Narrow Results

We consider a freely falling holographic screen for the Schwarzschild and Reissner–Nordström black holes and evaluate the entropic force à la Verlinde. When the screen crosses the event horizon, the temperature of the screen agrees to the Hawking temperature and the entropic force gives rise to the surface gravity for both of the black holes.

Recently, Harko et al. [Phys. Rev. D88, 044032 (2013)] have derived an exact solution of the spherically symmetric field equations in EiBI gravity, describing a compact star with decreasing pressure but increasing energy density. We have explored some features of this solution by restricting the range of the parameter $\kappa$ which satisfies four energy conditions for 10 equation of states (EOSs). Viability and deviations of these features in the light of updated observed properties of neutron stars (NS) have been explored completely. A comparison of those features with recent observations may uncover the future implication of this paper. Analysis of our results indicates that this solution may be used as an alternative EOS.

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.

Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the "surface gravity") is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose–Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a view to finding which experimental settings could magnify this effect and provide an observable signal. We discuss constraints and problems for our model and identify the issues that should be addressed in the near future in order to set up an experiment. In particular we identify an experimentally plausible configuration with a Hawking temperature of order 70 n K; to be contrasted with a condensation temperature of the order of 90 n K.

A nonvanishing value for the Rindler horizon energy is proposed, by an analogy with the "near horizon" Schwarzschild metric. We show that the Rindler horizon energy is given by the same formula E = α/2 obtained by Padmanabhan for the Schwarzschild space–time, where α is the gravitational radius.

In this paper we propose a class of embedded solutions of Einstein's field equations describing nonrotating Reissner–Nordstrom–Vaidya and rotating Kerr–Newman–Vaidya black holes. The Reissner–Nordstrom–Vaidya is obtained by embedding Reissner–Nordstrom solution into the nonrotating Vaidya. Similarly, we also find the Kerr–Newman–Vaidya black hole, when Kerr–Newman embeds into the rotating Vaidya solution. The Reissner–Nordstrom–Vaidya solution is type D whereas the Kerr–Newman–Vaidya metric is algebraically special of type II by the Petrov classification of space–time. These embedded solutions can be expressed in the Kerr–Schild ansatze on different backgrounds. The energy–momentum tensors for both nonrotating as well as rotating embedded solutions satisfy the energy conservation equations which show that they are solutions of Einstein's field equations. The surface gravity, area, temperature and entropy are also presented for each embedded black hole. It is observed that the area of the embedded black holes is greater than the sum of the areas of the individual ones. By considering the charge to be a function of radial coordinates it is shown that there is a change in the masses of the variably charged black holes. If such radiation continues, the mass of the black hole will evaporate completely thereby forming "instantaneous" charged black holes and creating embedded negative mass naked singularities describing the possible the life of radiation embedded black holes during their continuous radiation processes.

For distant observers, black holes are trapped spacetime domains bounded by apparent horizons. We review properties of the near-horizon geometry emphasizing the consequences of two common implicit assumptions of semiclassical physics. The first is a consequence of the cosmic censorship conjecture, namely, that curvature scalars are finite at apparent horizons. The second is that horizons form in finite asymptotic time (i.e. according to distant observers), a property implicitly assumed in conventional descriptions of black hole formation and evaporation. Taking these as the only requirements within the semiclassical framework, we find that in spherical symmetry only two classes of dynamic solutions are admissible, both describing evaporating black holes and expanding white holes. We review their properties and present the implications. The null energy condition is violated in the vicinity of the outer horizon and satisfied in the vicinity of the inner apparent/anti-trapping horizon. Apparent and anti-trapping horizons are timelike surfaces of intermediately singular behavior, which manifests itself in negative energy density firewalls. These and other properties are also present in axially symmetric solutions. Different generalizations of surface gravity to dynamic spacetimes are discordant and do not match the semiclassical results. We conclude by discussing signatures of these models and implications for the identification of observed ultra-compact objects.

Following the same treatment of Bellucci et al. we obtain, the hitherto unknown general solutions of the radial attractor flow equations for extremal black holes, both for non-BPS with non-vanishing and vanishing central charge Z for the so-called st² model, the minimal rank-two symmetric supergravity in d = 4 space-time dimensions.

We also make useful comparisons with results that already exist in literature, and introduce the fake supergravity (first-order) formalism to be used in our analysis. An analysis of the BPS bound all along the non-BPS attractor flows and of the marginal stability of corresponding D-brane charge configurations has also been presented.

The geodesics in various spherical Rindler frames are investigated. A display of some kinematical quantities of the spacetime is given. The constant acceleration from the metric acts as the surface gravity of the horizon $r=0$. The radial geodesics are computed both for the Balasubramanian et al. form of the spherical Rindler space and for the non-diagonal metric of Huang and Sun.

We derive and critically examine the consequences that follow from the formation of a regular black or white hole horizon in finite time of a distant observer. In spherical symmetry, only two distinct classes of solutions to the semiclassical Einstein equations are self-consistent. Both are required to describe the formation of physical black holes and violate the null energy condition in the vicinity of the outer apparent horizon. The near-horizon geometry differs considerably from that of classical solutions. If semiclassical physics is valid, accretion into a black hole is no longer possible after the horizon has formed. In addition, the two principal generalizations of surface gravity to dynamical spacetimes are irreconcilable, and neither can describe the emission of nearly-thermal radiation. Comparison of the required energy and timescales with established semiclassical results suggests that if the observed astrophysical black holes indeed have horizons, their formation is associated with new physics.