Vaidya Spacetime Research Articles

Conformal symmetries in Vaidya geometry and collapse

In this paper, we perform a comprehensive analysis of conformal symmetries in the generalized Vaidya spacetime and establish several new results. First, a proper conformal Killing vector is shown to exist in the radial direction and interestingly the generalized Vaidya spacetimes with this symmetry are shown to be the subclass of those, which are embeddable in five-dimensional Euclidean space. The general form of the mass function that enables the proper and planar conformal symmetry in the [Formula: see text]–[Formula: see text] plane is also determined. This treatment also includes earlier results. We also consider the gravitational collapse of these spacetimes with proper planar conformal symmetry in the context of cosmic censorship conjecture. We obtain an interesting and novel result that censorship is always obeyed for these spacetimes, and no locally naked central singularity forms as the end state of the continual collapse.

Collapsing scenarios of K-essence generalized Vaidya spacetime under [formula omitted] gravity

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of f(R̄,T̄) gravity, specifically in K-essence theory. In this study, the Dirac–Born–Infeld type non-standard Lagrangian is used to calculate the emergent metric Ḡμν, which is not conformally equivalent to the conventional gravitational metric. We use the function f(R̄,T̄) to reflect the additive nature of the emergent Ricci scalar (R̄) and the trace of the emergent energy–momentum tensor (T̄). Our study demonstrates that certain choices of f(R̄,T̄) may result in the existence of a naked singularity caused by gravitational collapse. The alternative f(R̄,T̄) values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. In addition, when a certain amount of kinetic energy is present in the K-essence scalar field, mass is entirely converted into energy, indicating that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena.

The Hawking temperature of dynamical black holes via conformal transformations

In this second part of our two-series on extracting the Hawking temperature of dynamical black holes, we focus into spacetimes that are conformal transformations of static spacetimes. Our previous investigation builds upon the Unruh–Hawking analogy, which relates the spacetime of a uniformly accelerating observer to the near-horizon region of a black hole, to obtain the Hawking temperature. However, in this work, we explicitly compute the Bogoliubov coefficients associated with incoming and outgoing modes, which not only yields the temperature but also thermal spectrum of particles emitted by a black hole. For illustration, we take the simplest nontrivial example of the linear Vaidya spacetime, which is conformal to the static metric and using this property, we analytically solve the massless scalar field in its background. This allows the explicit computations of the Bogoliubov coefficients to study the particle production in this spacetime. We also derive an expression for the total mass of such dynamical spacetimes using the conformal Killing vector. We then perform differential variations of the mass formula to determine whether the laws of dynamical black hole mechanics correspond to the laws of thermodynamics.

Gravitational collapse of relativistic compact objects in higher dimension

In this work, we present an iterative method for gravitational collapse in higher dimensions. A framework is developed in a post-quasi-static regime with non-comoving coordinates. The internal five-dimensional system is smoothly matched with the corresponding outer Vaidya space-time over the boundary surface (BS). This correspondence provides a set of dimensionless surface equations in higher dimensions. The physical quantities such as Doppler shift, luminosity, and redshift at the BS of gravitating systems can be described through these surface equations. This procedure offers valuable insights that facilitate comprehension of the behavior of compact objects.

A generalization of photon sphere based on escape/capture cone

In general asymptotically flat spacetimes, bearing the null geodesics reaching the future null infinity in mind, we propose new concepts, the “dark horizons” (outer dark horizon and inner dark horizon) as generalizations of the photon sphere. They are defined in terms of the structure of escape/capture cones of photons with respect to a unit timelike vector field to capture the motion of light sources. More specifically, considering a two-sphere that represents a set of emission directions of photons, the dark horizons are located at positions where a hemisphere is marginally included in the capture and escape cones, respectively. In addition, our definition succeeds in incorporating relativistic beaming effect. We show that the dark horizon is absent in the Minkowski spacetime, while they exist in spacetimes with black hole(s) under a certain condition. We derive the general properties of the dark horizons in spherically symmetric spacetimes and explicitly calculate the locations of the dark horizons in the Vaidya spacetime and the Kerr spacetime. In particular, in the Kerr spacetime, the outer dark horizon coincides with the shadow observed from infinity on the rotation axis.

Dynamical photon spheres in charged black holes and naked singularities

To understand the nature of a black hole shadow in dynamical spacetimes, we construct an analytical model of a dynamical photon sphere in the context of the Bonnor–Vaidya spacetime. Comparing the resulting photon sphere radius with the one in Vaidya spacetime, we find that the charge always decreases the radius of the photon sphere. We also prove that a naked singularity in Bonnor–Vaidya spacetime, unlike the static Reissner–Nordstrom naked singularity, may cast a shadow, and as a result, it cannot be distinguished from a black hole through its shadow.

