TY - JOUR
T1 - Scalar Fields in Multidimensional Gravity. No-Hair and Other No-Go Theorems
AU - Bronnikov, K. A.
AU - Fadeev, S. B.
AU - Michtchenko, A. V.
N1 - Funding Information:
We are grateful to Irina Dymnikova and Vitaly Melnikov for helpful discussions. KB and SF acknowledge partial financial support from the Russian Foundation for Basic Research and the Russian Ministry of Industry, Science and Technologies.
PY - 2003/4
Y1 - 2003/4
N2 - Global properties of static, spherically symmetric configurations with scalar fields of sigma-model type with arbitrary potentials are studied in D dimensions, including models where the space-time contains multiple internal factor spaces. The latter are assumed to be Einstein spaces, not necessarily Ricci-flat, and the potential V includes a contribution from their curvatures. The following results generalize those known in four dimensions: (A) a no-hair theorem on the nonexistence, in case V ≥ 0, of asymptotically flat black holes with varying scalar fields or moduli fields outside the event horizon; (B) nonexistence of particlelike solutions in field models with V ≥ 0; (C) nonexistence of wormhole solutions under very general conditions; (D) a restriction on possible global causal structures (represented by Carter-Penrose diagrams). The list of structures in all models under consideration is the same as is known for vacuum with a cosmological constant in general relativity: Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and horizons which bound a static region are always simple. The results are applicable to various Kaluza-Klein, supergravity and stringy models with multiple dilaton and moduli fields.
AB - Global properties of static, spherically symmetric configurations with scalar fields of sigma-model type with arbitrary potentials are studied in D dimensions, including models where the space-time contains multiple internal factor spaces. The latter are assumed to be Einstein spaces, not necessarily Ricci-flat, and the potential V includes a contribution from their curvatures. The following results generalize those known in four dimensions: (A) a no-hair theorem on the nonexistence, in case V ≥ 0, of asymptotically flat black holes with varying scalar fields or moduli fields outside the event horizon; (B) nonexistence of particlelike solutions in field models with V ≥ 0; (C) nonexistence of wormhole solutions under very general conditions; (D) a restriction on possible global causal structures (represented by Carter-Penrose diagrams). The list of structures in all models under consideration is the same as is known for vacuum with a cosmological constant in general relativity: Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and horizons which bound a static region are always simple. The results are applicable to various Kaluza-Klein, supergravity and stringy models with multiple dilaton and moduli fields.
KW - Black holes
KW - Multidimensional gravity
KW - Particlelike solutions
KW - Wormholes
UR - http://www.scopus.com/inward/record.url?scp=0346497964&partnerID=8YFLogxK
U2 - 10.1023/A:1022952314050
DO - 10.1023/A:1022952314050
M3 - Artículo
AN - SCOPUS:0346497964
SN - 0001-7701
VL - 35
SP - 505
EP - 525
JO - General Relativity and Gravitation
JF - General Relativity and Gravitation
IS - 4
ER -