Browsing by Author "Paranjape, Aseem"

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    Entropy of null surfaces and dynamics of spacetime
    (American Physical Society, 2007-03-02) Padmanabhan, T.; Paranjape, Aseem
    The 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.
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    Radiation from collapsing shells, semiclassical backreaction, and black hole formation
    (American Physical Society, 2009-08-14) Paranjape, Aseem; Padmanabhan, T.
    We provide a detailed analysis of quantum field theory around a collapsing shell and discuss several conceptual issues related to the emission of radiation flux and formation of black holes. Explicit calculations are performed using a model for a collapsing shell which turns out to be analytically solvable. We use the insights gained in this model to draw reliable conclusions regarding more realistic models. We first show that any shell of mass M which collapses to a radius close to r=2M will emit approximately thermal radiation for a period of time. In particular, a shell which collapses from some initial radius to a final radius 2M(1-ε²)-¹ (where ε łl 1) without forming a black hole, will emit thermal radiation during the period M≲ t ≲ Młn (1/ε²). Later on (tgg M łn(1/ε²)), the flux from such a shell will decay to zero exponentially. We next study the effect of backreaction computed using the vacuum expectation value of the stress tensor on the collapse. We find that, in any realistic collapse scenario, the backreaction effects do emphnot prevent the formation of the event horizon. The time at which the event horizon is formed is, of course, delayed due to the radiated flux -- which decreases the mass of the shell -- but this effect is not sufficient to prevent horizon formation. We also clarify several conceptual issues and provide pedagogical details of the calculations in the Appendices to the paper.