Professor T. Padmanabhan
Permanent URI for this communityhttp://localhost:4000/handle/11007/2
Browse
11 results
Search Results
Item Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity(American physical society, 2012-03-06) Padmanabhan, T.; Kothawala, Dawood; Kolekar, SanvedWe 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.Item Hydrodynamics of the atoms of spacetime: Gravitational field equation is navier-stokes equation(World Scientific, 2011-05-30) Padmanabhan, T.There is consider able evidence to suggest that field equations of gravity have the same conceptual status as the equations of hydrodynamics or elasticity. We add further sup-port to this paradigm by showing that Einsteins field equations are identical in form to Navier –Stokes equations of hydrodynamics , when projected on to any null surface. In fact, these equations can be obtained directly by extremizing of entropy associated with the deformations of null surfaces thereby providing a completely thermodynamic route to gravitational field equations . Several curious features of this remarkable connection (including a phenomenon of dissipation without dissipation) are described and the implications for the emergent paradigm of gravity is highlighted.Item Gravity as elasticity of spacetime: A paradigm to understand horizon thermodynamics and cosmological constant(World Scientific Publishing Company, 2004-05-20) Padmanabhan, T.It is very likely that the quantum description of spacetime is quite di erent from what we perceive at large scales, l (G~=c3)1=2. The long wavelength description of spacetime, based on Einstein's equations, is similar to the description of a continuum solid made of a large number of microscopic degrees of freedom. This paradigm provides a novel interpretation of coordinate transformations as deformations of \spacetime solid" and allows one to obtain Einstein's equations as a consistency condition in the long wave- length limit. The entropy contributed by the microscopic degrees of freedom reduces to a pure surface contribution when Einstein's equations are satis ed. The horizons arises as \defects" in the \spacetime solid" (in the sense of well-de ned singular points) and contributes an entropy which is one quarter of the horizon area. Finally, the response of the microstructure to vacuum energy leads to a near cancellation of the cosmological constant, leaving behind a tiny uctuation which matches with the observed value.Item Gravity: A new holographic perspective(World Scientific Publishing Company, 2005-12-15) Padmanabhan, T.A general paradigm for describing classical (and semiclassical) gravity is presented. This approach brings to the centre-stage a holographic relationship between the bulk and surface terms in a general class of action functionals and provides a deeper insight into several aspects of classical gravity which have no explanation in the conventional approach. After highlighting a series of unresolved issues in the conventional approach to gravity, I show that (i) principle of equivalence, (ii) general covariance and (iii)a reasonable condition on the variation of the action functional, suggest a generic Lagrangian for semiclassical gravity of the form L=QabcdRabcd with ∇b Qabcd=0. The expansion of Qabcd in terms of the derivatives of the metric tensor determines the structure of the theory uniquely. The zeroth order term gives the Einstein-Hilbert action and the first order correction is given by the Gauss-Bonnet action. Any such Lagrangian can be decomposed into a surface and bulk terms which are related holographically. The equations of motion can be obtained purely from a surface term in the gravity sector. Hence the field equations are invariant under the transformation Tab → Tab + λ gab and gravity does not respond to the changes in the bulk vacuum energy density. The cosmological constant arises as an integration constant in this approach. The implications are discussed.Item Gravity and the thermodynamics of horizons(Elsevier Science Publishers, 2004-12-08) Padmanabhan, T.Spacetimes with horizons showa resemblance to thermodynamic systems and it is possible to associate the notions of temperature andentrop y with them. Several aspects of this connection are reviewedin a manner appropriate for broadread ership. The approach uses two essential principles: (a) the physical theories must be formulatedfor each observer entirely in terms of variables any given observer can access and(b) consistent formulation of quantum field theory requires analytic continuation to the complex plane. These two principles, when usedtogether 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 continuation, standardresults of quantum fieldtheory in curvedspacetimes with horizons can be obtainedd irectly (Sections 3–7). 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 8). The review emphasises the thermodynamic aspects of horizons, which couldbe obtainedfrom general principles andis expectedto remain valid, independent of the microscopicdescription (‘statistical mechanics’) of horizons.Item Event horizon of a Schwarzschild black hole: Magnifying glass for Planck length physics(American Physical Society, 1999-05-17) Padmanabhan, T.An attempt is made to describe the “thermodynamics” of semiclassical spacetime without specifying the detailed “molecular structure” of quantum spacetime, using the known properties of black holes. I give detailed arguments, essentially based on the behavior of quantum systems near the event horizon, which suggest that the event horizon of a Schwarschild black hole acts as a magnifying glass to probe Planck length physics even in those contexts in which the spacetime curvature is arbitrarily low. The quantum state describing a black hole, in any microscopic description of spacetime, has to possess certain universal form of density of states which can be ascertained from general considerations. Since a black hole can be formed from the collapse of any physical system with a low energy Hamiltonian H, it is suggested that the high energy behavior of any system should be described by a modified Hamiltonian of the form Hmod2=A2ln(1+H2/A2) where A2∝EP2. I also show that it is possible to construct several physical systems which have the black hole density of states and hence will be indistinguishable from a black hole as far as thermodynamic interactions are concerned. In particular, black holes can be thought of as one-particle excitations of a class of nonlocal field theories with the thermodynamics of black holes arising essentially from the asymptotic form of the dispersion relation satisfied by these excitations. These field theoretic models have correlation functions with a universal short distance behavior, which translates into the generic behavior of semiclassical black holes. Several implications of this paradigm are discussed.Item 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.Item Quantum structure of spacetime and entropy of schwarschild black holes(American Physical Society, 1998-01-05) Padmanabhan, T.The gap between a microscopic theory for quantum spacetime and the semiclassical physics of Schwarschild black holes is bridged by treating the black hole spacetimes as highly excited states of a class of nonlocal field theories. All of the black hole thermodynamics are shown to arise from an asymptotic form of the dispersion relation satisfied by the elementary excitations of these field theories. These models involve, quite generically, fields which are (i) smeared over regions of the order of Planck length and (ii) possess correlation functions which have universal short distance behavior.Item On the validity of the geodesic motion near a black hole: A clarification(Springer, 1982-03-13) Dadhich, Naresh; Padmanabhan, T.Ot has recently been claimed by Tangherlini that the concept of a test particle following a geodesic breaks down near the Schwarzschild event horizon. We argue that this claim is not valid.Item On the quantum structure of horizons(Elsevier Science Publishers, 1986-05-29) Padmanabhan, T.It was shown by 't Hooft that a black hole event horizon provades a natural cutoff length for sermclassacal wave modes Here at is shown that tbas result as true m any spacetlme with a horizon.