Asymptotic latent solitons, black strings and black branes in f(R)-gravity

TL;DR

This paper explores nonlinear f(R) gravity theories in higher-dimensional Kaluza-Klein models, identifying two classes of asymptotic solutions called latent solitons, which include black strings and branes, with matter sources exhibiting tension in extra dimensions.

Contribution

It introduces two classes of asymptotic solutions in nonlinear f(R) gravity with extra dimensions, extending previous linear results and including black strings and branes as special cases.

Findings

Solutions satisfy gravitational tests similar to General Relativity

Existence of two classes of asymptotic latent solitons

Black strings and branes are particular solutions

Abstract

We investigate nonlinear f(R) theories in the Kaluza-Klein models with toroidal compactification of extra dimensions. A point-like matter source has the dust-like equation of state in our three dimensions and nonzero equations of state in the extra dimensions. We obtain solutions of linearized Einstein equations with this matter source taking into account effects of nonlinearity of the model. There are two asymptotic regions where solutions satisfy the gravitational tests at the same level of accuracy as General Relativity. According to these asymptotic regions, there are two classes of solutions. We call these solutions asymptotic latent solitons. The asymptotic latent solitons from the first class generalize the known result of the linear theory. The asymptotic black strings and black branes are particular cases of these asymptotic solutions. The second class of asymptotic solitons exists only in multidimensional nonlinear models. The main feature for both of these classes of solutions is that the matter sources have tension in the extra dimensions.