Symmetry and pseudosymmetry properties of Vaidya-Bonner-de Sitter spacetime

The primary focus of the current study is to explore the geometrical properties of the Vaidya-Bonner-de Sitter (briefly, VBdS) spacetime, which is a generalization of Vaidya-Bonner spacetime, Vaidya spacetime and Schwarzschild spacetime. In this study we have shown that the VBdS spacetime describes various types of pseudosymmetric structures, including pseudosymmetry due to conformal curvature, conharmonic curvature and other curvatures. Additionally, it is shown that such a spacetime is 2-quasi-Einstein, Einstein manifold of level 3, generalized Roter type, and that conformal 2-forms are recurrent. The geometric features of the Vaidya-Bonner spacetime, Vaidya spacetime, and Schwarzschild spacetime are obtained as a particular instance of the main determination. It is further established that the VBdS spacetime admits almost Ricci soliton and almost η-Yamabe soliton with respect to non-Killing vector fields. Also, it is proved that such a spacetime possesses generalized conharmonic curvature inheritance. It is interesting to note that in the VBdS spacetime the tensors Q(T,R), Q(S,R) and Q(g,R) are linearly dependent. Finally, this spacetime is compared with the Vaidya-Bonner spacetime with respect to their admitting geometric structures, viz., various kinds of symmetry and pseudosymmetry properties.

The generalized Vaidya spacetime with polytropic equation of state

The generalized Vaidya spacetime with polytropic equation of state

Thermodynamics with conformal Killing vector in the charged Vaidya metric

We investigate the charged Vaidya spacetime with conformal symmetry by classifying the horizons and finding its connection to Hawking temperature. We find a conformal Killing vector whose existence requires the mass and electric charge functions to be proportional, as well as linear in time. Solving the Killing equations for the conformally transformed metric from the linear charged Vaidya metric yields the required form of the conformal factor. From the vanishing of the norm of the conformal Killing vector, we find three conformal Killing horizons which, under the transformation, are mapped to the Killing horizons of the associated static spacetime, if the spherical symmetry is maintained. We find that the conformal factor is not uniquely determined, but can take any function of the ratio of the radial coordinate to the dynamical mass. As an example, we illustrate a static spacetime with our choice of the conformal factor and explicitly show that the surface gravity of the conformal Killing horizons, which is conformally invariant, yield the expected Hawking temperature in the static spacetime. This static black hole spacetime contains a cosmological horizon, but it is not asymptotically de Sitter. We also investigate the case when the mass parameter is equal to the constant electric charge. While in this case the standard pair of horizons, the loci of the time component of the metric, degenerate, the conformal Killing horizons do not degenerate. This therefore leads to a non-zero Hawking temperature in the associated static spacetime.

Geodesic Structure of Generalized Vaidya Spacetime through the K-Essence

This article investigates the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac–Born–Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great detail inside the comoving plane. Indications of the existence of wormholes can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein–Rosen bridge. In addition, we have also detected a distinctive indication of the quantum tunneling phenomenon around the singularity (r→0). Furthermore, we have found that for certain types of solutions, there exist circular orbits through the event horizon as well as quasicircular orbits. Also, we have noted that there is no central singularity in our spacetime where both r and t tend towards zero. The existence of a central singularity is essential for any generalized Vaidya spacetime. This indicates that spacetime can be geodesically complete, which correlates with the findings of Kerr’s recent work (2023).

Feasibility of singularity avoidance for a collapsing object due to a scalar field

We study the problem of the gravitational collapse of an object as seen by an external observer. We assume that the resultant spacetime is a match of an external Vaidya spacetime with an interior Friedmann-Lemaître-Robertson-Walker (FRLW) spacetime of any spatial curvature and with a scalar field both minimally and non-minimally coupled to the metric. With the goal of studying a contracting (collapsing) object, for the initial moment of observation we take that its energy density and pressure are positive, that there are no trapping surfaces, and that the null energy condition (NEC) and the strong energy condition (SEC) are fulfilled. We show that there are many cases where singularities could be avoided for both the minimal and non-minimal couplings, although the contexts for so are very different in both cases. For the minimal coupling, the avoidance of singularities could happen either through evaporation or altogether, triggered by a violation of the SEC for a period of time. For the non-minimal coupling, the complete singularity avoidance happens only if evaporation takes place, and a temporary violation of the SEC does not thwart the formation of singularities. The above results show the relevance of the global (the whole spacetime) validity of energy conditions for the singularity theorems to be applicable; otherwise, the fate of a collapsing star is not known a priori. At the same time, the surface behavior of a collapsing body offers partial diagnostics of what happens in the inaccessible regions of spacetime to external observers. Our analyses suggest that a bounce behavior of the surface of the initially collapsing object is a fingerprint of the SEC violation in its interior, and that could be due to the existence of scalar fields there.

