Vaidya Metric Research Articles

On maximal analytical extension of the Vaidya metric

The classical Vaidya metric is transformed to the special diagonal coordinates in the case of the linear mass function allowing rather easy treatment. We find the exact analytical expressions for metric functions in these diagonal coordinates. Using these coordinates, we elaborate the maximum analytic extension of the Vaidya metric with a linear growth of the black hole mass and construct the corresponding Carter–Penrose diagrams for different specific cases. The derived global geometry is also seemingly valid for a more general behavior of the black hole mass in the Vaidya metric.

Curvature properties of some class of warped product manifolds

We prove that warped product manifolds with [Formula: see text]-dimensional base, [Formula: see text] satisfy some pseudosymmetry type curvature conditions. These conditions are formed from the metric tensor [Formula: see text], the Riemann–Christoffel curvature tensor [Formula: see text], the Ricci tensor [Formula: see text] and the Weyl conformal curvature [Formula: see text] of the considered manifolds. The main result of the paper states that if [Formula: see text] and the fiber is a semi-Riemannian space of constant curvature (when [Formula: see text] is greater or equal to 5) then the [Formula: see text]-tensors [Formula: see text] and [Formula: see text] of such warped products are proportional to the [Formula: see text]-tensor [Formula: see text] and the tensor [Formula: see text] is a linear combination of some Kulkarni–Nomizu products formed from the tensors [Formula: see text] and [Formula: see text]. We also obtain curvature properties of this kind of quasi-Einstein and 2-quasi-Einstein manifolds, and in particular, of the Goedel metric, generalized spherically symmetric metrics and generalized Vaidya metrics.

Holographic thermalization of charged operators

We study a light-like charged collapsing shell in AdS-Reissner-Nordstrom spacetime, investigating whether the corresponding Vaidya metric is supported by matter that satisfies the null energy condition. We find that, if the absolute value of the charge decreases during the collapse, energy conditions are fulfilled everywhere in spacetime. On the other hand, if the absolute value of the charge increases, the metric does not satisfy energy conditions in the IR region. Therefore, from the gauge/gravity perspective, this last case is only useful to study the thermalization of the UV degrees of freedom. For all these geometries, we probe the thermalization process with two point correlators of charged operators, finding that the thermalization time grows with the charge of the operator, as well as with the dimension of space.

Linear mass Vaidya metric at the end of black hole evaporation

We discuss the near singularity region of the linear mass Vaidya metric for massless particles with nonzero angular momentum. In particular we look at massless geodesics near the vanishing point of a special subclass of linear mass Vaidya metrics. We also investigate this same structure in the numerical solutions for the scattering of the Maxwell field from the singularity. In both cases we find that the null-singularity effectively becomes repulsive close to the final vanishing point leading us to argue that this metric could be plausibly used as a semiclassical model for the endpoint of black hole evaporation.

Gravitational collapse in Husain space-time for Brans-Dicke gravity theory with power-law potential

The motive of this work is to study gravitational collapse in Husain space-time in Brans-Dicke gravity theory. Among many scalar-tensor theories of gravity, Brans-Dicke is the simplest and the impact of it can be regulated by two parameters associated with it, namely, the Brans-Dicke parameter, $\omega$, and the potential-scalar field dependency parameter $n$ respectively. V. Husain's work on exact solution for null fluid collapse in 1996 has influenced many authors to follow his way to find the end-state of the homogeneous/in-homogeneous dust cloud. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases(through tabular forms) and wide range contouring process have been applied. Precisely, perfect fluid's EoS satisfies a wide range of phenomena : from dust to exotic fluid like dark energy. We have used the EoS parameter $k$ to determine the end state of collapse in different cosmological era. Our main target is to check low $\omega$ (more deviations from Einstein gravity-more Brans Dicke effect) and negative $k$ zones. This particularly throws light on the nature of the end-state of collapse in accelerated expansion in Brans Dicke gravity. It is seen that for positive values of EoS parameter $k$, the collapse results in a black hole, whereas for negative values of $k$, naked singularity is the only outcome. It is also to be noted that "low $\omega$" leads to the possibility of getting more naked singularities even for a non-accelerating universe.

