Towards noncommutative quantum black holes

Lopez-Dominguez, J. C.; Obregón, O.; Sabido, M.; Ramı́rez, C.

doi:10.1103/physrevd.74.084024

Cited by 75 publications

(91 citation statements)

References 42 publications

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“…It might be mentioned that there are other approaches [13,14,15,16] of introducing noncommutativity in curved space time metric. Contrary to the present approach, however, there the metric is not spherically symmetric.…”

Section: Schwarzschild Black Hole In Noncommutative Spacementioning

confidence: 99%

Noncommutative black hole thermodynamics

2008

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Abstract:We give a general derivation, for any static spherically symmetric metric, of the relation T h = K 2π connecting the black hole temperature (T h ) with the surface gravity (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. IntroductionClassical general relativity gives the concept of black hole from which nothing can escape. This picture was changed dramatically when Hawking[1] incorporated the quantum nature into this classical problem. In fact he showed that black hole radiates a spectrum of particles which is quite analogous with a thermal black body radiation. Thus Hawking radiation emerges as a nontrivial consequence of combining gravity and quantum mechanics.After his original derivation which was based on the calculation of Bogoliubov coefficients in the asymptotic states, Hawking together with Hartle[2] gave a simpler, path integral derivation. Physically, black hole radiation can be interpreted as the quantum tunneling of vacuum fluctuations through the horizon. This picture was mathematically formulated in [3]. An important step of this method is the calculation of tunneling amplitude from which the Hawking temperature is obtained. This is done either by using the trajectory of a null geodesic [3] or by solving the Hamilton-Jacobi equation to calculate the imaginary part of the action variable [4].The tunneling approach was subsequently used to compute the Hawking temperature for black holes with different types of metric [5]. The results have agreed with the general *

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Section: Schwarzschild Black Hole In Noncommutative Spacementioning

confidence: 99%

Noncommutative black hole thermodynamics

2008

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“…Indeed, the metric (1) can be mapped by the KS metric [5,6], which, in the Misner parametrization, can be written as…”

Section: Phase-space Noncommutative Quantum Cosmologymentioning

confidence: 99%

“…In Ref. [6] only configuration space noncommutativity was considered: [Ω, β] = iθ, where Ω, β are the scale factors and θ is a real constant. However, it is found in the cosmological and BH context, that this type of noncommutativity does not lead to any new qualitative features with respect to the commutative problem.…”

Section: Introductionmentioning

confidence: 99%

Singularity problem and phase-space noncanonical noncommutativity

et al. 2010

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The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the Heisenberg-Weyl algebra. An integral of motion is used to factorize the wave function into an oscillatory part and a function of a configuration space variable. The latter is shown to be normalizable using asymptotic arguments. It is then shown that on the hypersufaces of constant value of the argument of the wave function's oscillatory piece, the probability vanishes in the vicinity of the black hole singularity.

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“…In recent years, in the search of suitable candidates of quantum gravity, that is, in the quest to understand microscopic states of black holes [26,27], a number of quantum corrections to BekensteinHawking (BH) entropy S BH have arisen. We are interested not only in the possible thermodynamic implications of quantum corrections to this entropy but also in the consequences of introducing noncommutativity as proposed by Obregon et al [28], considering that coordinates of minisuperspace are noncommutative. From a variety of approaches that have emerged in recent years to correct S BH , logarithmic ones are a popular choice among those.…”

Section: Schwarzschild and Kerr Black Holesmentioning

confidence: 99%

Deformed Phase Space in Cosmology and Black Holes

Mena-Barboza¹,

Escamilla-Herrera²,

Lopez-Dominguez³

et al. 2017

Trends in Modern Cosmology

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It is well known that one way to study canonical quantum cosmology is through the Wheeler DeWitt (WDW) equation where the quantization is performed on the minisuperspace variables. The original ideas of a deformed minisuperspace were done in connection with noncommutative cosmology, by introducing a deformation into the minisuperspace in order to incorporate an effective noncommutativity. Therefore, studying solutions to Cosmological models through the WDW equation with deformed phase space could be interpreted as studying quantum effects to Cosmology. In this chapter, we make an analysis of scalar field cosmology and conclude that under a phase space transformation and imposed restriction, the effective cosmological constant is positive. On the other hand, obtaining the wave equation for the noncommutativity KantowskiSachs model, we are able to derive a modified noncommutative version of the entropy. To that purpose, the Feynman-Hibbs procedure is considered in order to calculate the partition function of the system.

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Towards noncommutative quantum black holes

Cited by 75 publications

References 42 publications

Noncommutative black hole thermodynamics

Noncommutative black hole thermodynamics

Singularity problem and phase-space noncanonical noncommutativity

Deformed Phase Space in Cosmology and Black Holes

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