Asymptotically flat black hole solution in modified gravity

Abstract

From time to time, different observations suggest that Einstein's theory of general relativity (GR) may not be the ultimate theory of gravity. Various researchers have suggested that the $f(R)$ theory of gravity is the best alternative to replace GR. Using $f(R)$ gravity, one can elucidate the various unexplained physics of compact objects, such as black holes, neutron stars, and white dwarfs. Researchers have already put effort into finding the vacuum solution around a black hole in $f(R)$ gravity. However, for a long time, they could not find an asymptotically flat vacuum solution. In this article, we show that the asymptotically flat vacuum solution of $f(R)$ gravity is possible and thereby use it to explain the spherical accretion flow around the black hole.