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

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-12, Vol.84 (12), p.1271, Article 1271
• Main Authors: Ahmed, Faizuddin, Bouzenada, Abdelmalek
• Format: Article
• Language: English
• Subjects: Angular momentum; Astronomy; Astrophysics and Cosmology; Cosmological constant; Curvature; Elementary Particles; Geodesy; Hadrons; Heavy Ions; Mathematical analysis; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article; Relativity; Scalars; Spacetime; String Theory; Tensors
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13637-1

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.