Narrow Results

In our study, we delved into the profound ramifications of string tension on the collapse of a string fluid, culminating in the formation of a black hole within the realm of $f(R)$ gravity. A string fluid is a perfect fluid model, each whose particle admits a radially stretched string. The outer region for the collapsing object is assumed to be the Schwarzschild spacetime, while the fluid collapses in the internal region are supposed to be Friedman–Robertson–Walker spacetime. The junction conditions are developed leading to gravitational mass and energy. The time frame for apparent horizon and singularity formation was estimated, showing a black hole as the outcome. String tension emerged as a pivotal factor in prolonging horizon creation. Our findings illuminate the relation among $f(R)$ gravity, string tension, and collapse dynamics, enriching our understanding of cosmic phenomena.

Hawking radiation on the apparent horizon of a Vaidya black hole is investigated using Parikh's tunneling method. When back-reaction of particles is neglected, precisely thermal spectrum can be obtained. Then the black hole thermodynamics can be built successfully on the apparent horizon. When a relativistic perturbation is given to the apparent horizon, similar calculation can also lead to a purely thermal spectrum, which is corresponding to a modified temperature from the former. The first law of thermodynamics can also be constructed successfully at a new supersurface which has a small deviation from the apparent horizon. When the event horizon is thought as such a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be built on the event horizon. It is concluded that the thermodynamics should be constructed on the apparent horizon exactly while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.

We investigate the validity of the thermodynamical properties of the universe in a new parametric model of dark energy with the equation of state w = w₀ + w₁ · z(1 + z)/(1 + z²). In the spatially homogeneous and isotropic universe, assuming that the temperature and entropy in cosmology is as in a black hole, we examine the thermodynamical properties of the universe bounded by the apparent horizon and the event horizon respectively. By analysis, we find that the first and the second laws of thermodynamics are valid inside the apparent horizon, while they break down inside the event horizon.

In the context of modified f(R) gravity, we attempt to study the thermodynamic properties of the evolving Lorentzian wormholes at the apparent horizon. It is shown that the wormhole can be derived from a particular f(R) model in the radiation background. Moreover, it has been shown that the field equations can be cast to a similar form at the apparent horizon for the evolving Lorentzian wormhole. Compared to the case of Einstein's general relativity, an additional term appears here.

The spectroscopy of the apparent horizon of Vaidya black holes is investigated via adiabatic invariance. We obtain an equally spaced entropy spectrum with its quantum equal to the one given by Bekenstein [J. D. Bekenstein, Phys. Rev. D7, 2333 (1973)]. We demonstrate that the quantization of entropy and area is a generic property of horizon, not only for stationary black holes, and the results also exit in a dynamical black hole. Our work also shows that the quantization of black hole is closely related to the tunneling formalism for deriving the Hawking effect, which is interesting.

In this paper, the different properties of generalized Vaidya spacetime are considered. We define the location of horizons. We show that the apparent horizon can contain the event horizon. The locations of all types of horizons are compared with the ones in the usual Vaidya spacetime. We investigate the time-like geodesics in this spacetime. New corrections to Schwarzschild and Vaidya cases appear and we give conditions when these corrections are not negligible. Also, we consider the conformal Killing vector and transform the metric to conformally static coordinates. We introduce a new constant of motion along null and time-like geodesics, which is generated by a homothetic Killing vector. The conformally static coordinates allow diagonalizing of the generalized Vaidya spacetime. The surface gravity has been calculated for the dust and stiff fluid cases.

