International Journal of Modern Physics D

A procedure to derive a unitary evolution law for a quantised black hole has been proposed by the author. The proposal implies several assumptions, which seem almost unavoidable to this author. We start off with the question how to describe the energy eigenstates of a black hole. The background metric required for this cannot be the Vaidya metric let alone the metric proposed by Hawking, who included the effect of the final evaporation of the black hole. This however leads to the formation if firewalls at both the future and the past event horizon, unless one anticipates the effects that the firewalls have. These effects can be handled as new boundary conditions at the horizons, describing the flow of the participating particles. It is subsequently explained how these boundary conditions must involve the antipodes of the outside world. Imposing unitarity and continuity then automatically leads to a unique, unitary evolution operator. We exhibit the resulting, quite coherent picture.

The two main processes of black hole formation are collapse of a matter cloud under its own gravity and accretion of matter onto an already existing gravitating centre. The necessary condition for both the processes to operate is that overall force on collapsing fluid element or on test accreting particles is attractive. It turns out that this is not the case in general in higher dimensions greater than the usual four for collapsing or accreting matter having nonzero angular momentum. Thus, both these processes cannot operate in higher dimensions to form a rotating black hole. The only theory in which this is not the case in higher dimensions is the pure Lovelock gravity, where both these processes could in principle work for formation of black holes.

In this paper, we take a closer and new look at the effects of tidal forces on the free fall of a quantum particle inside a spherically symmetric gravitational field. We derive the corresponding Schrödinger equation for the particle by starting from the fully relativistic Klein–Gordon equation in order (i) to briefly discuss the issue of the equivalence principle and (ii) to be able to compare the relativistic terms in the equation to the tidal-force terms. To the second order of the nonrelativistic approximation, the resulting Schrödinger equation is that of a simple harmonic oscillator in the horizontal direction and that of an inverted harmonic oscillator in the vertical direction. Two methods are used for solving the equation in the vertical direction. The first method is based on a fixed boundary condition, and yields a discrete-energy spectrum with a wavefunction that is asymptotic to that of a particle in a linear gravitational field. The second method is based on time-varying boundary conditions and yields a quantized-energy spectrum that is decaying in time. Moving on to a freely-falling reference frame, we derive the corresponding time-dependent energy spectrum. The effects of tidal forces yield an expectation value for the Hamiltonian and a relative change in time of a wavepacket’s width that are mass-independent. The equivalence principle, which we understand here as the empirical equivalence between gravitation and inertia, is discussed based on these various results. For completeness, we briefly discuss the consequences expected to be obtained for a Bose–Einstein condensate or a superfluid in free fall using the nonlinear Gross–Pitaevskii equation.

The Randall–Sundrum models are expected to modify the short distance behaviour of general relativity. In this paper, we will propose an experimental test for this short distance modification due to Randall–Sundrum models. This will be done by the analysing motion of a particle which is moving in spherical gravitational field with a drag force. The position at which the particle stops will be different in general relativity and Randall–Sundrum model. This difference in the distance moved by the particle before stopping can be measured using a nanoelectromechanical setup. Thus, it is possible to experimentally test Randall–Sundrum models using currently available technology.

The non-Kerr black hole is an important metric to study the possible deviations from the Kerr black hole of general relativity. It has been constructed by applying the Newman–Janis algorithm on a deformed Schwarzschild black hole. This approach has been generalized to include two different deformation functions to obtain CPR black holes [V. Cardoso, P. Pani and J. Rico, Phys. Rev. D 89 (2014) 064007]. In this paper, we develop the charged analogue of this spacetime. The new metric is studied for the particle dynamics also.

This paper is dedicated to inspecting the appearance of electromagnetic field, which is caused by the presence of charge in the highly compact object named gravastar in the background of $f(R,G)$ theory. According to conjecture introduced by Mazur and Mottola gravastar must be consisted of three sectors. We have interpreted these sectors by using specific equations of states. Spherically static metric, perfect fluid and the isotropic pressure have been used in order to calculate a singularity free solution. Gravitational mass present in the inner sector of gravastar is changed into electromagnetic mass in the existence of charge. The electromagnetic mass model of inner sector is responsible for stability by providing balance to the repulsive pressure, which is caused by the presence of charge. It is observed that the presence of electrical charge has a significant effect on energy content, entropy and proper length of the shell that is demonstrated with the help of graphs.

