Professor T. Padmanabhan
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Item Reply to "Comment on 'Quasinormal modes in schwarzschild–de sitter spacetime: A simple derivation of the level spacing of the frequencies"(American Physical Society, 2011-05-23) Choudhury, T. Roy; Padmanabhan, T.Item Quasinormal modes in schwarzschild–de sitter spacetime: A simple derivation of the level spacing of the frequencies(American Physical Society, 2004-03-25) Choudhury, T. Roy; Padmanabhan, T.It is known that the imaginary parts of the quasinormal mode (QNM) frequencies for the Schwarzschild black hole are evenly spaced with a spacing that depends only on the surface gravity. On the other hand, for massless minimally coupled scalar fields, there exist no QNMs in the pure de Sitter spacetime. It is not clear what the structure of the QNMs would be for the Schwarzschild–de Sitter (SDS) spacetime, which is characterized by two different surface gravities. We provide a simple derivation of the imaginary parts of the QNM frequencies for the SDS spacetime by calculating the scattering amplitude in the first Born approximation and determining its poles. We find that, for the usual set of boundary conditions in which the incident wave is scattered off the black hole horizon, the imaginary parts of the QNM frequencies have an equally spaced structure with the level spacing depending on the surface gravity of the black hole. Several conceptual issues related to the QNM are discussed in the light of this result and a comparison with previous work is presented.Item Concept of temperature in multi-horizon spacetimes: analysis of Schwarzschild–De Sitter metric(Springer, 2007-07-26) Choudhury, T. Roy; Padmanabhan, T.In case of spacetimes with single horizon, there exist several well-established procedures for relating the surface gravity of the horizon to a thermodyna-mic temperature. Such procedures, however, cannot be extended in a straightforward manner when a spacetime has multiple horizons. In particular, it is not clear whether there exists a notion of global temperature characterizing the multi-horizon space-times. We examine the conditions under which a global temperature can exist for a spacetime with two horizons using the example of Schwarzschild–De Sitter (SDS) spacetime. We systematically extend different procedures (like the expectation value of stress tensor, response of particle detectors, periodicity in the Euclidean time etc.) for identifying a temperature in the case of spacetimes with single horizon to the SDS spacetime. This analysis is facilitated by using a global coordinate chart which covers the entire SDS manifold. We find that all the procedures lead to a consistent picture characterized by the following features: (a) In general, SDS spacetime behaves like a non-equilibrium system characterized by two temperatures. (b) It is not possible to associate a global temperature with SDS spacetime except when the ratio of the two surface gravities is rational. (c) Even when the ratio of the two surface gravities is rational, the thermal nature depends on the coordinate chart used. There exists a global coordinate chart in which there is global equilibrium temperature while there exist other charts in which SDS behaves as though it has two different temperatures. The coordinate dependence of the thermal nature is reminiscent of the flat spacetime in Minkowski and Rindler coordinate charts. The implications are discussed.