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The Birkhoff theorem and string clouds

Title
The Birkhoff theorem and string clouds
Authors
Bronnikov, K. A.Kim, S-WSkvortsova, M. V.
Ewha Authors
김성원
SCOPUS Author ID
김성원scopus
Issue Date
2016
Journal Title
CLASSICAL AND QUANTUM GRAVITY
ISSN
0264-9381JCR Link

1361-6382JCR Link
Citation
CLASSICAL AND QUANTUM GRAVITY vol. 33, no. 19
Keywords
general relativityBirkhoff theoremspherical symmetrycosmic stringsanisotropic fluidpure radiation
Publisher
IOP PUBLISHING LTD
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., (partial derivative r)(2) = 0). It is shown that solutions to the Einstein equations with r = const contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the tangential pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with (partial derivative r)(2) = 0 but r not equal 1 const, supported by an anisotropic fluid, contain a null Killing vector, which again indicates a Birkhoff-like behavior. Similar space-times supported by pure radiation (in particular, a massless radiative scalar field) contain a null Killing vector without additional assumptions, which leads to one more extension of the Birkhoff theorem. Exact radial wave solutions have been found (i) with an anisotropic fluid and (ii) with a gas of radially directed cosmic strings (or a 'string cloud') combined with pure radiation. Furthermore, it is shown that a perfect fluid with isotropic pressure and a massive or self-interacting scalar field cannot be sources of gravitational fields with a null but nonzero gradient of r.
DOI
10.1088/0264-9381/33/19/195006
Appears in Collections:
사범대학 > 과학교육과 > Journal papers
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