Existence of Ricci soliton vector fields on Vaidya spacetime

In this paper, we investigate the behaviour of the Vaidya spacetime admitting a Ricci soliton vector field, where we have found the expressions for the four components of the vector field, and we have shown, under this condition, that the spacetime reduces to the Schwarzschild spacetime. Moreover, we have found the desired expression for the potential function h to satisfy in order for a gradient Ricci soliton vector field to exist on the Vaidya spacetime.

Evaporation of a nonsingular Reissner–Nordström black hole and the information loss problem

Abstract One of the attractive solutions to the information loss problem is that the event horizon does not appear in the process of gravitational collapse and subsequent evaporation once the spacetime singularity is regularized by some mechanism, as pointed out by Hayward and Frolov. In this paper, we examine whether this Hayward–Frolov scenario holds for the evaporation of a charged black hole. The process of collapse and evaporation is modeled with the charged Vaidya spacetime and two kinds of regularization of the central singularity are considered. Analyzing the spacetime structure of the evaporating black hole, we find that the appropriately regularized evaporating Reissner–Nordström “black hole” has no event and Cauchy horizons, indicating the possibility that the Hayward–Frolov scenario may have sufficient generality as the solution to the information loss problem. In addition, the properties of the nonsingular evaporating Reissner–Nordström black hole are examined in detail.

Generalized Vaidya spacetime: Horizons, conformal symmetries, surface gravity and diagonalization

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.

Evaporation of Dynamical Horizon with the Hawking Temperature in the K‐essence Emergent Vaidya Spacetime

AbstractIn the K‐essence Vaidya Schwarzschild spacetime, the dynamical horizon equation to measure the mass‐loss due to Hawking radiation and the tunneling formalism (Hamilton‐Jacobi method) to calculate the hawking temperature is applied. Assuming the Dirac‐Born‐Infeld kind of non‐standard action for the K‐essence here, the background physical spacetime is a static spherically symmetric black hole, and the K‐essence scalar field to be a function only of either forward or backward time is constrained. The K‐essence emergent gravity and the generalizations of Vaidya spacetime have been linked by Manna et al. In this paper, Sawayama's modified description of the dynamical horizon to show that the obtained findings deviate from the standard Vaidya spacetime geometry are used.

Peeling-off behavior of wave equation in the Vaidya spacetime

We study the peeling for the wave equation on the Vaidya spacetime following the approach developed by Mason and Nicolas in Mason–Nicolas 2009. The idea is to encode the regularity at null infinity of the rescaled field, characterized by Sobolev-type norms, in terms of corresponding function spaces of initial data. All function spaces are obtained from energy fluxes associated with an observer constructed from the Morawetz vector field on Minkowski spacetime. We combine conformal techniques and energy estimates to obtain the optimal classes of initial data ensuring a given regularity of the rescaled field. The classes of data are equivalent to those obtained on Minkowski and Schwarzschild spacetimes in that they impose the same decay at infinity and regularity.

Extraction energy from charged Vaidya black hole via the Penrose process

In this paper, we consider the analogy of the Penrose process in charged Vaidya spacetime. We calculate the border of the generalized ergosphere, in which the charged particles with negative energy might exist, and show that it is temporary. We show that there are no closed orbits for particles with negative energy inside the generalized ergosphere. We investigate the question about the efficiency of the Penrose process and show that one cannot extract large energies from a black hole if the velocities of ingoing and outgoing particles are of the same order. In the case of the extremal black hole, we show that the upper limit is restricted by the absolute value of the electric charge per mass.

Geometry of conformally symmetric generalized Vaidya spacetimes

In this paper, we consider conformally symmetric generalized Vaidya spacetimes with a composite null dust and null string matter distribution using the semi-tetrad covariant [Formula: see text] decomposition method. The important and novel result that emerges from our analysis is that all the geometric variables related to the time-like and the preferred space-like congruences are completely determined by the conformal vector and conformal factor. This result is unique to the specific matter distribution of the generalized Vaidya configuration. We further show that in the case of the pure null dust (or Vaidya) spacetime, a proper conformal Killing vector cannot be admitted.

Vaidya and Generalized Vaidya Solutions by Gravitational Decoupling

In this paper, we apply the gravitational decoupling method for dynamical systems in order to obtain a new type of solution that can describe a hairy dynamical black hole. We consider three cases of decoupling. The first one is the simplest and most well known when the mass function is the function only of space coordinate r. The second case is a Vaidya spacetime case when the mass function depends on time v. Finally, the third case represents the generalization of these two cases: the mass function is the function of both r and v. We also calculate the apparent horizon and singularity locations for all three cases.

The structure of the generalized Vaidya space–time containing the eternal naked singularity

In this paper, the structure of the generalized Vaidya space–time when the type-II of the matter field satisfies the equation of the state [Formula: see text] is investigated. Satisfying all energy conditions, we show that this space–time contains the “eternal” naked singularity. It means that once the singularity is formed it will never be covered with the apparent horizon. However. in the case of the apparent horizon formation the resulting object is a white hole. We also prove that this space–time contains only null naked singularity.