Exact and asymptotic black branes with spherical compactification

TL;DR

This paper derives exact and approximate black brane solutions with spherical internal space compactification in a six-dimensional Kaluza-Klein model, analyzing their properties and consistency with gravitational experiments.

Contribution

It presents the first exact black brane solutions with spherical compactification in six-dimensional Kaluza-Klein models, including matter sources and asymptotic behaviors.

Findings

Exact solutions exist with and without cosmological constant.

Solutions satisfy gravitational tests at the same level as general relativity.

Asymptotic solutions tend to the exact black brane in the weak-field limit.

Abstract

In the six-dimensional Kaluza-Klein model with the multidimensional cosmological constant $\Lambda_6$, we obtain the black brane with spherical compactification of the internal space. The matter source for this exact solution consists of two parts. First, it is a fine-tuned homogeneous perfect fluid which provides spherical compactification of the internal space. Second, it is a gravitating massive body with the dustlike equation of state in the external space and tension $\hat p_1=-(1/2)\hat\varepsilon$ in the internal space. This solution exists both in the presence and absence of $\Lambda_6$. In the weak-field approximation, we also get solutions of the linearized Einstein equations for the model with spherical compactification. Here, the gravitating matter source has the dustlike equation of state in the external space and an arbitrary equation of state $\hat p_1=\Omega \hat\varepsilon$ in the internal space. In the case $\Lambda_6>0$ and $\Omega\neq -1/2$, these approximate solutions tend asymptotically to the weak-field limit of the exact black brane solution. Both the exact and asymptotic black branes satisfy the gravitational experiments at the same level of accuracy as general relativity.