Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models

TL;DR

This paper explores soliton solutions in Kaluza-Klein models, revealing conditions under which these solutions align with general relativity and identifying black strings and branes as stable, indistinguishable solutions with specific equations of state.

Contribution

It introduces the concept of latent solitons in Kaluza-Klein models and derives conditions for stability and equations of state for black strings and branes.

Findings

Point-like mass soliton has dust-like equations of state in all spaces.

Experimental constraints restrict model parameters, favoring solutions indistinguishable from GR.

Black strings and branes satisfy stability conditions and specific equations of state.

Abstract

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: $\tau = -(2.1\pm 2.3)\times 10^{-5}$. The point-like mass solution contradicts this restriction. The condition $\tau=0$ satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state $p_i=-\epsilon/2$, in the internal spaces and to the number of the external dimensions $d_0=3$. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.