TY - JOUR
T1 - Scalar field in a minimally coupled brane world
T2 - No-hair and other no-go theorems
AU - Bronnikov, K. A.
AU - Fadeev, S. B.
AU - Michtchenko, A. V.
N1 - Funding Information:
K. A. Bronnikov and S. B. Fadeev acknowledge partial financial support from the RFBR Grant 01-0217312a, the Russian Ministry of Education and the Russian Ministry of Industry, Science and Technologies.
PY - 2004/4
Y1 - 2004/4
N2 - In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (∂φ)2/2 - V (φ), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the conventional stress tensor Tμν, the tensor IIμν which is quadratic in Tμν, and Eμ ν describing interaction with the bulk. For models under study, the tensor IIμν has zero divergence, allowing one to consider Eμν = 0. Such a brane, whose 4D gravity is decoupled from the bulk geometry, may be called minimally coupled. Assuming Eμν = 0, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a cosmological constant in GR: Minkowski, Schwarzschild, (anti-) de Sitter and Schwarzschild-(anti-)de Sitter. A no-hair theorem, saying that, given a potential V ≥ 0, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.
AB - In the brane-world framework, we consider static, spherically symmetric configurations of a scalar field with the Lagrangian (∂φ)2/2 - V (φ), confined on the brane. We use the 4D Einstein equations on the brane obtained by Shiromizu et al., containing the conventional stress tensor Tμν, the tensor IIμν which is quadratic in Tμν, and Eμ ν describing interaction with the bulk. For models under study, the tensor IIμν has zero divergence, allowing one to consider Eμν = 0. Such a brane, whose 4D gravity is decoupled from the bulk geometry, may be called minimally coupled. Assuming Eμν = 0, we try to extend to brane worlds some theorems valid for scalar fields in general relativity (GR). Thus, the list of possible global causal structures in all models under consideration is shown to be the same as is known for vacuum with a cosmological constant in GR: Minkowski, Schwarzschild, (anti-) de Sitter and Schwarzschild-(anti-)de Sitter. A no-hair theorem, saying that, given a potential V ≥ 0, asymptotically flat black holes cannot have nontrivial external scalar fields, is proved under certain restrictions. Some objects, forbidden in GR, are allowed on the brane, e.g, traversable wormholes supported by a scalar field, but only at the expense of enormous matter densities in the strong field region.
KW - Black holes
KW - Brane world
KW - Causal structure
KW - Scalar field
UR - http://www.scopus.com/inward/record.url?scp=13844321573&partnerID=8YFLogxK
U2 - 10.1142/S0218271804003561
DO - 10.1142/S0218271804003561
M3 - Artículo
AN - SCOPUS:13844321573
SN - 0218-2718
VL - 13
SP - 593
EP - 606
JO - International Journal of Modern Physics D
JF - International Journal of Modern Physics D
IS - 4
ER -