Comment on “Accelerated Detectors and Temperature in (Anti) de Sitter Spaces”

It is shown how the results of Deser and Levin on the response of accelerated detectors in anti-de Sitter space can be understood from the same general perspective as other thermality results in spacetimes with bifurcate Killing horizons. A detector with linear acceleration a in the Minkowski vacuum sees a thermal bath at the temperature TU = a/2π [1], while an inertial detector in de Sitter (dS) space of radius R sees a thermal bath in the de Sitter vacuum at the temperature TGH = 1/2πR [2]. What does an accelerated detector see in de Sitter space? This detector also sees a thermal bath, but at the temperature[3, 4, 5] TdS = (R −2 + a)/2π. (1) Deser and Levin (DL) recently showed [5] that the same formula with R → −R gives in anti-de Sitter (adS) space the temperature seen by some uniformly accelerated detectors in any of three vacuum states, while the temperature for some other uniformly accelerated detectors vanishes! (In the adS case the class of accelerated world lines yielding (1) has acceleration bounded below by R so the argument of the square root is bounded below by zero.) E-mail: [email protected]