Research Papers (TP)

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Author: search.filters.author.Kothawala, Dawood

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    Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity
    (American physical society, 2012-03-06) Padmanabhan, T.; Kothawala, Dawood; Kolekar, Sanved
    We consider two specific approaches to evaluate the black hole entropy which are known to produce correct results in the case of Einstein’s theory and generalize them to Lanczos- Lovelock models. In the first approach (which could be called extrinsic) we use a procedure motivated by earlier work by Pretorius, Vollick and Israel, and by Oppenheim, and evaluate the entropy of a configuration of densely packed gravitating shells on the verge of forming a black hole in Lanczos-Lovelock theories of gravity. We find that this matter entropy is not equal to (it is less than) Wald entropy, except in the case of Einstein theory, where they are equal. The matter entropy is proportional to the Wald entropy if we consider a specific m-th order Lanczos-Lovelock model, with the proportionality constant depending on the spacetime dimensions D and the order m of the Lanczos-Lovelock theory as (D−2m)/(D−2). Since the proportionality constant depends on m, the proportionality between matter entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock actions involving different m. In the second approach (which could be called intrinsic) we generalize a procedure, previ- ously introduced by Padmanabhan in the context of GR, to study off-shell entropy of a classof metrics with horizon using a path integral method. We consider the Euclidean action of Lanczos-Lovelock models for a class of metrics off-shell and interpret it as a partition function. We show that in the case of spherically symmetric metrics, one can interpret the Euclidean action as the free energy and read off both the entropy and energy of a black hole spacetime. Surprisingly enough, this leads to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock models obtained by other methods. We comment on possible implications of the result.
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    Is gravitational entropy quantized?
    (American Physical Society, 2008-11-18) Kothawala, Dawood; Padmanabhan, T.; Sarkar, Sudipta
    In Einstein’s gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equallyspaced spectrum for large quantum numbers. But in more general theories (like, for example, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is not proportional to area and the question arises as to which of the two (if at all) will have this property. We give a general argument that in all Lanczos-Lovelock theories of gravity, it is the entropy that has an equally-spaced spectrum. In the case of Gauss-Bonnet gravity, we use the asymptotic form of quasinormal mode frequencies to explicitly demonstrate this result. Hence, the concept of a quantum of area in Einstein- Hilbert gravity needs to be replaced by a concept of quantum of entropy in a more general context.
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    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.
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    Einstein’s equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons
    (Elsevier Science Publishers, 2007-07-19) Kothawala, Dawood; Sarkar, Sudipta; Padmanabhan, T.
    There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity as well as for a wider class of Lanczos–Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity T dS = dE + P dV. We study this approach further and generalize the results to two more generic cases: stationary axis-symmetric horizons and time dependent evolving horizons within the context of general relativity. In both the cases, the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon. This result demonstrates the fact that the thermodynamic interpretation of gravitational dynamics is not restricted to spherically symmetric or static horizons but is quite generic in nature and indicates a deeper connection between gravity and thermodynamics.
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    Response of unruh–deWitt detector with time-dependent acceleration
    (Elsevier Science Publishers, 2010-05-19) Kothawala, Dawood; Padmanabhan, T.
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    Path integral duality modified propagators in spacetimes with constant curvature
    (American Physical Society, 2009-08-10) Kothawala, Dawood; Sriramkumar, L.; Shankaranarayanan, S.; Padmanabhan, T.
    The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length LP in a locally Lorentz invariant manner. We use this prescription to evaluate the duality modified propagators in spacetimes with constant curvature (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that (i) the modified propagators are ultraviolet finite, (ii) the modifications are nonperturbative in LP, and (iii) LP seems to behave like a "zero point length" of spacetime intervals such that σ2(x,x') =[σ2(x,x')+O(1)LP2], where σ(x,x') is the geodesic distance between the two spacetime points x and x', and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.