IUCAA Preprints

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    Holography of gravity encoded in a relation between entropy, horizon area and action for gravity
    (2002-05-20) Padmanabhan, T.
    I provide a general proof of the conjecture that one can attribute an en- tropy to the area of any horizon. This is done by constructing a canonical ensemble of a subclass of spacetimes with a fixed value for the temperature T = β−1 and evaluating the exact partition function Z(β). For spherically symmetric spacetimes with a horizon at r = a, the partition function has the generic form Z ∝ exp[S −βE], where S = (1/4)4πa2 and |E| = (a/2). Both S and E are determined entirely by the properties of the metric near the horizon. This analysis reproduces the conventional result for the black-hole spacetimes and provides a simple and consistent interpretation of entropy and energy for De Sitter spacetime. For the Rindler spacetime the entropy per unit transverse area turns out to be (1/4) while the energy is zero. Further, I show that the relationship between entropy and area allows one to construct the action for the gravitational field on the bulk and thus the full theory. In this sense, gravity is intrinsically holographic.
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    Gravity and the thermodynamics of horizons
    (2011-07-05) Padmanabhan, T.
    Abstract Spacetimes with horizons show a resemblance to thermodynamic systems and it is possible to associate the notions of temperature and entropy with them. Several as- pects of this connection are reviewed in a manner appropriate for broad readership. The approach uses two essential principles: (a) the physical theories must be formu- lated for each observer entirely in terms of variables any given observer can access and (b) consistent formulation of quantum field theory requires analytic continua- tion to the complex plane. These two principles, when used together in spacetimes with horizons, are powerful enough to provide several results in a unified manner. Since spacetimes with horizons have a generic behaviour under analytic continua- tion, standard results of quantum field theory in curved spacetimes with horizons can be obtained directly (Sections III to VII). The requirements (a) and (b) also put strong constraints on the action principle describing the gravity and, in fact, one can obtain the Einstein-Hilbert action from the thermodynamic considerations (Section VIII). The review emphasises the thermodynamic aspects of horizons, which could be obtained from general principles and is expected to remain valid, independent of the microscopic description (‘statistical mechanics’) of horizons.
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    Entropy changes in the clustering of galaxies in an expanding universe
    (2011-05-26) Iqbal, Naseer; Khan, Mohammad Shafi; Masood, Tabasum
    In the present work the approach-thermody-namics and statistical mechanics of gravitating systems is applied to study the entropy changein gravitational clustering of galaxies in an ex-panding universe. We derive analytically the expressions for gravitational entropy in terms of temperature T and average density n of the par-ticles (galaxies) in the given phase space cell. It is found that during the initial stage of cluster-ing of galaxies, the entropy decreases and finally seems to be increasing when the system attains virial equilibrium. The entropy changes are studied for different range of measuring correlation parameter b. We attempt to provide a clearer account of this phenomena. The entropy esults for a system consisting of extended mass (non-point mass) particles show a imilar behaviour with that of point mass particles clustering gravitationally in an expanding uni-verse.