arXiv subjects

T. Padmanabhan

Publications and source records attributed to T. Padmanabhan.

At least 55 records · Page 3Linked to original sources

arXiv2016

Extracting information about the initial state from the black hole radiation

The crux of the black hole information paradox is related to the fact that the complete information about the initial state of a quantum field in a collapsing spacetime is not available to future asymptotic observers, belying the expectations from a unitary quantum theory. We study the imprints of the initial quantum state contained in a specific class of distortions of the black hole radiation and identify the classes of in-states which can be partially/fully reconstructed from the information contained within. Even for the general in-state, we can uncover some specific information. These results suggest that a \textit{classical} collapse scenario ignores this richness of information in the resulting spectrum and a consistent quantum treatment of the entire collapse process might allow us to retrieve much more information from the spectrum of the final radiation.

gr-qc↗

arXiv2015

One hundred years of General Relativity: Summary, Status and Prospects

General Relativity (GR) revolutionized the way we thought about gravity. After briefly describing the key successes of GR and its impact, I will discuss the major conceptual challenges it faces today. I conclude by outlining the prospective future directions of development, which hold the promise of deepening our understanding of the nature of gravity.

gr-qc↗

arXiv2015

Gravity and/is Thermodynamics

The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical systems. Restoring this symmetry to gravity and demanding that gravitational field equations should also remain invariant under the addition of a constant to a Lagrangian, leads to the interpretation of gravity as the thermodynamic limit of the kinetic theory of atoms of space. This approach selects, in a very natural fashion, Einstein's general relativity in $d=4$. Developing this paradigm at a deeper level, one can obtain the distribution function for the atoms of space and connect it up with the thermodynamic description of spacetime. This extension relies on a curious fact that the quantum spacetime endows each event with a finite area but zero volume. This approach allows us determine the numerical value of the cosmological constant and suggests a new perspective on cosmology.

gr-qc↗

arXiv2015

Distribution function of the Atoms of Spacetime and the Nature of Gravity

The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1) the metric cannot be varied in any extremum principle to obtain the field equations; and (2) the stress-tensor of matter should appear in the variational principle through the combination $T_{ab}n^an^b$ where $n_a$ is an auxiliary null vector field, which could be varied to get the field equations. This procedure selects naturally the Lanczos-Lovelock models of gravity in $D$-dimensions and Einstein's theory in $D=4$. Identifying $n_a$ with the normals to the null surfaces in the spacetime leads to a thermodynamic interpretation for gravity, in the macroscopic limit. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the ``atoms of spacetime'', which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area!

gr-qc↗

arXiv2015

Thermodynamical interpretation of the geometrical variables associated with null surfaces

The emergent gravity paradigm interprets gravitational field equations as describing the thermodynamic limit of the underlying statistical mechanics of microscopic degrees of freedom of the spacetime. The connection is established by attributing a heat density Ts to the null surfaces where T is the appropriate Davies-Unruh temperature and s is the entropy density. The field equations can be obtained from a thermodynamic variational principle which extremizes the total heat density of all null surfaces. The explicit form of s determines the nature of the theory. We explore the consequences of this paradigm for an arbitrary null surface and highlight the thermodynamic significance of various geometrical quantities. In particular, we show that: (a) A conserved current, associated with the time development vector in a natural fashion, has direct thermodynamic interpretation in all Lanczos-Lovelock models of gravity. (b) One can generalize the notion of gravitational momentum, introduced in arXiv 1506.03814 to all Lanczos-Lovelock models of gravity such that the conservation of the total momentum leads to the relevant field equations. (c) The thermodynamic variational principle which leads to the field equations of gravity can also be expressed in terms of the gravitational momentum in all Lanczos-Lovelock models. (d) Three different projections of gravitational momentum related to an arbitrary null surface in the spacetime lead to three different equations, all of which have thermodynamic interpretation. The first one reduces to a Navier-Stokes equation for the transverse drift velocity. The second can be written as a thermodynamic identity TdS = dE + P dV. The third describes the time evolution of the null surface in terms of suitably defined surface and bulk degrees of freedom. The implications are discussed.

gr-qc↗

arXiv2015

Gravitational field equations near an arbitrary null surface expressed as a thermodynamic identity

