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Accelerated detectors and temperature in (anti-) de Sitter spaces. (English) Zbl 0884.53059

Summary: We show, in complete accord with the usual Rindler picture, that detectors with constant acceleration \(a\) in de Sitter (dS) and anti-de Sitter (AdS) spaces with cosmological constants \(\Lambda\) measure temperatures \(2\pi T= (\Lambda/3+ a^2)^{1/2} \equiv a_5\), the detector ‘5-acceleration’ in the embedding flat 5-space. For dS, this recovers a known result; in AdS, where \(\Lambda\) is negative, the temperature is well-defined down to the critical value \(a_5=0\), again in accord with the underlying kinematics. The existence of a thermal spectrum is also demonstrated for a variety of candidate wave functions in AdS backgrounds.

MSC:

53Z05 Applications of differential geometry to physics
83C10 Equations of motion in general relativity and gravitational theory
83C47 Methods of quantum field theory in general relativity and gravitational theory
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