Conformal symmetries in generalised Vaidya spacetimes

Abstract

In this paper we excavate, for the first time, the most general class of conformal Killing vectors, that lies in the two dimensional subspace described by the null and radial co-ordinates, that are admitted by the generalised Vaidya geometry. Subsequently we find the most general class of generalised Vaidya mass functions that give rise to such conformal symmetry. From our analysis it is clear that why some well known subclasses of generalised Vaidya geometry, like pure Vaidya or charged Vaidya solutions, admit only homothetic Killing vectors but no proper conformal Killing vectors with non constant conformal factors. We also study the gravitational collapse of generalised Vaidya spacetimes that posses proper conformal symmetry to show that if the central singularity is naked then in the vicinity of the central singularity the spacetime becomes almost self similar. This study definitely sheds new light on the geometrical properties of generalised Vaidya spacetimes.

Physics Nobel 2020 and Kolkata Connections

“…One does not find any solution set for Ṫ and Ṙ admitting this infalling condition while solving Eqs. (31) and (32). However, there is no physical reason behind the non-existence of an infalling timelike geodesic in this spacetime as we know Vaidya spacetime can describe the infall of massive particles.…”

“…where m 4 (u, r) is the Misner-Sharp mass function in 4-dimensions [31,32]. This tells about the amount of energy inside radial distance r at retarded time u and dΩ 2 2 is the metric on a 2-dimensional unit sphere.…”

“…al. stated in [32] that there exists a homothetic Killing vector field, for which the spacetime is self-similar and the mass function for the same is as follows.…”

On particle collisions during gravitational collapse of Vaidya spacetimes

“…The Vaidya spacetime (1) is time-depended and because of it one has only one conserved quantitythe angular momentum L. In the general case, the Vaidya spacetime doesn't possess any additional symmetry. However, for the particular choice of the mass function, the metric (1) admits the conformal Killing vector (Ojako et al 2020). In this case, M must have the following form (Nielsen 2014):…”

Generalized compact star models with conformal symmetry

“…A number of approaches have been used by researchers in searching for exact solutions to the Einstein-Maxwell field equations. a e-mail: japecjonas@gmail.com b e-mail: maharaj@ukzn.ac.za (corresponding author) c e-mail: jefta@aims.ac.za d e-mail: jmkenyeleye@gmail.com Some of these approaches include finding an equation of state that relates the pressure and the matter density as indicated in Sunzu et al [2,3], Brassel et al [4], Nillson and Uggla [5,6], Varela et al [7], and Mafa Takisa and Maharaj [8], choosing one form of the gravitational potential on physical grounds that can predict the behaviour of the other metric function and the matter variables as adopted in Thirukkanesh et al [9], Komathiraj et al [10], Hansraj [11], and Mafa Takisa et al [12], utilizing embedding of dimensions on the spacetime manifold as adopted in Singh et al [13], Maurya and Maharaj [14], and Maurya and Govender [15], utilizing the group theoretic approach discussed in Abebe et al [16,17], Govinder and Govender [18], Mohanlal et al [19,20], and the existence of symmetries on the spacetime manifold as adopted in Rahaman et al [21,22], Singh et al [23], Ojako et al [24], Hansraj et al [25], Esculpi and Aloma [26], Maurya et al [27], Kileba Matondo et al [28], and Manjonjo et al [29].…”