arXiv subjects

Dawood Kothawala

Publications and source records attributed to Dawood Kothawala.

50 records · Page 3Linked to original sources

arXiv2013

Box of Ideal Gas in Free Fall

We study the \textit{quantum} partition function of non-relativistic, ideal gas in a (non-cubical) box falling freely in arbitrary curved spacetime with centre 4-velocity u^a. When perturbed energy eigenvalues are properly taken into account, we find that corrections to various thermodynamic quantities include a very specific, sub-dominant term which is independent of \textit{kinematic} details such as box dimensions and mass of particles. This term is characterized by the dimensionless quantity, Ξ=R_00 Λ^2, where R_00=R_ab u^a u^b and Λ=β\hbar c, and, quite intriguingly, produces Euler relation of homogeneity two between entropy and energy -- a relation familiar from black hole thermodynamics.

gr-qc↗

arXiv2012

Generalized uncertainty principles and quantum field theory

Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm βp^2$. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green's function for $f_+$ exhibits a remarkable transition from Lorentz to Galilean invariance, whereas for $f_-$ such modes effectively do not propagate. For both cases Lorentz invariance is recovered at long wavelengths.

hep-th↗

arXiv2012

Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity

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, previously introduced by Padmanabhan in the context of GR, to study off-shell entropy of a class of 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.

gr-qc↗

arXiv2012

Holographic repulsion and confinement in gauge theory

We show that for asymptotically anti-deSitter backgrounds with negative energy, such as the AdS soliton and regulated negative mass AdS-Schwarzshild metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a Coulomb to confinement transition. We also show that the quark-antiquark ($q \bar q$) potential can be interpreted as affine time along null geodesics on the minimal string world sheet,and that its intrinsic curvature provides a signature of transition to confinement phase. The result demonstrates a UV/IR relation in that the boundary separation of the $q \bar{q}$ pair exhibits an inverse relationship with the radial descent of the world sheet into the bulk. Our results suggest a generic (holographic) relationship between confinement in gauge theory and repulsive gravity, which in turn is connected with singularity avoidance in quantum gravity.

hep-th↗

arXiv2012

Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity

We study the membrane paradigm for horizons in Lanczos-Lovelock models of gravity in arbitrary D dimensions and find compact expressions for the pressure p and viscosity coefficients ηand ζof the membrane fluid. We show that the membrane pressure is intimately connected with the Noether charge entropy S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature and A is the area of the horizon. Similarly, the viscosity coefficients are expressible in terms of entropy and quasi-local energy associated with the horizons. The bulk and shear viscosity coefficients are found to obey the relation ζ=-2(D-3)/(D-2)η.

gr-qc↗

arXiv2011

Duality of force laws and Conformal transformations

As was first noted by Isaac Newton, the two most famous ellipses of classical mechanics, arising out of the force laws F~r and F~1/r^2, can be mapped onto each other by changing the location of center-of-force. What is perhaps less well known is that this mapping can also be achieved by the complex transformation, z -> z^2. We give a simple derivation of this result (and its generalization) by writing the Gaussian curvature in its "covariant" form, and then changing the \emph{metric} by a conformal transformation which "mimics" this mapping of the curves. The final result also yields a relationship between Newton's constant G, mass M of the central attracting body in Newton's law, the energy E of the Hooke's law orbit, and the angular momenta of the two orbits. We also indicate how the conserved Laplace-Runge-Lenz vector for the 1/r^2 force law transforms under this transformation, and compare it with the corresponding quantities for the linear force law. Our main aim is to present this duality in a geometric fashion, by introducing elementary notions from differential geometry.

physics.class-ph↗

arXiv2011

The thermodynamic structure of Einstein tensor

We analyze the generic structure of Einstein tensor projected onto a 2-D spacelike surface S defined by unit timelike and spacelike vectors u_i and n_i respectively, which describe an accelerated observer (see text). Assuming that flow along u_i defines an approximate Killing vector X_i, we then show that near the corresponding Rindler horizon, the flux j_a=G_ab X^b along the ingoing null geodesics k_i normalised to have unit Killing energy, given by j . k, has a natural thermodynamic interpretation. Moreover, change in cross-sectional area of the k_i congruence yields the required change in area of S under virtual displacements \emph{normal} to it. The main aim of this note is to clearly demonstrate how, and why, the content of Einstein equations under such horizon deformations, originally pointed out by Padmanabhan, is essentially different from the result of Jacobson, who employed the so called Clausius relation in an attempt to derive Einstein equations from such a Clausius relation. More specifically, we show how a \emph{very specific geometric term} [reminiscent of Hawking's quasi-local expression for energy of spheres] corresponding to change in \emph{gravitational energy} arises inevitably in the first law: dE_G/dλ α\int_{H} dA R_(2) (see text) -- the contribution of this purely geometric term would be missed in attempts to obtain area (and hence entropy) change by integrating the Raychaudhuri equation.

