Research Papers (TP)
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Item Thermodynamic structure of lanc zos-lovelock field equations from near-horizon symmetries(American Physical Society, 2009-05-15) Kothawala, Dawood; Padmanabhan, T.It is well known that, for a wide class of spacetimes with horizons, Einstein equations near the horizon can be written as a thermodynamic identity. It is also known that the Einstein tensor acquires a highly symmetric form near static, as well as stationary, horizons. We show that, for generic static spacetimes, this highly symmetric form of the Einstein tensor leads quite naturally and generically to the interpretation of the near-horizon field equations as a thermodynamic identity. We further extend this result to generic static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon field equations again represent a thermodynamic identity in all these models. These results confirm the conjecture that this thermodynamic perspective of gravity extends far beyond Einstein’s theory.Item Thermodynamics and/of horizons: A comparison of schwarschild, rindler and deSitter spacetimes(World Scientific Publishing Company, 2002-04-28) Padmanabhan, T.Item Thermodynamic route to field equations in lanczos-lovelock gravity(American Physical Society, 2006-11-10) Padmanabhan, T.Item Entropy of null surfaces and dynamics of spacetime(American Physical Society, 2007-03-02) Padmanabhan, T.; Paranjape, AseemThe null surfaces of a spacetime act as oneway membranes and can block information for a corresponding family of observers (timelike curves). Since lack of information can be related to entropy, this suggests the possibility of assigning an entropy to the null surfaces of a spacetime. We motivate and introduce such an entropy functional for any vector field in terms of a fourth-rank divergence-free tensor Pcd ab with the symmetries of the curvature tensor. Extremizing this entropy for all the null surfaces then leads to equations for the background metric of the spacetime. When Pcd ab is constructed from the metric alone, these equations are identical to Einstein’s equations with an undetermined cosmological constant (which arises as an integration constant). More generally, if Pcd ab is allowed to depend on both metric and curvature in a polynomial form, one recovers the Lanczos-Lovelock gravity. In all these cases: (a)We only need to extremize the entropy associated with the null surfaces; the metric is not a dynamical variable in this approach. (b) The extremal value of the entropy agrees with standard results, when evaluated on shell for a solution admitting a horizon. The role of the full quantum theory of gravity will be to provide the specific form of Pcd ab which should be used in the entropy functional. With such an interpretation, it seems reasonable to interpret the Lanczos-Lovelock type terms as quantum corrections to classical gravity.Item Duality and Zero-Point Length of Spacetime(American Physical Society, 1997-03-10) Padmanabhan, T.The action for a relativistic free particle of mass m receives a contribution 2mds from a path of infinitesimal length ds. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass m. Assuming that the path integral amplitude is invariant under the “duality” transformation ds ! L2 P yds, one can calculate the modified Feynman propagator. I show that this propagator is the same as the one obtained by assuming that quantum effects of gravity lead to modification of the spacetime interval sx 2 yd2 to sx 2 yd2 1 L2 P . The implications of this result are discussed.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 Quantum structure of spacetime and entropy of schwarschild black holes(American Physical Society, 1998-01-05) Padmanabhan, T.The gap between a microscopic theory for quantum spacetime and the semiclassical physics of Schwarschild black holes is bridged by treating the black hole spacetimes as highly excited states of a class of nonlocal field theories. All of the black hole thermodynamics are shown to arise from an asymptotic form of the dispersion relation satisfied by the elementary excitations of these field theories. These models involve, quite generically, fields which are (i) smeared over regions of the order of Planck length and (ii) possess correlation functions which have universal short distance behavior.Item Gravitational Entropy o f static spacetimes and microscopic density o f states(Institute of Physics Publishing, 2004-08-03) Padmanabhan, T.A general ansatz for gravitational entropy can be provided using the criterion that any patch of area which acts as a horizon for a suitably defined accelerated observer must have an entropy proportional to its area. After providing a brief justification for this ansatz, several consequences are derived. (i) In any static spacetime with a horizon and associated temperature β−1, this entropy satisfies the relation S = (1/2)βE where E is the energy source for gravitational acceleration, obtained as an integral of (Tab − (1/2)T gab)ua ub. (ii) With this ansatz of S, the minimization of Einstein–Hilbert action is equivalent to minimizing the free energy F with βF = βU − S where U is the integral of Tabua ub. We discuss the conditions under which these results imply S ∝ E2 and/or S ∝ U2 thereby generalizing the results known for black holes. This approach links with several other known results, especially the holographic views of spacetime.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.Item Comparison between semiclassical gravity and semiclassical electrodynamics(IOP Publishing, 1991-05-14) Kiefer, C.; Padmanabhan, T.; Singh, T. P.It is known how the equation of motion for a quantum tieid in a classical CUM spacetime can be derived as an approximation lo the Wheeler-DeWLtt equation. In order 10 obtain a better understanding of ths derivation, we develop an analogous approximation for quanrum electrodynamics. We show lhat quantum field lheory in an erternal, classical electromagnetic field can be oblained as a limiting case of quantum electrodynamics, by expanding the full wavefunctional in a power series in the coupling constant e2. The important difference in the yo derivalions is that unlike the metric, Lhe electromagnetic potential has to be scaled wilh respect to the coupling constant before the semiclassical limit can be obtained.