Kruskal-Szekeres coordinates of spherically symmetric solutions in theories of gravity

Abstract

Understanding the missing matter problem in cosmological phenomena and scales of astrophysical is usually studied by modifying general relativity theory. In this article, we formulated the Kruskal-Szekeres coordinate of vacuum modified gravity model in f (R ) theory. The generalization of the field equation was obtained by generalizing Hilbert-Einstein’s action with gravitational Lagrangian in terms of f (r)function. By consider a special class of f(R) theory by taking R = R0 , we found the solution of static spherically symmetric spacetime that was known as de Sitter-Schwarzschild spacetime. The transformation rules were constructed from Kruskal-Szekeres coordinates in f (r)theory of modified general relativity to the Kruskal-Szekeres coordinate in general relativity theory. For λ ≈ 0, the Schwarzschild and Kruskal-Szekeres metric for static spherically symmetric on f (r)theory reduced to the standard Schwarzschild and Kruskal-Szekeres metric on general relativity. We also show the spacetime structure of de Sitter-Schwarzschild and Kruskal-Szekeres coordinate. This work could open a promising way to understand some features of a black hole in the f (r)theory of gravity.