Double-null formulation of the general Vaidya metric

We present here the field equations describing a non-stationary spherically symmetric n-dimensional charged black hole with a varying mass m(v) and/or electric charge q(v), described by a generic charged Vaidya metric with a cosmological constant Λ in double-null coordinates. This formulation of the metric has been shown to be particularly useful for perturbative studies and it was used in some recent works. Here, we also discuss some issues related to the apparent and event horizons of the black hole.

Quasinormal modes for the charged Vaidya metric

The scalar wave equation is considered in the background of a charged Vaidya metric in double null coordinates (u,v) describing a non-stationary charged black hole with varying mass m(v) and charge q(v). The resulting time-dependent quasinormal modes are presented and analyzed. We show, in particular, that it is possible to identify some signatures in the quasinormal frequencies from the creation of a naked singularity.

Nonstationary regime for quasinormal modes of the charged Vaidya metric

We consider nonstationary spherically symmetric $n$-dimensional charged black holes with varying mass $m(v)$ and/or electric charge $q(v)$, described by generic charged Vaidya metrics with cosmological constant $\ensuremath{\Lambda}$ in double-null coordinates and perform a comprehensive numerical analysis of the fundamental quasinormal modes (QNM) for minimally coupled scalar fields. We show that the instantaneous quasinormal frequencies exhibit the same sort of nonstationary behavior reported previously for the four-dimensional uncharged case with $\ensuremath{\Lambda}=0$. Such property seems to be very robust, independent of the spacetime dimension and of the metric parameters, provided they be consistent with the existence of an event horizon. The study of time-dependent Reissner-Nordstr\"om black holes allows us to go a step further and quantify the deviation of the stationary regime for QNM with respect to charge variations as well. We also look for signatures in the quasinormal frequencies from the creation of a Reissner-Nordstr\"om naked spacetime singularity. Even though one should expect the breakdown of our approach in the presence of naked singularities, we show that it is possible, in principle, to obtain some information about the naked singularity from the QNM frequencies, in agreement with the previous results of Ishibashi and Hosoya showing that it would be indeed possible to have regular scattering from naked singularities.

Invariance analysis and conservation laws of the wave equation on Vaidya manifolds

In this paper we discuss symmetries of classes of wave equations that arise as a consequence of some Vaidya metrics. We show how the wave equation is altered by the underlying geometry. In particular, a range of consequences on the form of the wave equation, the symmetries and number of conservation laws, inter alia, are altered by the manifold on which the model wave rests. We find Lie and Noether point symmetries of the corresponding wave equations and give some reductions. Some interesting physical conclusions relating to conservation laws such as energy, linear and angular momenta are also determined. We also present some interesting comparisons with the standard wave equations on a flat geometry. Finally, we pursue the existence of higher-order variational symmetries of equations on nonflat manifolds.

CHARGED BLACK HOLES IN VAIDYA BACKGROUNDS: HAWKING'S RADIATION

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.

Model for nonsingular black hole collapse and evaporation

We study the formation of a black hole and its subsequent evaporation in a model employing a minisuperspace approach to loop quantum gravity. In previous work the static solution was obtained and shown to be singularity-free. Here, we examine the more realistic dynamical case by generalizing the static case with help of the Vaidya metric. We track the formation and evolution of trapped surfaces during collapse and evaporation and examine the buildup of quantum gravitationally caused stress-energy preventing the formation of a singularity.

Relativistic model of radiating massive fluid sphere

In this paper we present a new class of nonsingular solutions representing time dependent balls of perfect fluid with matter-radiation in general relativity. The solution of the class is suitable for interior modeling of a quasar i.e. a massive radiating star. The interior solution is matched with a zero pressure Vaidya metric. From this solution we constructed a quasar model by assuming the life time of the quasar of ≈107 year. We obtained a mass of the quasar of ≈109 M θ , linear dimension ≈1017 km and a rate of emission L ∞≈1047 erg/s.

