Dawood Kothawala

Is gravitational entropy quantized

In Einsteins 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 example, in the black hole solutions of Gauss-Bonnet or Lanczos-Lovelock gravity) the horizon entropy is 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 entropy that has an equally-spaced spectrum. In the case of Gauss-Bonnet gravity, we use the asymptotic form of quasinormal mode frequencies to explicitly demonstrate this result. Hence, the concept of a quantum of area in Einstein-Hilbert gravity needs to be replaced by a concept of quantum of entropy in a more general context.

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 Td S= dE + Pd V. We study this approach further and generalize the results to two more generic cases: stationary axis-symmetric horizons and time dependent evolving horizons within the context of general relativity. 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.

Lanczos-Lovelock models of gravity

Lanczos–Lovelock models of gravity represent a natural and elegant generalization of Einstein’s theory of gravity to higher dimensions. They are characterized by the fact that the field equations only contain up to second derivatives of the metric even though the action functional can be a quadratic or higher degree polynomial in the curvature tensor. Because these models share several key properties of Einstein’s theory they serve as a useful set of candidate models for testing the emergent paradigm for gravity. This review highlights several geometrical and thermodynamical aspects of Lanczos–Lovelock models which have attracted recent attention.

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 Einsteins theory.

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

Abstract We present a derivation of Hawking radiation through tunneling mechanism for a general class of asymptotically flat, spherically symmetric spacetimes. The tunneling rate Γ ∼ exp ( Δ S ) arises as a consequence of the first law of thermodynamics, T d S = d E + P d V . 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, T d S = d E + P d V .

Response of Unruh-DeWitt detector with time-dependent acceleration

Abstract 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 / 2 π ) . 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 = g ˙ / g 2 . In this case, we have three length scales in the problem: g − 1 , ( 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 ≪ g − 1 ≪ ( 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 ≪ ω − 1 ≪ ( g ˙ / g ) − 1 , we find that the spectrum is modified even at the order O ( η ) . This is counter-intuitive because, in this case, the relevant frequency does not probe the rate of change of the acceleration since ( g ˙ / g ) ≪ ω and we certainly do not have deviation from the thermal spectrum when g ˙ = 0 . This result shows that there is a subtle discontinuity in the behavior of detectors with g ˙ = 0 and 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.

Spacetime with Zero Point Length is Two-Dimensional at the Planck Scale

It is generally believed that any quantum theory of gravity should have a generic feature—a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such that the spacetime acquires a zero-point-length

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

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