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Register a new userNoncommutative Black Hole Thermodynamics
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Added by
Bibhas Majhi Ranjan
Publication date
2008
fields
Physics
and research's language is
English
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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.
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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 $r_h=3.0sqrt{theta}$.
In this paper we investigate quasinormal modes (QNM) for a scalar field around a noncommutative Schwarzschild black hole. We verify the effect of noncommutativity on quasinormal frequencies by applying two procedures widely used in the literature. The first is the Wentzel-Kramers-Brillouin (WKB) approximation up to sixth order. In the second case we use the continuous fraction method developed by Leaver. We find that the quasinormal frequencies obtained for nonzero noncommutative parameter resemble those of the Reissner-Nordstr{o}m geometry. Besides, we also show that due to noncommutativity, the shadow radius is reduced when we increase the noncommutative parameter. In addition, we find that the shadow radius is nonzero even at the zero mass limit for finite noncommutative parameter.
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