Application of T − curvature Tensor in Spacetimes

Abstract

In this paper we show that T -flat spacetime is Einstein with constant curvature and the energy momentum tensor of this spacetime satisfying the Einstein’s field equation with the cosmological constant is covariant constant. Then we find the length of the Ricci operator and derive some geometric properties for a T -flat general relativistic viscous fluid spacetime. We also see that for a purely electromagnetic distribution the scalar curvature of a T -flat spacetime satisfying the Einstein’s field equation without cosmological constant vanishes. Lastly we study the general relativistic viscous fluid spacetime with the divergence-free T -curvature tensor with respect to some conditions and the possible local cosmological structure is of Petrov type I, D or O.

Key words and phrases. T -curvature tensor, killing vector field, general relativistic spacetime.

2020 Mathematics Subject Classification. 53C50; 53C15; 53C25