Entanglement Entropy Renormalization for the NC scalar field coupled to classical BTZ geometry

Abstract

In this work, we consider a noncommutative (NC) massless scalar field coupled to the classical nonrotational BTZ geometry. In a manner of the theories where the gravity emerges from the underlying scalar field theory, we study the effective action and the entropy derived from this noncommutative model. In particular, the entropy is calculated by making use of the two different approaches, the brick wall method and the heat kernel method designed for spaces with conical singularity. We show that the UV divergent structures of the entropy, obtained through these two different methods, agree with each other. It is also shown that the same renormalization condition that removes the infinities from the effective action can also be used to renormalize the entanglement entropy for the same system. Besides, the interesting feature of the NC model considered here is that it allows an interpretation in terms of an equivalent system comprising of a commutative massive scalar field, but in a modified geometry; that of the rotational BTZ black hole, the result that hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole.

28 pages; LaTex

References in corpus (15)

• A Gravity Theory on Noncommutative Spaces
• Entanglement entropy, conformal invariance and extrinsic geometry
• Kappa-Minkowski space-time and the star product realizations
• Twisted Statistics in kappa-Minkowski Spacetime
• Noncommutative Gravity
• Towards Noncommutative Quantum Black Holes
• Improved Z -> gamma gamma decay in the renormalizable gauge sector of the noncommutative standard model
• Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
• Noncommutative BTZ Black Hole and Discrete Time
• Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole
• Noncommutative Two Dimensional Gravities
• Effects of Noncommutativity on the Black Hole Entropy
• Entanglement entropy of two-dimensional Anti-de Sitter black holes
• Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
• Analogy between the Schwarzschild solution in a noncommutative gauge theory and the Reissner-Nordström metric

Cited by in corpus (10)

• Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole
• Noncommutativity and logarithmic correction to the black hole entropy
• Noncommutative correction to the entropy of charged BTZ black hole
• Three-dimensional AdS black holes in massive-power-Maxwell theor
• Quantum space and quantum completeness
• Tunneling of Hawking radiation for BTZ black hole revisited
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field
• Thermodynamics and phase transitions of $\kappa$-deformed Schwarzschild-AdS black holes
• Noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole