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 Kruskal-Szekeres coordinate vacuum modified gravity model f ( R ) The generalization field equation was obtained generalizing Hilbert-Einstein’s action with gravitational Lagrangian terms (r) function. By consider a special class f(R theory taking = 0 , found solution static spherically symmetric spacetime that known as de Sitter-Schwarzschild spacetime. transformation rules were constructed from coordinates to For λ ≈ 0, Schwarzschild metric for on reduced standard relativity. We also show structure coordinate. This work could open promising way understand some features black hole gravity.