On Spherically Symmetric Minimally Coupled Brane Worlds |
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Authors: | K A Bronnikov S B Fadeev A V Michtchenko |
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Institution: | (1) VNIIMS, 3-1 M, Ulyanovoy St., Moscow, 117313, Russia;(2) Institute of Gravitation and Cosmology, PFUR, 6 Miklukho-Maklaya St., Moscow, 117198, Russia;(3) SEPI–ESIME, IPN, Zacatenco, México, D.F., CP07738, Mexico |
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Abstract: | For a static, spherically symmetric brane in the framework of the RS2 concept, we study the conditions under which the 4D tensor E
v, arising from the 5D Weyl tensor, vanishes on the brane. Gravity on the brane is then decoupled from the bulk geometry, it is the so-called minimally coupled brane world (MCBW). Assuming E
v =0 in the whole bulk, we try to solve the 5D Einstein equations G
AB
+ 5gAB
=0 and obtain an overdetermined set of equations for functions of the radial coordinate. Some special solutions are found, among which are the well-known black string solution with the Schwarzschild metric on the brane and its generalizations with Schwarzschild–(A)dS on-brane metrics. It is concluded that a MCBW can be embedded, in general, in a bulk where E v is not identically zero but only vanishes on the brane. We also present some previous results on the general properties of scalar fields on the brane and give an example of a wormhole supported by a scalar field in a MCBW. |
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Keywords: | multidimensional gravity brane world scalar field black hole wormhole |
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