Previous work has demonstrated that the gravitational field equations in all Lanczos-Lovelock models imply a thermodynamic identity TdS=dE+PdV (where the variations are interpreted as changes due to virtual displacement along the affine parameter) in the near-horizon limit in static spacetimes. Here we generalize this result to any arbitrary null surface in an arbitrary spacetime and show that certain components of the Einstein's equations can be expressed in the form of the above thermodynamic identity. We also obtain an explicit expression for the thermodynamic energy associated with the null surface. Under appropriate limits, our expressions reduce to those previously derived in the literature. The components of the field equations used in obtaining the current result are orthogonal to the components used previously to obtain another related result, viz. that some components of the field equations reduce to a Navier-Stokes equation on any null surface, in any spacetime. We also describe the structure of Einstein's equations near a null surface in terms of three well-defined projections and show how the different results complement each other.

gr-qc↗

arXiv2015

Indistinguishability of thermal and quantum fluctuations

The existence of Davies-Unruh temperature in a uniformly accelerated frame shows that quantum fluctuations of the inertial vacuum state appears as thermal fluctuations in the accelerated frame. Hence thermodynamic experiments cannot distinguish between phenomena occurring in a thermal bath of temperature T in the inertial frame from those in a frame accelerating through inertial vacuum with the acceleration $a=2πT$. We show that this indisguishability between quantum fluctuations and thermal fluctuations goes far beyond the fluctuations in the vacuum state. We show by an exact calculation, that the reduced density matrix for a uniformly accelerated observer when the quantum field is in a thermal state of temperature $T^\prime$ is symmetric between acceleration temperature $T = a/(2π)$ and the thermal bath temperature $T^\prime$. Thus thermal phenomena cannot distinguish whether (i) one is accelerating with $a = 2πT$ through a bath of temperature $T^\prime$ or (ii) accelerating with $a=2πT^\prime$ through a bath of temperature T. This shows that thermal and quantum fluctuations in an accelerated frame affect the observer in a symmetric manner. The implications are discussed.

gr-qc↗

arXiv2015

A quantum peek inside the black hole event horizon

We solve the Klein-Gordon equation for a scalar field, in the background geometry of a dust cloud collapsing to form a black hole, everywhere in the (1+1) spacetime: that is, both inside and outside the event horizon and arbitrarily close to the curvature singularity. This allows us to determine the regularized stress tensor expectation value, everywhere in the appropriate quantum state (viz., the Unruh vacuum) of the field. We use this to study the behaviour of energy density and the flux measured in local inertial frames for the radially freely falling observer at any given event. Outside the black hole, energy density and flux lead to the standard results expected from the Hawking radiation emanating from the black hole, as the collapse proceeds. Inside the collapsing dust ball, the energy densities of both matter and scalar field diverge near the singularity in both (1+1) and (1+3) spacetime dimensions; but the energy density of the field dominates over that of classical matter. In the (1+3) dimensions, the total energy (of both scalar field and classical matter) inside a small spatial volume around the singularity is finite (and goes to zero as the size of the region goes to zero) but the total energy of the quantum field still dominates over that of the classical matter. Inside the event horizon, but \textit{outside} the collapsing matter, freely falling observers find that the energy density and the flux diverge close to the singularity. In this region, even the integrated energy inside a small spatial volume enclosing the singularity diverges. This result holds in both (1+1) and (1+3) spacetime dimensions with a \emph{milder} divergence for the total energy inside a small region in (1+3) dimensions. These results suggest that the back-reaction effects are significant even in the region \emph{outside the matter but inside the event horizon}, close to the singularity.

gr-qc↗

arXiv2015

Momentum density of spacetime and the gravitational dynamics

I introduce a covariant four-vector $\mathcal{G}^a[v]$, which can be interpreted as the momentum density attributed to the spacetime geometry by an observer with velocity $v^a$, and describe its properties: (a) Demanding that the total momentum of matter plus geometry is conserved for all observers, leads to the gravitational field equations. Thus, how matter curves spacetime is entirely determined by this principle of momentum conservation. (b) The $\mathcal{G}^a[v]$ can be related to the gravitational Lagrangian in a manner similar to the usual definition of Hamiltonian in, say, classical mechanics. (c) Geodesic observers in a spacetime will find that the conserved total momentum vanishes on-shell. (d) The on-shell, conserved, total energy in a region of space, as measured by the comoving observers, will be equal to the total heat energy of the boundary surface. (e) The off-shell gravitational energy in a region will be the sum of the ADM energy in the bulk plus the thermal energy of the boundary. These results suggest that $\mathcal{G}^a[v]$ can be a useful physical quantity to probe the gravitational theories.

