Research Papers (TP)

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    Secret Life of the Spacetime
    (World scientific, 2012-03-28) Padmanabhan, T.
    Just as the thermal properties of normal matterdemandsthe existence of microscopic degrees of freedom, the thermal properties of null surfaces — perceived as local Rindler horizons by accelerated observers — demands the existence of microscopic degrees of freedom to spacetime. The distortion of the null surfaces, just like the deformation of an elastic solid, costs entropy. I show how, just like in the case of an elastic solid, one can describe the dynamics of thespacetime solid by introducing an entropy density to the distortion of null surfaces in the spacetime.
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    What can classical gravity tell us about quantum structure of spacetime?
    (IOP Publishing, 2011-09-12) Padmanabhan, T.
    Several features of classical gravity, combined with the existence of Davies-Unruh temperature of horizon s, support the following paradigm: Gravitational field equations in a wide class of theories, including Einstein ’s theory, should be viewed as describing the thermodynamic limit of the statistical mechanics of (as yet unknown) atoms of spacetime. I present the conceptual evidence for this emergent paradigm and discuss several facets of this approach.
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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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    Thermodynamics and/of horizons: A comparison of schwarschild, rindler and deSitter spacetimes
    (World Scientific Publishing Company, 2002-04-28) Padmanabhan, T.
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    Thermodynamic route to field equations in lanczos-lovelock gravity
    (American Physical Society, 2006-11-10) Padmanabhan, T.
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    Surface density of spacetime degrees of freedom from equipartition law in theories of gravity
    (American Physical Society, 2010-06-22) Padmanabhan, T.
    I show that the principle of equipartition, applied to area elements of a surface @V which are in equilibrium at the local Davies-Unruh temperature, allows one to determine the surface number density of the microscopic spacetime degrees of freedom in any diffeomorphism invariant theory of gravity. The entropy associated with these degrees of freedom matches with theWald entropy for the theory. This result also allows one to attribute an entropy density to the spacetime in a natural manner. The field equations of the theory can then be obtained by extremizing this entropy. Moreover, when the microscopic degrees of freedom are in local thermal equilibrium, the spacetime entropy of a bulk region resides on its boundary.
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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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    Entropy density of spacetime and the Navier-Stokes fluid dynamics of null surfaces
    (American Physical Society, 2011-02-24) Padmanabhan, T.
    It has been known for several decades that Einstein’s field equations, when projected onto a null surface, exhibit a structure very similar to the nonrelativistic Navier-Stokes equation. I show that this result arises quite naturally when gravitational dynamics is viewed as an emergent phenomenon. Extremizing the spacetime entropy density associated with the null surfaces leads to a set of equations which, when viewed in the local inertial frame, becomes identical to the Navier-Stokes equation. This is in contrast to the usual description of the Damour-Navier-Stokes equation in a general coordinate system, in which there appears a Lie derivative rather than a convective derivative. I discuss this difference, its importance, and why it is more appropriate to view the equation in a local inertial frame. The viscous force on fluid, arising from the gradient of the viscous stress-tensor, involves the second derivatives of the metric and does not vanish in the local inertial frame, while the viscous stress-tensor itself vanishes so that inertial observers detect no dissipation. We thus provide an entropy extremization principle that leads to the Damour-Navier-Stokes equation, which makes the hydrodynamical analogy with gravity completely natural and obvious. Several implications of these results are discussed.
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    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.
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