Abstract

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.

Details

Title
Embedding with Vaidya geometry
Author
Nikolaev, A V 1   VIAFID ORCID Logo  ; Maharaj, S D 2   VIAFID ORCID Logo 

1  University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban, South Africa (GRID:grid.16463.36) (ISNI:0000 0001 0723 4123); Ulyanovsk State Pedagogical University named after I.N. Ulyanov, Ulyanovsk, Russia (GRID:grid.446270.3) 
2  University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban, South Africa (GRID:grid.16463.36) (ISNI:0000 0001 0723 4123) 
Publication year
2020
Publication date
Jul 2020
Publisher
Springer Nature B.V.
ISSN
14346044
e-ISSN
14346052
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1140/epjc/s10052-020-8231-0
ProQuest document ID
2425435688
Copyright
© The Author(s) 2020. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.