gr-qc↗

arXiv2015

Inertial non-vacuum states viewed from the Rindler frame

The appearance of the inertial vacuum state in Rindler frame has been extensively studied in the literature, both from the point of view of QFT developed using Rindler foliation and using the response of an Unruh-Dewitt Detector (UDD). In comparison, less attention has been devoted to the study of inertial non-vacuum states when viewed from the Rindler frame. We provide a comprehensive study of this issue in this paper. We first present a general formalism describing characterization of an arbitrary inertial state when described using (i) an arbitrary foliation and (ii) the response of UDD moving along an arbitrary trajectory. We use this formalism to explicitly compute the results for the Rindler frame and uniformly accelerated detectors. Any arbitrary inertial state will always have a thermal component in the Rindler frame with additional contributions arising from the non-vacuum nature of the inertial state. We classify the nature of the additional contributions in terms of functions characterizing the inertial state. We establish that for all physically well behaved normalizable inertial states, the correction terms decay with the energy of the Rindler mode so that the high frequency limit is dominated by the thermal noise. However, inertial states which are not strictly normalizable, lead to a constant contribution at all high frequencies in the Rindler frame. A similar behavior arises in the response of the UDD as well. In the case of the detector response, we provide a physical interpretation for the constant contribution at high frequencies in terms of total detection rate of co-moving inertial detectors. We discuss two different approaches for defining a transition rate for the UDD, when the two-point function lacks the time translation invariance and discuss several features of different definitions of transition rates. The implications are discussed.

gr-qc↗

arXiv2014

Geometrical variables with direct thermodynamic significance in Lanczos-Lovelock gravity

It has been shown in an earlier work [arXiv:1303.1535] that there exists a pair of canonically conjugate variables $(f^{ab},N^a_{bc})$ in general relativity which also act as thermodynamically conjugate variables on any horizon. In particular their variations $(f^{bc}δN^a_{bc}, N^a_{bc}δf^{bc})$, which occur in the surface term of the Einstein-Hilbert action, when integrated over a null surface, have direct correspondence with $(SδT,TδS)$ where $(T,S)$ are the temperature and entropy. We generalize these results to Lanczos-Lovelock models in this paper. We identify two such variables in Lanczos-Lovelock models such that (a) our results reduce to that of general relativity in the appropriate limit and (b) the variation of surface term in the action, when evaluated on a null surface, has direct thermodynamic interpretation as in the case of general relativity. The variations again correspond to $SδT$ and $TδS$ where $S$ is now the appropriate Wald entropy for the Lanczos-Lovelock model. The implications are discussed.

gr-qc↗

arXiv2014

Evolution of Spacetime arises due to the departure from Holographic Equipartition in all Lanczos-Lovelock Theories of Gravity

In the case of general relativity one can interpret the Noether charge in any bulk region as the heat content $TS$ of its boundary surface. Further, the time evolution of spacetime metric in Einstein's theory arises due to the difference $(N_{sur}-N_{bulk})$ of suitably defined surface and bulk degrees of freedom. We show that this thermodynamic interpretation generalizes in a natural fashion to all Lanczos-Lovelock models of gravity. The Noether charge, related to time evolution vector field, in a bulk region of space is equal to the heat content $TS$ of the boundary surface with the temperature $T$ defined using local Rindler observers and $S$ being the Wald entropy. Using the Wald entropy to define the surface degrees of freedom $N_{sur}$ and Komar energy density to define the bulk degrees of freedom $N_{bulk}$, we can also show that the time evolution of the geometry is sourced by $(N_{sur}-N_{bulk})$. When it is possible to choose the foliation of spacetime such that metric is independent of time, the above dynamical equation yields the holographic equipartition for Lanczos-Lovelock gravity with $N_{sur}=N_{bulk}$. The implications are discussed.

gr-qc↗

arXiv2014

Grin of the Cheshire cat: Entropy density of spacetime as a relic from quantum gravity

There is considerable evidence to suggest that the field equations of gravity have the same status as, say, the equations describing an emergent phenomenon like elasticity. In fact, it is possible to derive the field equations from a thermodynamic variational principle in which a set of normalized vector fields are varied rather than the metric. We show that this variational principle can arise as a low energy ($L_P = (G\hbar/c^3)^{1/2} \to 0$) relic of a plausible nonperturbative effect of quantum gravity, viz. the existence of a zero-point-length in the spacetime. Our result is nonperturbative in the following sense: If we modify the geodesic distance in a spacetime by introducing a zero-point-length, to incorporate some effects of quantum gravity, and take the limit $L_P \to 0$ of the Ricci scalar of the modified metric, we end up getting a nontrivial, leading order ($L_P$ - independent) term. \textit{This term is identical to the expression for entropy density of spacetime used previously in the emergent gravity approach.} This reconfirms the idea that the microscopic degrees of freedom of the spacetime, when properly described in the full theory, could lead to an effective description of geometry in terms of a thermodynamic variational principle. This is conceptually similar to the emergence of thermodynamics from mechanics of, say, molecules. The approach also has important implications for cosmological constant which are briefly discussed.

