Using the brick-wall method we compute the statistical entropy of a scalar field in a nontrivial background, in two different cases. These backgrounds are generated by four- and five-dimensional black holes with four and three U(1) charges respectively. The Bekenstein entropy formula is generally obeyed, but corrections are discussed in the latter case.
Some thermodynamical properties of Lovelock gravity are discussed in several space-time dimensions, the holographic principle being one of the ingredients of the discussion. As it turns out, the area law and the brickwall method, though correct for the Einstein-Hilbert theory, may fail to work in general.Since the work of Bekenstein and Hawking [1,2] our knowlegde about black hole physics has improved quite considerably. Moreover, black hole physics is also the main gate towards understanding of gravity in extreme conditions, and as a consequence, of quantum gravity. This led t'Hooft and Susskind [3,4] to generalize the area law relating entropy and the area of a black hole to any gravitational system by means of the introduction of the holographic principle, which in the last few years turned into a powerful means to the understanding of possible ways towards the quantization of gravity.Under such a motivation, the holographic principle was put forward, suggesting that microscopic degrees of freedom that build up the gravitational dynamics do not reside in the bulk space-time but on its boundary [3,4].This principle is a large conceptual change in our thinking about gravity. Maldacena's conjecture on AdS/CFT correspondence [5] is the first example realizing such a principle. Subsequently, Witten [5] convincingly argued that the entropy, energy and temperature of CFT at high temperatures can be identified with the entropy, mass and Hawking temperature of the AdS black hole [6], which further supports the holographic principle. In cosmological settings, testing the holographic principle is somewhat subtle. Fischler and Susskind (FS) [7] have shown that for flat and open Friedmann-Lemaitre-Robertson-Walker(FLRW) universes the area of the particle horizon should bound the entropy on the backward-looking light cone. However violation of FS bound was found for closed FLRW universes. Various different modifications of the FS version of the holographic principle have been raised subsequently [8]. In addition to the study of holography in homogeneous cosmologies, attempts to generalize the holographic principle to a generic realistic inhomogeneous cosmological setting were carried out in [9].It is now natural to ask which premises should be forcefully fullfilled in order to acomodate the holographic principle. In particular, what kind of dynamics requires holography as an outcome. This could provide a mecha-
Thermal corrections to the entropy of black holes in the Lovelock gravity are calculated. As the thermodynamic behavior of the black holes of this theory falls into two classes, the thermodynamic quantities are computed in each case. Finally, the logarithmic prefactors are obtained in two different limits.
We discuss the validity of the holographic principle in a (4 + n) dimensional universe in an asymmetric inflationary phase. In such a case, the size of these extra dimensions should be in the submillimiter scale in order to conform to the phenomenological constraints. Indeed, using Gauss's law in (4 + n) dimensions it is possible to relate the Planck scale in the (4 + n) dimensional theory(M * ) with that of the 4-dimensional theory (M P l ) by means of the size of the n compactified dimensions (b 0 ). It is easy to find [5]Assuming the usual value M P l ≃ 10 19 GeV and M * ≃ 1 TeV, we find b 0 ∼
−17+30 n cm. For n = 2 we obtain the (reasonable) value b 0 ≃ 1 mm. We would thus find deviation from Newtonian gravitation in a range within experimental search in the near future.There are several papers discussing the theoretical and phenomenological aspects of this idea [2]. From the fundamental point of view, gravity can 1
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