We investigate the effects of geometric optics as deflection of light-ray around gravitating compact object surrounded by a plasma in conformal Weyl gravity. We have obtained that the expression for the deflection angle of the light in a vacuum is modified due to the effect of $\gamma$ responsible for the Weyl correction to the gravity. The effect of the plasma surrounding the black hole in Weyl gravity to the deflection angle has been also studied. We have also provided the analysis of the magnification of image source due to gravitational lensing around black hole in Weyl gravity in the presence of plasma environment. Finally, we have analyzed the shadow of the black hole in Weyl gravity in the presence of plasma.

In this paper, we study the effects of the presence of the tachyon field around the black hole. We show that in presence of the tachyon field, unlike the ordinary canonical scalar field, the time evolution of the black hole mass depends on the potential of this field. By considering several types of potential, we study the behavior of the black hole mass and its time evolution and find some interesting results. We find that the presence of the tachyon field causes the accretion of the mass into the black hole. We also show that with linear and hilltop potentials, in some ranges of the parameters space, the mass of the black hole can decrease even without any Hawking radiation.

In this paper, two numerical methods are used to calculate quasi-normal modes (QNMs) of near-extremal black holes/strings in the generalized spherically/cylindrically symmetric background, the Asymptotic Iteration Method (AIM) and the Spectral Method. The numerical results confirm the accuracy of the approximate analytic formula using the Pöschl–Teller potential. Our analytic formula is used to investigate the Strong Cosmic Censorship conjecture of extremal and near-extremal black holes in (P. Burikham, S. Ponglertsakul and T. Wuthicharn, Eur. Phys. J. C 80 (2020) 954, arXiv:2010.05879 [gr-qc]).

This study explores the emission of massive charged spin-1 particles from the background of Bardeen regular spacetime by the semi-classical method used to study the Hawking radiation spectrum. We employed the Hamilton–Jacobi method and Wentzel–Kramers–Brillouin approximation technique with the suitable form of the wave function to solve the Proca field equation. We calculated the tunneling probability of outgoing spin-1 particles and the corresponding thermodynamic temperature. Furthermore, we obtained the modified thermodynamic quantities like temperature, entropy as well as heat capacity by utilizing the quadratic form of generalized uncertainty principle (GUP) and minimal length. In the end, we investigated the local stability as well as phase transitions of the Bardeen black hole in the context of GUP-modified heat capacity.

This work is an example of the application of the dynamical system analysis in the context of cosmology. Here cosmic evolution is considered in the background of homogeneous and isotropic flat FLRW spacetime with interacting dark energy and varying mass dark matter as the matter content. The DE is chosen as phantom scalar field with self-interacting potential while the DM is in the form of dust. The potential of the scalar field and the mass function of dark matter are chosen as exponential or power-law form or in their product form. Using suitable dimensionless variables, the Einstein field equations and the conservation equations constitute an autonomous system. The stability of the nonhyperbolic critical points is analyzed by using center manifold theory. Finally, cosmological phase transitions have been detected through bifurcation analysis which has been done by Poincaré index theory.

The assumptions of the Hawking–Penrose singularity theorem are not covariant under field redefinitions. Following the works on the covariant formulation of quantum field theory initiated by Vilkovisky and DeWitt in the 80s, we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with the other fields in the theory. From this viewpoint, a spacetime singularity might be just a singularity in the field-space coordinates, analogously to the standard coordinate singularities in General Relativity. Objects invariant under field-space coordinate transformations can then reveal whether certain spacetime singularity is indeed singular. We recall that observables in quantum field theory are scalar functionals in field space. Therefore, in principle, spacetime singularities corresponding to regular field-space curvature invariants would not affect physical observables. In this paper, we show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development.