Exact and asymptotic black branes with spherical compactification

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 ${\hat{p}}_1=-(1/2)\hat{\epsilon }$ 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 ${\hat{p}}_1=\Omega \hat{\epsilon }$ in the internal space. In the case ${\Lambda }_6>0$ and $\Omega \ne -1/2$, 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.

arXiv comment6 pages, no figures

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Cited by in corpus (6)

• Kaluza-Klein models with spherical compactification: observational constraints and possible examples
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• Problematic aspects of Kaluza-Klein excitations in multidimensional models with Einstein internal spaces
• Significance of tension for gravitating masses in Kaluza-Klein models
• Weak-field limit of Kaluza-Klein model with non-linear perfect fluid
• Effects of nonlinearity of $f(R)$ gravity and perfect fluid in Kaluza-Klein models with spherical compactification