This article investigates on 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 details inside the comoving plane. Indications of the existence of wormhole 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 the distinctive indication of the quantum tunneling phenomenon around the central singularity.
In this paper, we study the gravitational collapse in the {\bf k-}essence emergent gravity using a generalized Vaidya-type metric as a background. We also analyze the cosmic censorship hypothesis for this system. We show that the emergent gravity metric resembles closely to the new type of the generalized Vaidya metrics for null fluid collapse with the {\bf k-}essence emergent mass function, where we consider the {\bf k-}essence scalar field being a function solely of the advanced or the retarded time. This new type of {\bf k-}essence emergent Vaidya metric has satisfied the required energy co…
In this paper, we study the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric resembles closely to the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is…
We establish a formal connection between the {\bf K}-essence emergent gravity scenario and generalizations of Vaidya spacetime. Choosing the {\bf K}-essence action to be of the Dirac-Born-Infeld variety, the physical spacetime to be a general static spherically symmetric black hole and restricting the {\bf K}-essence scalar field to be a function solely of the advanced or the retarded time, we show that the emergent gravity metric resembles closely the generalized Vaidya metrics for null fluid collapse proposed by Husain. Imposing null energy conditions on the emergent energy-momentum tensor d…
Ringdown in Vaidya spacetimes: time-dependent frequencies, Penrose limit and time-domain analyses
Graduate School of Science, Nagoya University（名古屋大学理学研究科）；Kobayashi-Maskawa Institute for the Origin of Particles and the Universe (KMI)（小林-益川粒子宇宙起源研究所）；Department of Information, Artificial Intelligence and Data Science, Daiichi Institute of Technology（第一工业大学信息、人工智能与数据科学系）；Department of Physics, Rikkyo University（立教大学物理学系）
We discuss the near singularity region of the linear mass Vaidya metric for massless particles with non-zero angular momentum. In particular we look at massless geodesics with non-zero angular momentum 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 massless scalars from the singularity. Finally we make some comments on the possibility of using this metric as a semi-classical model for the end-point of black hole evaporation.
For a particular type of {\bf k-}essence scalar field, the {\bf k-}essence emergent gravity metric is exactly mapped on to the Barriola-Vilenkin (BV) type metric for Schwarzschild background established by Gangopadhyay and Manna. Based on the S. Chandrasekhar, we report the exciting features of the time-like geodesic structure in the presence of dark energy in an emergent gravity scenario for this Barriola-Vilenkin type metric. We trace the different kinds of trajectories for time-like geodesic in the presence of dark energy for the {\bf k-}essence emergent Barriola-Vilenkin spacetime, which i…
We study the gravitational collapse of a generalised Vaidya spacetime in the context of the Cosmic Censorship hypothesis. We develop a general mathematical framework to study the conditions on the mass function so that future directed non-spacelike geodesics can terminate at the singularity in the past. Thus our result generalises earlier works on gravitational collapse of the combinations of Type-I and Type-II matter fields. Our analysis shows transparently that there exist classes of generalised Vaidya mass functions for which the collapse terminates with a locally naked central singularity.…
A regular Vaidya-type line-element is proposed in this work. The mass function depends both on the temporal and the spatial coordinates. The curvature invariants and the source stress tensor $T^{a}_{~b}$ are finite in the whole space. The energy conditions for $T^{a}_{~b}$ are satisfied if $k^{2}<2vr$, where $k$ is a positive constant and $v,r$ are coordinates. It is found that the radial pressure has a maximum very close to $r = 2m~ (r>2m), v = 2m$. The energy crossing a sphere of constant radius is akin to Lundgren-Schmekel-York quasilocal energy. The Newtonian acceleration of the timelike g…
In this paper we consider the negative energy problem in generalized Vaidya spacetime. We consider several models when we have the naked singularity as a result of the gravitational collapse. In these models we investigate the geodesics for particles with negative energy when the II type of the matter field satisfies the equation of the state $P=αρ$ ($α\in [0\,, 1]$).
