Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in f(R) gravity

Alberto Guilabert; Pelayo V. Calzada; Pedro Bargueño; Salvador Miret-Artés

doi:10.1140/epjc/s10052-024-13063-3

EPJ

a
b
c
d
e
ap
st
h
plus
ds
pv
ti
qt
am
n

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 678
https://doi.org/10.1140/epjc/s10052-024-13063-3

Regular Article - Theoretical Physics

Static and spherically symmetric vacuum spacetimes with non-expanding principal null directions in f(R) gravity

Alberto Guilabert¹^,2^a, Pelayo V. Calzada², Pedro Bargueño² and Salvador Miret-Artés³

¹ Fundacion Humanismo y Ciencia, Guzmán el Bueno, 66, 28015, Madrid, Spain
² Departamento de Física Aplicada, Universidad de Alicante, Campus de San Vicente del Raspeig, 03690, Alicante, Spain
³ Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006, Madrid, Spain

^a alberto.guilabert@ua.es

Received: 14 May 2024
Accepted: 25 June 2024
Published online: 9 July 2024

Abstract

In this work we characterize all the static and spherically symmetric vacuum solutions in f(R) gravity when the principal null directions of the Weyl tensor are non-expanding. In contrast to General Relativity, we show that the Nariai spacetime is not the only solution of this type when general f(R) theories are considered. In particular, we find four different solutions for the non-constant Ricci scalar case, all of them corresponding to the same theory, given by $f (R) = r_{0}^{- 1} {| R - 3 / r_{0}^{2} |}^{1 / 2}$ $f(R) = r_0^{-1}\left|R-3/r_0^2\right|^{1/2}$ , where $r_{0}$ $$r_0$$ is a non-null constant. Finally, we briefly present some geometric properties of these solutions.

© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.