Timelike and Spacelike Matter Inheritance Vectors in Specific Forms of Energy-Momentum Tensor

TL;DR

This paper explores conditions under which specific energy-momentum tensors in string cosmology and perfect fluid spacetimes admit timelike and spacelike matter inheritance vectors, comparing these with conformal Killing vectors.

Contribution

It develops necessary and sufficient conditions for matter inheritance vectors in string cosmology and perfect fluid spacetimes, and compares these with conformal Killing vector conditions.

Findings

Conditions for matter inheritance vectors are derived for string cosmology and perfect fluid.

Comparison with conformal Killing vectors reveals additional constraints.

Results are discussed for special cases of the studied spacetimes.

Abstract

This paper is devoted to the investigation of the consequences of timelike and spacelike matter inheritance vectors in specific forms of energy-momentum tensor, i.e., for string cosmology (string cloud and string fluid) and perfect fluid. Necessary and sufficient conditions are developed for a spacetime with string cosmology and perfect fluid to admit a timelike matter inheritance vector, parallel to $u^a$ and spacelike matter inheritance vector, parallel to $x^a$. We compare the outcome with the conditions of conformal Killing vectors. This comparison provides us the conditions for the existence of matter inheritance vector when it is also a conformal Killing vector. Finally, we discuss these results for the existence of matter inheritance vector in the special cases of the above mentioned spacetimes.