gr-qc↗

arXiv2014

Quantum Evolution Leading to Classicality: A Concrete Example

Can certain degrees of freedom of a closed physical system, described by a time-independent Hamiltonian, become more and more classical as they evolve from some state? This question is important because our universe seems to have done just that! We construct an explicit, simple, example of such a system with just two degrees of freedom, of which one achieves `spontaneous classicalization'. It starts from a quantum state and under the usual Hamiltonian evolution, becomes more and more classical (in a well-defined manner in terms of the Wigner function) as time progresses. This is achieved without the usual procedures of integrating out a large number of environmental degrees of freedom or conventional decoherence. We consider different ranges of parameter space and identify the conditions under which spontaneous classicalization occurs in our model. The mutual interaction between the sub-systems of a larger system can indeed drive some of the subsystems to a classical configuration, with a phase space trajectory of evolution. We also argue that the results of our toy model may well be general characteristics of certain class of interacting systems. Several implications are discussed.

gr-qc↗

arXiv2014

General Relativity from a Thermodynamic Perspective

I show that the gravitational dynamics in a bulk region of space can be connected to a thermodynamic description in the boundary of that region, thereby providing clear physical interpretations of several mathematical features of classical general relativity: (1) The Noether charge contained in a bulk region, associated with a specific time evolution vector field, has a direct thermodynamic interpretation as the gravitational heat content of the boundary surface. (2) This result, in turn, shows that all static spacetimes maintain holographic equipartition; in these spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk. (3) In a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of bulk and boundary degrees of freedom. It is this departure from the holographic equipartition which drives the time evolution of the spacetime. (4) When the equations of motion hold, the (naturally defined) total energy of the gravity plus matter within a bulk region, will be equal to the boundary heat content. (5) After motivating the need for an alternate description of gravity (if we have to solve the cosmological constant problem), I describe a thermodynamic variational principle based on null surfaces to achieve this goal. The concept of gravitational heat density of the null surfaces arises naturally from the Noether charge associated with the null congruence. The null surface variational principle, in fact, extremises the total heat content of the matter plus gravity system. Several variations on this theme and implications are described. [Abridged]

gr-qc↗

arXiv2014

Emergent Gravity Paradigm: Recent Progress

Research during the last one decade or so suggests that the gravitational field equations in a large class of theories (including, but not limited to, general relativity) have the same status as the equations of, say, gas dynamics or elasticity. This paradigm provides a refreshingly different way of interpreting spacetime dynamics and highlights the fact that several features of classical gravitational theories have direct thermodynamic interpretation. I review the recent progress in this approach, achieved during the last few years.

gr-qc↗

arXiv2014

Zero modes and divergence of entanglement entropy

We investigate the cause of the divergence of the entanglement entropy for the free scalar fields in $(1+1)$ and $(D + 1)$ dimensional space-times. In a canonically equivalent set of variables, we show explicitly that the divergence in the entanglement entropy of the continuum field in $(1 + 1)-$ dimensions is due to the accumulation of large number of near-zero frequency modes as opposed to the commonly held view of divergence having UV origin. The feature revealing the divergence in zero modes is related to the observation that the entropy is invariant under a hidden scaling transformation even when the Hamiltonian is not. We discuss the role of dispersion relations and the dimensionality of the space-time on the behavior of entanglement entropy.

hep-th↗

arXiv2014

Entropy density of spacetime from the zero point length

It is possible to obtain the gravitational field equations in a large class of theories from a thermodynamic variational principle which uses the gravitational heat density $\mathcal{S}_g$ associated with null surfaces. This heat density is related to the discreteness of spacetime at Planck scale, $L_P^2 = (G\hbar / c^3)$, which assigns $A_{\perp}/L_P^2$ degrees of freedom to any area $A_{\perp}$. On the other hand, it is also known that the surface term $K\sqrt{h}$ in the gravitational action principle correctly reproduces the heat density of the null surfaces. We provide a link between these ideas by obtaining $\mathcal{S}_g$, used in emergent gravity paradigm, from the surface term in the action in Einstein's gravity. This is done using the notion of a nonlocal qmetric -- introduced recently [arXiv:1307.5618, arXiv:1405.4967] -- which allows us to study the effects of zero-point-length of spacetime at the transition scale between quantum and classical gravity. Computing $K\sqrt{h}$ for the qmetric in the appropriate limit directly reproduces the entropy density $\mathcal{S}_g$ used in the emergent gravity paradigm.

gr-qc↗