https://doi.org/10.1140/epjc/s10052-024-13637-1
Regular Article
Stationary BTZ space-time in Ricci-inverse and
gravity theories
1
Department of Physics, University of Science and Technology Meghalaya, 793101, Ri-Bhoi, Meghalaya, India
2
Laboratory of Theoretical and Applied Physics, Echahid Cheikh Larbi Tebessi University, 12001, Tebessa, Algeria
a
abdelmalekbouzenada@gmail.com
Received:
14
October
2024
Accepted:
20
November
2024
Published online:
9
December
2024
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 , with
and
representing the Ricci and anti-curvature scalars, respectively and
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
-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,
, (ii) massless BTZ space-time,
and
, and (iii)
, that is
-type, and analyze the results in modified gravity theories and compare with the general relativity case.
© The Author(s) 2024
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