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.


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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