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 . The spacetime has two distinct time scales, and , where is the radius of the black-hole horizon, the radius of the cosmological horizon, and c the speed of light. When the field’s time evolution can be separated into three epochs. At times the field behaves as if it were in pure Schwarzschild spacetime; the structure of spacetime far from 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 the power-law behavior gives way to a faster, exponential decay. In this intermediate epoch, the conditions at radii and both play an important role. Finally, at times the field behaves as if it were in pure de Sitter spacetime; the structure of spacetime near the black hole no longer influences the evolution in a significant way. In this late epoch, the field’s behavior depends on the value of the curvature-coupling constant . If is less than a critical value , the field decays exponentially, with a decay constant that increases with increasing . If the field oscillates with a frequency that increases with increasing ; the amplitude of the field still decays exponentially, but the decay constant is independent of . We establish these properties using a combination of numerical and analytical methods.
- Received 3 February 1999
DOI:https://doi.org/10.1103/PhysRevD.60.064003
©1999 American Physical Society