ON TIME-DEPENDENT BLACK HOLES AND COSMOLOGICAL MODELS FROM A KALUZA–KLEIN MECHANISM

Novel static, time-dependent and spatial–temporal solutions to Einstein field equations, displaying singularities, with and without horizons, and in several dimensions, are found based on a dimensional reduction procedure widely used in Kaluza–Klein-type theories. The Kerr–Newman black hole entropy as well as the Reissner–Nordstrom, Kerr and Schwarzschild black hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a black hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya's metric (associated with the Hawking radiation of black holes) by interchanging t ↔ r, which might render our universe a dynamical black hole.

Perturbation method for classical spinning particle motion. II. Vaidya space-time

This paper describes an application of the Mathisson-Papapetrou-Dixon (MPD) equations in analytic perturbation form to the case of circular motion around a radially accreting or radiating black hole described by the Vaidya metric. Based on the formalism presented earlier, this paper explores the effects of mass accretion or loss of the central body on the overall dynamics of the orbiting spinning particle. This includes changes to its squared mass and spin magnitude due to the classical analog of radiative corrections from spin-curvature coupling. Various quantitative consequences are explored when considering orbital motion near the black hole's event horizon. An analysis on the orbital stability properties due to spin-curvature interactions is examined briefly, with conclusions in general agreement with previous work performed for the case of circular motion around a Kerr black hole.

Thermodynamics and evaporation of the noncommutative black hole

We investigate the thermodynamics of the noncommutative black hole whose static picture is similar to that of the nonsingular black hole known as the de Sitter-Schwarzschild black hole. It turns out that the final remnant of extremal black hole is a thermodynamically stable object. We describe the evaporation process of this black hole by using the noncommutativity-corrected Vaidya metric. It is found that there exists a close relationship between thermodynamic approach and evaporation process.

A linear approximation to black hole evaporation

An evaporating Schwarzschild black hole is analysed including back reaction in a linear approximation. The analysis assumes a massless scalar field propagating in a spacetime consisting of two Vaidya metrics corresponding respectively to outgoing radiation and an infalling negative energy flux. For times late relative to the collapse but early relative to the lifetime of the hole, the standard rate is reproduced and has the correct time dependence. The event horizon shrinks at the expected rate. These results are independent of the exact location of the boundary between the regions. The magnitude of the quantum fluxes at various radii suggests that most of the pair production occurs far from the horizon.

Charged sphere of shear-free fluids with $$\frac{\partial}{\rho} \partial r \leq 0$$

The Einstein-Maxwell equations for non-static charged shear-free spherically symmetric perfect fluid distribution reduce to a second-order non-linear differential equation in the radial parameter. Several solutions of this equation have been obtained in earlier work without considering the general requirement for physical relevance of the solutions. Generally physically acceptable relativistic fluid models demand that the solutions satisfy the reality conditions ρ ≥ 0, p ≥ 0, ρr ≤ 0, etc. throughout the fluid model. In this article the expression for density gradient ρ x (or ρr) has been utilized to produce charged shear-free relativistic fluid models with non-positive density gradient (NDG)ρr ≤ 0. Eventually, we have found that none of the Riccati solutions have NDG including Vaidya metric. Also, the solutions with NDG neither possess Lie-symmetries nor Painleve property. Further, it is observed that the solutions with NDG have no uncharged analogue.

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy-momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space-time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt-Deser-Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space-time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.

On gravitational radiation and the energy flux of matter

AbstractA suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.

GRAVITATIONAL COLLAPSE OF SPHERICAL STRING FLUIDS

We discuss the spherical collapse of a two fluid system: a string fluid and a null fluid described by a generalized Vaidya metric. This led us to explicitly describe the effect of a string fluid on the established picture of a null fluid collapse (Vaidya collapse). It is found that there is a shrinkage of the initial data space for naked singularities of Vaidya collapse upon taking into account a string fluid. The implications of the results in the context of the cosmic censorship conjecture are discussed.