The purpose of this paper is to investigate the quantum vacua directly implied by the wave function of a gravitational configuration characterized by the presence of an apparent horizon, namely the Vaidya space–time solution. Spherical symmetry is a main feature of this configuration, with a scalar field constituting a source [a Klein–Gordon geon or Berger–Chitre–Moncrief–Nutku (BCMN) type model]. The subsequent analysis requires solving a Wheeler–DeWitt equation near the apparent horizon (following the guidelinesintroduced by A. Tomimatsu,¹⁸; M. Pollock,¹⁹ and developed by A. Hosoya and I. Oda^20,21) with the scalar field herein expanded in terms of S² spherical harmonics: midisuperspace quantization. The main results present in this paper are as follows. It is found that the mass function characteristic of the Vaidya metric is positive definite within this quantum approach. Furthermore, the inhomogeneous matter sector determines a descrip-tion in terms of open quantum (sub)systems, namely in the form of an harmonic oscillator whose frequency depends on the mass function. For this open (sub)system, a twofold approach is employed. On the one hand, an exact invariant observable is obtained from the effective Hamiltonian for the inhomogeneous matter modes. It is shown that this invariant admits a set of discrete eigenvalues which depend on the mass function. The corresponding set of eigenstates is constructed from a particular vacuum state. On the other hand, exact solutions are found for the Schrädinger equation associated with the inhomogeneous matter modes. This paper is concluded with a discussion, where two other issues are raised: (i) the possible application to realistic black hole dynamics of the results obtained for a simplified (BCMN) model and (ii) whether such vacuum states could be related with others defined instead within scalar field theories constructed in classical backgrounds.

Vector particles' Hawking radiation as tunneling from the apparent horizon of Vaidya black holes is investigated. By applying the WKB approximation and the appropriate ansatz for the form of the action to the Proca equation, we obtain the tunneling spectrum of vector particles. As a result, the expected Hawking temperature is recovered by vector particles tunneling from the apparent horizon of Vaidya black holes.

This paper deals with the study of quasi-spherical gravitational collapse in the framework of $f(R,T)$ theory. We will divide geometry of the star into two distinct portions i.e. interior portion and exterior portion. In the interior portion, we consider quasi-spherical Szekeres line element and in the exterior portion we take Vaidya line element. The interior and exterior portions will be glued by using Israel’s junction conditions [W. Israel, Il Nuovo Cimento B (1965–1970) 44, 1 (1966); W. Israel, Phys. Lett. A 24, 184 (1967)]. The field equations will be derived in the context of $f(R,T)$ theory for a particular model. Apparent horizons and their time configuration for various desirable cases will also be discussed.

There are numerous derivations of the Hawking effect available in the literature. They emphasise different features of the process, and sometimes make markedly different physical assumptions. This article presents a "minimalist" argument, and strips the derivation of as much excess baggage as possible. All that is really necessary is quantum physics plus a slowly evolving future apparent horizon (not an event horizon). In particular, neither the Einstein equations nor Bekenstein entropy are necessary (nor even useful) in deriving Hawking radiation.

We show that (3+1) Einstein–Maxwell spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional spacetime metric is otherwise completely arbitrary. We discuss the implications of this result for the hoop and cosmic censorship conjectures.

An analysis is made for relations between the tunneling rate and the unified first law of thermodynamics at the trapping horizons of two kinds of spherically symmetric dynamical black holes. The first kind is the Vaidya–Bardeen black hole; the tunneling rate Γ ~ e^△S can be obtained naturally from the unified first law at the apparent horizon, which holds the form dE_H = TdS + WdV. The second kind is the McVittie solution; the action of the radial null geodesic of the outgoing particles does not always have a pole at the apparent horizon, while the ingoing mode always has one. The solution of the ingoing mode of the radiation can be mathematically reduced to the case in the FRW universe smoothly. However, as a black hole, the physical meaning is unclear and even puzzling.

We show that for an RSII braneworld filled with interacting viscous dark energy and dark matter, one can always rewrite the Friedmann equation in the form of the first law of thermodynamics, dE = T_hdS_h + WdV, at the apparent horizon. In addition, the generalized second law of thermodynamics can be fulfilled in a region enclosed by the apparent horizon on the brane for both constant and time-variable five-dimensional Newton's constant G₅. These results hold regardless of the specific form of the dark energy. Our study further supports the belief that in an accelerating universe with spatial curvature, the apparent horizon is a physical boundary from the thermodynamical point of view.

