Abstract
Hawking radiation from the black hole in Hořava–Lifshitz gravity is discussed by a reformulation of the tunneling method given in Banerjee and Majhi (2009) [17]. Using a density matrix technique the radiation spectrum is derived which is identical to that of a perfect black body. The temperature obtained here is proportional to the surface gravity of the black hole as occurs in usual Einstein gravity. The entropy is also derived by using the first law of black hole thermodynamics. Finally, the spectrum of entropy/area is obtained. The latter result is also discussed from the viewpoint of quasi-normal modes. Both methods lead to an equispaced entropy spectrum, although the value of the spacing is not the same. On the other hand, since the entropy is not proportional to the horizon area of the black hole, the area spectrum is not equidistant, a finding which also holds for the Einstein–Gauss–Bonnet theory.
Highlights
Inspired by condensed matter models of dynamical critical system, Horava proposed a new four dimensional theory of gravity [1], popularly known as Horava-Lifshitz gravity
We find that the distribution function exactly matches with the black body radiation with a temperature proportional to the surface gravity of the black hole
Some aspects of the quantum nature of black holes were studied for the black hole solution recently found in Horava-Lifshitz gravity
Summary
Inspired by condensed matter models of dynamical critical system, Horava proposed a new four dimensional theory of gravity [1], popularly known as Horava-Lifshitz gravity. We will discuss the Hawking effect by a physically intuitive picture - a reformulation [17, 18] of the standard tunneling formalism 2 [19, 20, 21] The advantage of this approach [17, 18] is that, in contrast to [19, 20, 27, 28, 29], the spectrum is directly obtained instead of just the temperature. In this case the entropy is not proportional to the area of the event horizon as happens in Einstein gravity; rather it has an extra additive logarithmic term involving the area Another purpose of this paper is to study the nature of entropy/area spectrum of the HoravaLifshitz black hole. In section-2 a short discussion on the black hole solution of Horava-Lifshitz gravity and the expressions of the modes of the scalar particle as seen by an asymptotic observer are presented.
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