On singular solutions in multidimensional gravity
On singular solutions in multidimensional gravity
It is proved that the Riemann tensor squared is divergent as $��\ra 0$ for a wide class of cosmological metrics with non-exceptional Kasner-like behaviour of scale factors as $��\ra 0$, where $��$ is synchronous time. Using this result it is shown that any non-trivial generalization of the spherically-symmetric Tangherlini solution to the case of $n$ Ricci-flat internal spaces \cite{FIM} has a divergent Riemann tensor squared as $R \ra R_0$, where $R_0$ is parameter of length of the solution. Multitemporal naked singularities are also considered.
16 pages, LaTex. Submitted to Gravitation and Cosmology (new Russian journal)
Kasner-like behaviour, divergent Riemann tensor, multidimensional gravity, FOS: Physical sciences, Kaluza-Klein and other higher-dimensional theories, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Relativistic cosmology
Kasner-like behaviour, divergent Riemann tensor, multidimensional gravity, FOS: Physical sciences, Kaluza-Klein and other higher-dimensional theories, General Relativity and Quantum Cosmology (gr-qc), General Relativity and Quantum Cosmology, Relativistic cosmology
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