In this paper, the generalized second law (GSL) of thermodynamics is studied at the apparent horizon of the evolving wormhole. It is shown that the GSL holds at the apparent horizon of the evolving wormhole together with the assumption that the horizon temperature is equal to the temperature of the phantom energy.

The spherical symmetry black holes are considered in expanding background. The singularity line and the marginally trapped tube surface behavior are discussed. In particular, we address the conditions whether dynamical horizon forms for these cosmological black holes. We also discuss about the cosmological constant effect on these black hole and the redshift of the light which comes from the marginally trapped tube surface.

Based on the chiral effective action method, we derive the thermal radiation from the apparent horizon in a Friedmann–Robertson–Walker (FRW) universe. The dimension reduction technique plays a crucial role in the derivation. The result further confirms the thermal properties of the apparent horizon in a FRW universe.

We study the time evolution of the Misner-Sharp mass and the apparent horizon for gravitational collapse of a massless scalar field in the $Ad{S}_5$ spacetime for both cases of narrow and broad waves by numerically solving the Einstein’s equations coupled to a massless scalar field. This is done by relying on the full dynamics of the collapse including the concept of the dynamical horizon. It turns out that the Misner-Sharp mass is everywhere constant except for a rapid change across a thin shell defined by the density profile of the collapsing wave. By studying the evolution of the apparent horizon, indicating the formation of a black hole at different times we see how asymptotically an event horizon forms. The dependence of the thermalization time on the radius of the initial black hole event horizon is also studied.

Recently $d$-dimensional spherically symmetric charged Vaidya black hole solution has been constructed. We observe that this nonstationary solution admits extremal limit and study its near horizon geometry. We show that the symmetry of the near horizon geometry is $\mathrm{\text{SO}}(2,1)\times \mathrm{\text{SO}}(d-1)$. Our analysis shows that the theorems for the near horizon geometry of stationary extremal black holes, may be extended to nonstationary cases.

A new perspective toward Einstein’s theory of general relativity, called mimetic gravity, was suggested in [A. H. Chamseddine and V. Mukhanov, J. High Energy Phys.1311 (2013) 135] by isolating the conformal degree of freedom in a covariant fashion through a re-parametrization of the physical metric in terms of an auxiliary metric and a mimetic field. In this paper, we first derive the Friedmann equations of the Friedmann–Robertson–Walker (FRW) universe with any spatial curvature in mimetic gravity. Then, we disclose that one can always rewrite the Friedmann equations of mimetic cosmology in the form of the first law of thermodynamics, $d{E}_{\mathrm{\text{eff}}}=T_{h}d{S}_h+WdV$, on the apparent horizon. We confirm that the entropy associated with the apparent horizon in mimetic cosmology still obeys the area law of entropy which is useful in studying the thermodynamical properties of the black holes in mimetic gravity. We also examine the time evolution of the total entropy in mimetic cosmology and show that, with the local equilibrium assumption, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. Our study further supports the viability of the mimetic gravity from a thermodynamic viewpoint and provides a strong consistency check of this model.

We show that the recipe for computing the expansions ${𝜃}_{\ell }$ and ${𝜃}_n$ of outgoing and ingoing null geodesics normal to a surface admits a covariance group with nonconstant scalar $\kappa (x)$, corresponding to the mapping ${𝜃}_{\ell }\to \kappa {𝜃}_{\ell }$, ${𝜃}_n\to {\kappa }^{-1}{𝜃}_n$. Under this mapping, the product ${𝜃}_{\ell }{𝜃}_n$ is invariant, and thus the marginal surface computed from the vanishing of ${𝜃}_{\ell }$, which is used to define the apparent horizon, is invariant. This covariance group naturally appears in comparing the expansions computed with different choices of coordinate system.