Noncommutativity and logarithmic correction to the black hole entropy

Abstract

We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a $\kappa$-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding quantum effects in curved spacetime.

14 pages, slightly differs from the published JHEP version

References in corpus (7)

• Noncommutative Black Hole Thermodynamics
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Noncommutative D=4 gravity coupled to fermions
• Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Noncommutative BTZ Black Hole and Discrete Time
• Sub-leading contributions to the black hole entropy in the brick wall approach

Cited by in corpus (11)

• Constructing noncommutative black holes
• Noncommutative correction to the entropy of charged BTZ black hole
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Newtonian cosmology and Evolution of kappa-deformed universe
• Neutron Star in Quantized-space-time
• Influence of the cosmological constant on $\kappa$-deformed Neutron Star
• Non-commutative correction of ideal gas thermodynamics
• Entropy of black holes, charged probes and noncommutative generalization
• Hawking area law in quantum gravity
• Regularized Black Hole Solution from a New String Cloud Source
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes