Analytically approximation solution to gravity

S. N. Sajadi; Ali Hajilou; S. H. Hendi

doi:10.1140/epjc/s10052-023-11176-9

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 45
https://doi.org/10.1140/epjc/s10052-023-11176-9

Regular Article - Theoretical Physics

Analytically approximation solution to $R^{2}$ $R^{2}$ gravity

S. N. Sajadi¹^,2^,3^a, Ali Hajilou⁴^,5 and S. H. Hendi¹^,2^,6

¹ Department of Physics, School of Science, Shiraz University, 71454, Shiraz, Iran
² Biruni Observatory, School of Science, Shiraz University, 71454, Shiraz, Iran
³ School of Physics, Institute for Research in Fundamental Sciences (IPM), P. O. Box 19395-5531, Tehran, Iran
⁴ School of Particles and Accelerators, Institute for Research in Fundamental Science (IPM), P.O. Box 19395-5746, Tehran, Iran
⁵ Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina str. 8, 119991, Moscow, Russia
⁶ Canadian Quantum Research Center 204-3002 32 Ave Vernon, V1T 2L7, BC, Canada

^a naseh.sajadi@gmail.com

Received: 24 August 2022
Accepted: 27 December 2022
Published online: 19 January 2023

Abstract

In this paper, we obtain analytical approximate black hole solutions in the framework of f(R) gravity and the absence of a cosmological constant. In this area, we apply the equations of motion of the theory to a spherically symmetric spacetime with one unknown function and derive black hole solutions without any constraints on the Ricci scalar. To do so, first, we obtain the near horizon and asymptotic solutions and then use both of them to obtain a complete solution by utilizing a continued-fraction expansion. Finally, we investigate the stability of the solutions by employing the thermodynamics and quasi-normal modes.

© The Author(s) 2023

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