We consider static, spherically symmetric solutions of general relativity with a non-linear sigma model (NSM) as a source, i.e., a set of scalar fields Φ = (Φ1,...,Φn) (so-called chiral fields) parametrizing a target space with a metric hab(Φ). For NSM with zero potential V (Φ), it is shown that the space-time geometry is the same as with a single scalar field but depends on hab. If the matrix hab is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out. © Pleiades Publishing, Ltd., 2009.

Authors

Journal

Number of issue

3

Language

English

Pages

241-246

Status

Published

Link

Volume

15

Year

2009

Organizations

^{1}Center of Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya ul. 46, Moscow 117361, Russian Federation^{2}Institute of Gravitation and Cosmology, PFUR, Miklukho-Maklaya ul. 6, Moscow 117198, Russian Federation^{3}Department of Theoretical Physics, Ulyanovsk State University, Lev Tolstoy ul. 42, Ulyanovsk 432000, Russian Federation^{4}Department of General Physics, Ulyanovsk State Pedagogical University, Lenin's 100 years pl., 4, Ulyanovsk 432700, Russian Federation^{5}Department of General Relativity and Gravitation, Kazan State University, Kremlyovskaya ul. 18, Kazan 420008, Russian Federation^{6}Department of Mathematics, Tatar State University of Humanities and Education, Tatarstan ul. 2, Kazan 420021, Russian Federation

Date of creation

19.10.2018

Date of change

19.10.2018

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Doklady Mathematics.
Vol. 80.
2009.
P. 521-524

Gravitation and Cosmology.
Vol. 15.
2009.
P. 199-212