The Existence of Gradient Yamabe Solitons on Spacetimes

Abstract

The main aim of the present article is to study generalized quasi-Yamabe gradient solitons on warped product manifolds. First, we obtain some necessary and sufficient conditions for the existence of generalized quasi-Yamabe gradient solitons equipped on a warped product structure. Then we study some important applications in the Lorentzian and the neutral settings for the particular class, called as gradient Yamabe soliton. More explicitly, we prove the existence of the non-trivial gradient Yamabe soliton on generalized Robertson-Walker spacetimes, standard static spacetimes, Walker manifolds and pp-wave spacetimes.

Characterizations of -flat curvature tensor on spacetimes and f(r,T) -gravity

“…A -flat GRW spacetime is of Petrov type I, D or O. 6. -flat spacetimes obeying f r,  ( )-gravity and r f , m  ( )-gravity…”

“…A spacetime is a Lorentzian manifold M n  n 4 ( ) which admits a globally timelike vector field. Different types of spacetimes have been studied in various ways, such as [1][2][3][4][5][6][7] and many others.…”

Existence of Ricci soliton vector fields on Vaidya spacetime

“…Different aspects of the Vaidya spacetime have been extensively studied by many geometers (see for instance [18][19][20][21][22][23]). Moreover, many authors [7,[24][25][26][27][28]30] investigate solitons on different spacetimes which became one of the most active research areas during the recent years.…”