gr-qc↗

arXiv2010

Response of Unruh-DeWitt detector with time-dependent acceleration

It is well known that a detector, coupled linearly to a quantum field and accelerating through the inertial vacuum with a constant acceleration $g$, will behave as though it is immersed in a radiation field with temperature $T=(g/2π)$. We study a generalization of this result for detectors moving with a time-dependent acceleration $g(τ)$ along a given direction. After defining the rate of excitation of the detector appropriately, we evaluate this rate for time-dependent acceleration, $g(τ)$, to linear order in the parameter $η= \dot g / g^2$. In this case, we have three length scales in the problem: $g^{-1}, (\dot g/g)^{-1}$ and $ω^{-1}$ where $ω$ is the energy difference between the two levels of the detector at which the spectrum is probed. We show that: (a) When $ω^{-1} \ll g^{-1} \ll (\dot g/g)^{-1}$, the rate of transition of the detector corresponds to a slowly varying temperature $T(τ) = g(τ)/2 π$, as one would have expected. (b) However, when $ g^{-1}\ll ω^{-1} \ll (\dot g/g)^{-1}$, we find that the spectrum is modified \textit{even at the order $\mathcal{O}(η)$}. This is counter-intuitive because, in this case, the relevant frequency does not probe the rate of change of the acceleration since $(\dot g/g) \ll ω$ and we certainly do not have deviation from the thermal spectrum when $\dot g =0$. This result shows that there is a subtle discontinuity in the behaviour of detectors with $\dot g = 0$ and $\dot g/g^2$ being arbitrarily small. We corroborate this result by evaluating the detector response for a particular trajectory which admits an analytic expression for the poles of the Wightman function.

gr-qc↗

arXiv2010

Quantum gravitational corrections to the propagator in spacetimes with constant curvature

The existence of a minimal and fundamental length scale, say, the Planck length, is a characteristic feature of almost all the models of quantum gravity. The presence of the fundamental length is expected to lead to an improved ultra-violet behavior of the semi-classical propagators. The hypothesis of path integral duality provides a prescription to evaluate the modified propagator of a free, quantum scalar field in a given spacetime, taking into account the existence of the fundamental length in a locally Lorentz invariant manner. We use this prescription to compute the quantum gravitational modifications to the propagators in spacetimes with constant curvature, and show that: (i) the modified propagators are ultra-violet finite, and (ii) the modifications are non-perturbative in the Planck length. We discuss the implications of our results.

hep-th↗

arXiv2009

Path integral duality modified propagators in spacetimes with constant curvature

The hypothesis of path integral duality provides a prescription to evaluate the propagator of a free, quantum scalar field in a given classical background, taking into account the existence of a fundamental length, say, the Planck length, $\lp$, in a {\it locally Lorentz invariant manner}. We use this prescription to evaluate the duality modified propagators in spacetimes with {\it constant curvature} (exactly in the case of one spacetime, and in the Gaussian approximation for another two), and show that: (i) the modified propagators are ultra violet finite, (ii) the modifications are {\it non-perturbative} in $\lp$, and (iii) $\lp$ seems to behave like a `zero point length' of spacetime intervals such that $ł< σ^2(x,x')\r> = ł[σ^{2}(x,x')+ {\cal O}(1) \lp^2 \r]$, where $σ(x,x')$ is the geodesic distance between the two spacetime points $x$ and $x'$, and the angular brackets denote (a suitable) average over the quantum gravitational fluctuations. We briefly discuss the implications of our results.

hep-th↗

arXiv2009

Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries

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.

gr-qc↗

arXiv2008

Is gravitational entropy quantized ?

In Einstein's gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equally spaced spectrum for large quantum numbers. But in more general theories (like, for e.g, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is \emph{not} proportional to area and the question arises as to which of the two (if at all) will have this property. We give a general argument that in all Lanczos-Lovelock theories of gravity, it is the \emph{entropy} that has equally spaced spectrum. In the case of Gauss-Bonnet gravity, we use the asymptotic form of quasi normal mode frequencies to explicitly demonstrate this result. Hence, the concept of a quantum of area in Einstein Hilbert (EH) gravity needs to be replaced by a concept of \emph{quantum of entropy} in a more general context.

gr-qc↗

arXiv2007

Hawking radiation as tunneling for spherically symmetric black holes: A generalized treatment

We present a derivation of Hawking radiation through tunneling mechanism for a general class of asymptotically flat, spherically symmetric spacetimes. The tunneling rate $Γ\sim \exp{(ΔS)}$ arises as a consequence of the first law of thermodynamics, TdS=dE + PdV. Therefore, this approach demonstrates how tunneling is intimately connected with the first law of thermodynamics through the principle of conservation of energy. The analysis is also generally applicable to any reasonable theory of gravity so long as the first law of thermodynamics for horizons holds in the form, TdS=dE + PdV.

gr-qc↗

arXiv2006

Einstein's equations as a thermodynamic identity: The cases of stationary axisymmetric horizons and evolving spherically symmetric horizons

There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field equations near any spherically symmetric horizon as a thermodynamic identity TdS = dE + PdV. We study this approach further and generalize the results to two more generic cases within the context of general relativity: (i) stationary axis-symmetric horizons and (ii) time dependent evolving horizons. In both the cases, the near horizon structure of Einstein equations can be expressed as a thermodynamic identity under the virtual displacement of the horizon. This result demonstrates the fact that the thermodynamic interpretation of gravitational dynamics is not restricted to spherically symmetric or static horizons but is quite generic in nature and indicates a deeper connection between gravity and thermodynamics.

gr-qc↗