Radiative falloff in Schwarzschild-de Sitter spacetime - art. no. 064003

Citation
Pr. Brady et al., Radiative falloff in Schwarzschild-de Sitter spacetime - art. no. 064003, PHYS REV D, 6006(6), 1999, pp. 4003
Citations number
31
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW D
ISSN journal
0556-2821 → ACNP
Volume
6006
Issue
6
Year of publication
1999
Database
ISI
SICI code
0556-2821(19990915)6006:6<4003:RFISSS>2.0.ZU;2-5
Abstract
We consider the evolution of a scalar field propagating in Schwarzschild-de Sitter spacetime. The field is non-minimally coupled to curvature through a coupling constant xi. The spacetime has two distinct time scales, t(e) = r(e)/c and t(c) = r(c)/c, where r(e) is the radius of the black-hole horizo n, r(c) the radius of the cosmological horizon, and c the speed of light. W hen r(c) much greater than r(e). the field's time evolution can be separate d into three epochs. At times t much less than t(c), the field behaves as i f it were in pure Schwarzschild spacetime; the structure of spacetime far f rom the black hole has no influence on the evolution. In this early epoch, the field's initial outburst is followed by quasi-normal oscillations, and then by an inverse power-law decay. At times t less than or similar to t(c) , the Fewer-law behavior gives way to a faster, exponential decay. In this intermediate epoch, the conditions at radii r greater than or similar to r( e), and r less than or similar to r(c), both play an important role. Finall y, at times t much greater than t(c), the field behaves as if it were in pu re de Sitter spacetime; the structure of spacetime near the black hole no l onger influences the evolution in a significant way. In this late epoch, th e field's behavior depends on the value of the curvature-coupling constant xi. If xi is less than a critical value xi(c)= 3/16, the held decays expone ntially, with a decay constant that increases with increasing xi. If xi > x i(c), the field oscillates with a frequency Chat increases with increasing xi the amplitude of the field still decays exponentially, but the decay con stant is independent of xi. We establish these properties using a combinati on of numerical and analytical methods. [S0556-2821(99)06416-4].