https://doi.org/10.1140/epjc/s10052-020-8231-0
Regular Article - Theoretical Physics
Embedding with Vaidya geometry
1
Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa
2
Ulyanovsk State Pedagogical University named after I.N. Ulyanov, Ulyanovsk, Russia
* e-mail: maharaj@ukzn.ac.za
Received:
28
February
2020
Accepted:
11
July
2020
Published online:
20
July
2020
The Vaidya metric is important in describing the exterior spacetime of a radiating star and for describing astrophysical processes. In this paper we study embedding properties of the generalized Vaidya metric. We had obtained embedding conditions, for embedding into 5-dimensional Euclidean space, by two different methods and solved them in general. As a result we found the form of the mass function which generates a subclass of the generalized Vaidya metric. Our result is purely geometrical and may be applied to any theory of gravity. When we apply Einstein’s equations we find that the embedding generates an equation of state relating the null string density to the null string pressure. The energy conditions lead to particular metrics including the anti/de Sitter spacetimes.
© The Author(s), 2020
