Stationary BTZ space-time in Ricci-inverse and f(R) gravity theories.

In this paper, we explore a stationary BTZ space-time within the framework of modified gravity theory, specifically focusing on Ricci-inverse gravity. It is important to clarify that "Ricci-inverse" refers to the inverse of the Ricci tensor, not the Ricci scalar. We consider a general class of this gravity theory, where the function f is defined by f (R , A , A μ ν A μ ν) , with R and A representing the Ricci and anti-curvature scalars, respectively and A μ ν is the anti-curvature tensor. We demonstrate that stationary BTZ space-time is a valid solution in this gravity theory, wherein the cosmological constant undergoes modifications due to the coupling constants. Moreover, we study another modified gravity theory known as f (R) -gravity and analyze the stationary BTZ space-time. Subsequently, we fully integrate the geodesic equations for BTZ space-time constructed within the Ricci-Inverse gravity, expressing the solutions in terms of elementary functions and compared with the GR result. We classify different types of geodesics, including null and time-like geodesics, under three conditions: (i) nonzero mass and angular momentum, M ≠ 0 , J ≠ 0 , (ii) massless BTZ space-time, M = 0 and J = 0 , and (iii) M = - 1 , J = 0 , that is A d S 3 -type, and analyze the results in modified gravity theories and compare with the general relativity case. [ABSTRACT FROM AUTHOR]