Hans Stephani 1982 Cambridge: Cambridge University Press xvi + 298 pp price £25 This textbook provides a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students. It covers Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/033/pdf

General Relativity: An Introduction to the Theory of the Gravitational Field

In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field $$\xi $$
 are described and Ricci soliton in perfect fluid spacetime with torse-forming vector field $$\xi $$
 are determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given.

Ricci soliton and geometrical structure in a perfect fluid spacetime with torse-forming vector field

In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal η-Ricci soliton with torse-forming vector field ξ. Condition for the...

Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime

Relativistic magneto-fluid spacetimes

In this paper we consider conformally ﬂat (QE)4 spacetime and obtained several important results. We study application of conformally ﬂat (QE)4 spacetime in general relativity and Ricci soliton structure in a conformally ﬂat (QE)4 perfect ﬂuid spacetime.

/pdf/a-study-of-conformally-flat-quasi-einstein-spacetimes-with-4nuun166op.pdf

A Study of Conformally Flat Quasi-Einstein Spacetimes with Applications in General Relativity

The object of the present paper is to introduce spacetimes with pseudosymmetricenergy-momentum tensor. In this paper at first we consider the relation $R(X,Y)\cdot T=fQ(g,T)$, that is, the energy-momentumtensor $T$ of type (0,2) is pseudosymmetric. It is shown that in a general relativistic spacetimeif the energy-momentum tensor is pseudosymmetric, then the spacetime is also Ricci pseudosymmetricand the converse is also true. Next we characterize the perfect fluid spacetimewith pseudosymmetric energy-momentum tensor. Finally, we consider conformally flat spacetime withpseudosymmetric energy-momentum tensor.

/pdf/spacetimes-with-pseudosymmetric-energy-momentum-tensor-1blcohmlwc.pdf

Sahanous Mallick

Papers

Spacetimes with Pseudosymmetric Energy-momentum Tensor