A new way to study on generalized Friedmann–Robertson–Walker spacetime

Abstract

In this paper, we study the generalized Friedmann–Robertson–Walker spacetime in a new way. We know that the generalized Friedmann-Robertson-Walker metric and solutions of the Einstein field equations can be expressed in terms of Lorentzian warped products. We consider a multiply warped product metric of the generalized Friedmann-Robertson-Walker spacetime of type M¯=B×h1F1×h2F2 with the warping functions h1, h2 associated to the submanifolds F1, F2 with dimensions n1, n2, respectively and the submanifold F1 is conformal to (Rn1,g), a pseudo-Euclidean space. Then we show that the Einstein equations G¯AB=-κ¯g¯AB on (M¯ , g¯) with a cosmological constant κ¯ is reduced to the Einstein equations Gij=-κ2g2ij on the submanifold (F2, g2) with the cosmological constant κ2. Furthermore, we consider some black hole solutions as typical examples. Then we derive the corresponding Einstein equations and the reduced Einstein equations for each black hole solution. © 2022, Indian Association for the Cultivation of Science.