Browsing by Author "Kolekar, Sanved"

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Action principle for the fluid-gravity correspondence and emergent gravity
(Astronomical Society of India, 2012-01-04) Kolekar, Sanved; Padmanabhan, T.
It has been known for a long time that Einstein’s field equations when projected onto a black hole horizon look very similar to a Navier-Stokes equation in suitable variables. More recently, it was shown that the projection of Einstein’s equation onto any null surface in any spacetime reduces exactly to the Navier-Stokes form when viewed in the freely falling frame. We develop an action principle, the extremization of which leads to the above result, in an arbitrary spacetime. The degrees of freedom varied in the action principle are the null vectors in the spacetime and not the metric tensor. The same action principle was introduced earlier in the context of the emergent gravity paradigm wherein it was shown that the corresponding Lagrangian can be interpreted as the entropy density of spacetime. The current analysis strengthens this interpretation and reinforces the idea that field equations in gravity can be thought of as emergent. We also find that the degrees of freedom on the null surface are equivalent to a fluid with equation of state PA = TS. We demonstrate that the same relation arises in the context of a spherical shell collapsing to form a horizon
Drift, Drag and Brownian motion in the Davies-Unruh bath
(2013-08-06) Kolekar, Sanved; Padmanabhan, T.
An interesting feature of the Davies-Unruh effect is that a uniformly accelerated observer sees an isotropic thermal spectrum of particles even though there is a preferred direction in this context, determined by the direction of the acceleration g. We investigate the thermal fluctuations in the Unruh bath by studying the Brownian motion of particles in the bath, especially as regards to isotropy. We find that the thermal fluctuations are anisotropic and induce different frictional drag forces on the Brownian particle depending on whether it has a drift velocity along the direction of acceleration g or in a direction transverse to it. Using the fluctuation-dissipation theorem, we argue that this anisotropy arises due to quantum correlations in the fluctuations at large correlation time scales.
Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity
(American physical society, 2012-07-03) Padmanabhan, T.; Kolekar, Sanved; Sarkar, Sudipta
We study quasistationary physical process for black holes within the context of Lanczos-Lovelock gravity. We show that the Wald entropy of the stationary black holes in Lanczos-Lovelock gravity monotonically increases for quasistationary physical processes in which the horizon is perturbed by the accretion of positive energy matter and the black hole ultimately settles down to a stationary state. This result reinforces the physical interpretation of Wald entropy for Lanczos-Lovelockmodels and takes a step towards proving the analogue of the black hole area increase theorem in a wider class of gravitational theories.
Holography in action
(American Physical Society, 2010-07-28) Kolekar, Sanved; Padmanabhan, T.
The Einstein-Hilbert action and its natural generalizations to higher dimensions (like the Lanczos- Lovelock action) have certain peculiar features. All of them can be separated into a bulk and a surface term, with a specific (‘‘holographic’’) relationship between the two, so that either term can be used to extract information about the other. Further, the surface term leads to entropy of the horizons on shell. It has been argued in the past that these features are impossible to understand in the conventional approach but find a natural explanation if we consider gravity as an emergent phenomenon. We provide further support for this point of view in this paper. We describe an alternative decomposition of the Einstein- Hilbert action and the Lanczos-Lovelock action into a new pair of surface and bulk terms, such that the surface term becomes the Wald entropy on a horizon and the bulk term is the energy density (which is the Arnowitt-Deser-Misner Hamiltonian density for Einstein gravity).We show that this new pair also obeys a holographic relationship, and we give a thermodynamic interpretation of this relation in this context. Since the bulk and surface terms, in this decomposition, are related to the energy and entropy, the holographic condition can be thought of as analogous to inverting the expression for entropy given as a function of energy S = S(E, V) to obtain the energy E = E(S, V) in terms of the entropy in a normal thermodynamic system. Thus the holographic nature of the action allows us to relate the descriptions of the same system in terms of two different thermodynamic potentials. Some further possible generalizations and implications are discussed.
Ideal gas in a strong gravitational field: Area dependence of entropy
(American Physical Society, 2011-03-24) Kolekar, Sanved; Padmanabhan, T.
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.