Black hole solutions with constant Ricci scalar in a model of Finsler gravity

Abstract

Ricci scalar being zero is equivalent to the vacuum field equation in Finsler space-time. The Schwarzschild metric can be concluded from the field equation's solution if the space-time conserves spherical symmetry. This research aims to investigate Finslerian Schwarzschild-de Sitter space-time. Recent studies based on Finslerian space-time geometric models are becoming more prevalent because the local anisotropic structure of space-time influences the gravitational field and gives rise to modified cosmological relations. We suggest a gravitational field equation with a non-zero cosmological constant in Finslerian geometry and apprehend that the presented Finslerian gravitational field equation corresponds to the non-zero Ricci scalar. In Finsler geometry, the peer of spherical symmetry is the Finslerian sphere. Assuming space-time to conserve the “Finslerian sphere” symmetry, the counterpart of the Riemannian sphere (Finslerian sphere) must have a constant flag curvature (λ). It is demonstrated that the Finslerian covariant derivative of the geometric part of the gravitational field equation is preserved under a condition using the Chern connection. According to the string theory, string clouds can be defined as a pool of strings made due to symmetry breaking in the universe's early stages. We find that for λ ≠ 1, this solution resembles a black hole surrounded by a cloud of strings. Furthermore, we investigate null and time-like geodesics for λ = 1. In this regard, the photon geodesics are obtained that are the closest paths to the photon sphere of the first photons visible at the black hole shadow limit. Also, circular orbit conditions are obtained for the effective potential.

Anisotropic conformal change of conic pseudo-Finsler surfaces, I*

“…. This example has been used to find black hole solutions with constant Ricci scalar in a model of Finsler gravity in dimension two [23].…”

“…Conic pseudo-Finsler surfaces are used widely in applications, especially in physics. For example, in [23], Nekouee et al showed that the Finslerian sphere plays a crucial role in the classical Schwarzschild-de Sitter metric perturbation. In other words, they found a Finslerian Schwarzschild-de Sitter solution with the symmetry of Finslerian sphere from the Finsler structure of Randers type.…”