project<br><br>The classical description of black holes in general relativity predicts singularities—points of infinite density and curvature—which pose significant challenges to our understanding of physics. Resolving these singularities is a crucial step toward unifying general relativity with quantum mechanics. In this work, we explore a novel approach by proposing that black holes have finite-density cores composed of ultra-dense crystalline matter formed under extreme pressure.Analogous to neutron stars, where matter is compressed to nuclear densities, we hypothesize that black holes compress matter even further. At these extreme conditions, subatomic particles form a crystalline lattice, possibly involving new states of matter where even electrons are broken down into smaller constituents. This exotic matter would only exist under specific temperatures and pressures near the Planck scale.

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 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

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.

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.

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.

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.

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

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

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.

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.

An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity.