Special standard static space–times

Abstract

Essentially, some conditions for the Riemannian factor and the warping function of a standard static space-time are obtained in order to guarantee that no nontrivial warping function on the Riemannian factor can make the standard static space-time Einstein.

Curvature in Special Base Conformal Warped Products

“…Analogously, in several articles the following problem has been studied (see [12,26,36,37,38,42,43,44,74,108] among others).…”

Curvature of multiply warped products

“…In Lorentzian geometry, it was first noticed that some well known solutions to Einstein's field equations can be expressed in terms of warped products in [12] and after that Lorentzian warped products have been used to obtain more solutions to Einstein's field equations (see [12,13,19,20,44,59,65]). Moreover, geometric properties such as geodesic structure or curvature of Lorentzian warped products have been studied by many authors because of their relativistic applications (see [2,3,4,5,10,11,14,17,22,23,28,30,32,33,34,36,37,45,50,55,56,63,67,68,69,70,71,74,75]). …”

“…Moreover, in [56], the conformal tensor on standard static space-times with perfect fluid is studied and it is shown that a standard static space-time with perfect fluid is conformally flat if and only if its fiber is Einstein and hence of constant curvature. In [28], this problem is considered for arbitrary standard static space-times, more explicitly, an essential investigation of conditions for the fiber and warping function for a standard static space-time (not necessarily with perfect fluid) is carried out so that there exists no nontrivial function on the fiber guaranteing that the standard static space-time is Einstein. Duggal studied the scalar curvature of 4-dimensional triple Lorentzian products of the form L × B × f F and obtained explicit solutions for the warping function f to have a constant scalar curvature for this class of products (see [30]).…”

On Quasi-Einstein Sequential Warped Product Manifolds

“…Generalized Robertson-Walker space-times and standard static space-times are two well known solutions to Einstein's field equations. The standard static space-times can be considered as a generalization of the Einstein static universe [12]. In addition, the Robertson-Walker models in general relativity describe a simply connected homogeneous isotropic expanding or contracting universe.…”