In this paper we derive exact analytical formulas for the evolution of the photon sphere and for the angular radius of the shadow in a special Vaidya spacetime. The Vaidya metric describes a spherically symmetric object that gains or loses mass, depending on a mass function $m(v)$ that can be freely chosen. Here we consider the case that $m(v)$ is a linearly increasing or decreasing function. The first case can serve as a simple model for an accreting black hole, the second case for a (Hawking) radiating black hole. With a linear mass function the Vaidya metric admits a conformal Killing vecto…
We examine the five-region holographic entropy cone inequalities for the special case of the AdS$_3$-Vaidya metric for a variety of boundary configurations. This is done by numerically solving the geodesic equation in the bulk for various boundary configurations. In all the cases we examine, we find that all the inequalities are satisfied when the bulk satisfies the null energy condition, while the inequalities are all violated when the bulk spacetime violates the null energy condition. A proof of the five-region holographic entropy cone inequalities for the dynamical bulk case remains an open…
The motive of this work is to study gravitational collapse in Vaidya space-time embedded in Galileon gravity theory. Galileon gravity is in fact an infrared modification of Einstein gravity, which was proposed as a generalization of the 4D effective theory in DGP brane model. 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…
We investigate the geometrical structure of Vaidya's spacetime in the case of a white hole with decreasing mass, stabilising to a black hole in finite or infinite time or evaporating completely. Our approach relies on a detailed analysis of the ordinary differential equation describing the incoming principal null geodesics, among which are the generators of the past horizon. We devote special attention to the case of a complete evaporation in infinite time and establish the existence of an asymptotic light-like singularity of the conformal curvature, touching both the past space-like singulari…
In the present work, we study the general surrounded Vaidya solution by the various cosmological fields and its nature describing the possibility of the formation of naked singularities or black holes. Motivated by the fact that real astrophysical black holes as non-stationary and non-isolated objects are living in non-empty backgrounds, we focus on the black hole subclasses of this general solution describing a dynamical evaporating-accreting black holes in the dynamical cosmological backgrounds of dust, radiation, quintessence, cosmological constant-like and phantom fields, the so called sur…
In this work, we have assumed the generalized Vaidya solution in Lovelock theory of gravity in $(n+2)$-dimensions. It has been shown that Gauss-Bonnet gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can be constructed by suitable choice of parameters. We have investigated the occurrence of singularities formed by the gravitational collapse in above three particular forms of Lovelock theory of gravity. The dependence of the nature of singularity on the existence of radial null geodesic for Vaidya space-time has been specially considered. In all the three models, we h…
Wilczek Quantum Center, Shanghai Institute for Advanced Studies（上海高等研究院）；University of Science and Technology of China（中国科学技术大学）；Herzen state Pedagogical University of Russia（俄罗斯赫尔岑国立师范大学）；Khazar University（阿塞拜疆卡扎尔大学）；SPB branch of SAO RAS（俄罗斯科学院天体物理研究所圣彼得堡分部）；Eastern Mediterranean University（东地中海大学）
Boltzmann Dynamics in K-essence Cosmology: Photon Propagation in an Emergent Spacetime
University of Calcutta（加尔各答大学）；Sister Nivedita University（西塔·尼维迪塔大学）；Inter-University Center for Astronomy and Astrophysics（跨大学天文与天体物理中心）；Prabhat Kumar College（普拉巴特·库马尔学院）；Institute of Astronomy, Space and Earth Science（天文、空间与地球科学研究院）
Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularized de…
We continue the programme of exploring the means of holographically decoding the geometry of spacetime inside a black hole using the gauge/gravity correspondence. To this end, we study the behaviour of certain extremal surfaces (focusing on those relevant for equal-time correlators and entanglement entropy in the dual CFT) in a dynamically evolving asymptotically AdS spacetime, specifically examining how deep such probes reach. To highlight the novel effects of putting the system far out of equilibrium and at finite volume, we consider spherically symmetric Vaidya-AdS, describing black hole fo…
Causal concept for the general black hole shadow is investigated, instead of the photon sphere. We define several `wandering null geodesics' as complete null geodesics accompanied by repetitive conjugate points, which would correspond to null geodesics on the photon sphere in Schwarzschild spacetime. We also define a `wandering set', that is, a set of totally wandering null geodesics as a counterpart of the photon sphere, and moreover, a truncated wandering null geodesic to symbolically discuss its formation. Then we examine the existence of a wandering null geodesic in general black hole spac…
In this paper, we consider the gravitational collapse of generalized Vaidya space-time when the matter satisfies the equation of the state either $P=0$ or $P=-αρ$, where $0 < α< 1$. We show that in the case when type I of matter field is dust, then the apparent horizon will never appear, but there is now a family of null radial future-directed geodesics which terminated at the central singularity in the past. Also, we show that in the case of negative pressure, the result of the gravitational collapse might be the naked singularity and the apparent horizon appears and in very short time disapp…
The method of non-Riemannian (metric-independent) spacetime volume-forms (alternative generally-covariant integration measure densities) is applied to construct a modified model of gravity coupled to a single scalar field providing an explicit unification of dark energy (as a dynamically generated cosmological constant) and dust fluid dark matter flowing along geodesics as an exact sum of two separate terms in the scalar field energy-momentum tensor. The fundamental reason for the dark species unification is the presence of a non-Riemannian volume-form in the scalar field action which both tri…
Spherically symmetric spacetimes are ambient spaces for models of stellar collapse and inhomogeneous cosmology. We obtain results for the Weyl tensor and the covariant form of the Ricci tensor on general doubly warped (DW) spacetimes. In a spherically symmetric metric, the Ricci and electric tensors become rank-2, built with a velocity vector field and its acceleration. Their structure dictates the general form of the energy-momentum tensor in the Einstein equations in DW spherical metrics. The anisotropic pressure and the heat current of an imperfect fluid descend from the gradient of the acc…
Analytical approach for calculating shadow of dynamical black hole
Herzen state Pedagogical University of Russia（俄罗斯赫尔岑国立师范大学）；Center for Theoretical Physics, Khazar University（哈扎尔大学理论物理中心）；SPB branch of SAO RAS（俄罗斯科学院天体物理研究所圣彼得堡分部）；Physics Department, Eastern Mediterranean University（东地中海大学物理系）
In this note we explore a non-static spacetime in quantum regime in the background of $f(R)$ gravity. The time dependent Vaidya metric which represents the spacetime of a radiating body like star is studied in an energy dependent gravity's rainbow, which is a UV completion of General Relativity. In our quest we have used gravitational collapse as the main tool. The focus is to probe the nature of singularity (black hole or naked singularity) formed out of the collapsing procedure. This is achieved via a geodesic study. For our investigation we have considered two different models of $f(R)$ gra…
