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Register a new userTowards Noncommutative Quantum Black Holes
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Added by
J. C. Lopez-Dominguez
Publication date
2006
fields
Physics
and research's language is
English
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In this paper we study noncommutative black holes. We use a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate the Hawkings temperature and entropy for the noncommutative Schwarzschild black hole.
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In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.
The evolution of black holes in confining boxes is interesting for a number of reasons, particularly because it mimics the global structure of Anti-de Sitter geometries. These are non-globally hyperbolic space-times and the Cauchy problem may only be well defined if the initial data is supplemented by boundary conditions at the time-like conformal boundary. Here, we explore the active role that boundary conditions play in the evolution of a bulk black hole system, by imprisoning a black hole binary in a box with mirror-like boundary conditions. We are able to follow the post-merger dynamics for up to two reflections off the boundary of the gravitational radiation produced in the merger. We estimate that about 15% of the radiation energy is absorbed by the black hole per interaction, whereas transfer of angular momentum from the radiation to the black hole is only observed in the first interaction. We discuss the possible role of superradiant scattering for this result. Unlike the studies with outgoing boundary conditions, both the Newman-Penrose scalars Psi_4 and Psi_0 are non-trivial in our setup, and we show that the numerical data verifies the expected relations between them.
We give a general derivation, for any static spherically symmetric metric, of the relation $T_h=frac{cal K}{2pi}$ connecting the black hole temperature ($T_h$) with the surface gravity ($cal K$), following the tunneling interpretation of Hawking radiation. This derivation is valid even beyond the semi classical regime i. e. when quantum effects are not negligible. The formalism is then applied to a spherically symmetric, stationary noncommutative Schwarzschild space time. The effects of back reaction are also included. For such a black hole the Hawking temperature is computed in a closed form. A graphical analysis reveals interesting features regarding the variation of the Hawking temperature (including corrections due to noncommutativity and back reaction) with the small radius of the black hole. The entropy and tunneling rate valid for the leading order in the noncommutative parameter are calculated. We also show that the noncommutative Bekenstein-Hawking area law has the same functional form as the usual one.
Using a graphical analysis, we show that for the horizon radius $r_hgtrsim 4.8sqrttheta$, the standard semiclassical Bekenstein-Hawking area law for noncommutative Schwarzschild black hole exactly holds for all orders of $theta$. We also give the corrections to the area law to get the exact nature of the Bekenstein-Hawking entropy when $r_h<4.8sqrttheta$ till the extremal point $r_h=3.0sqrt{theta}$.
We propose a correspondence between an Anyon Van der Waals fluid and a (2+1) dimensional AdS black hole. Anyons are particles with intermediate statistics that interpolates between a Fermi-Dirac statistics and a Bose-Einstein one. A parameter $alpha$ ($0<alpha<1$) characterizes this intermediate statistics of Anyons. The equation of state for the Anyon Van der Waals fluid shows that it has a quasi Fermi-Dirac statistics for $alpha > alpha_c$, but a quasi Bose-Einstein statistics for $alpha< alpha_c$. By defining a general form of the metric for the (2+1) dimensional AdS black hole and considering the temperature of the black hole to be equal with that of the Anyon Van der Waals fluid, we construct the exact form of the metric for a (2+1) dimensional AdS black hole. The thermodynamic properties of this black hole is consistent with those of the Anyon Van der Waals fluid. For $alpha< alpha_c$, the solution exhibits a quasi Bose-Einstein statistics. For $alpha > alpha_c$ and a range of values of the cosmological constant, there is, however, no event horizon so there is no black hole solution. Thus, for these values of cosmological constants, the AdS Anyon Van der Waals black holes have only quasi Bose-Einstein statistics.
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