On a class of gradient almost ricci solitons

Abstract

In this study, we provide some classifications for half-conformally flat gradient f - almost Ricci solitons, denoted by (M, g, f ), in both Lorentzian and neutral signature. First, we prove that if ||∇ f || is a non-zero constant, then (M, g, f )is locally isometric to a warped product of the form I ×ϕ N, where I ⊂ R and N is of constant sectional curvature. On the other hand, if ||∇ f || = 0, then it is locally a Walker manifold. Then, we construct an example of 4-dimensional steady gradient f -almost Ricci solitons in neutral signature. At the end, we give more physical applications of gradient Ricci solitons endowed with the standard static spacetime metric.