General Relativity and Gravitation

, Volume 44, Issue 5, pp 1199–1205 | Cite as

Quantum geometry and entanglement entropy of a black hole

  • L. Mullick
  • P. Bandyopadhyaya
Research Article


We have studied here black hole entropy in the framework of quantum geometry. It is pointed out that the black hole radiation consistent with Hawking spectrum can be realized as an effect of quantum geometry using a dynamical formalism for diffeomorphism invariance which envisages a discretized unit of time in the Planck scale. This formalism suggests that torsion acts within a quantized area unit (area bit) associated with a loop and this eventually forbids the Hamiltonian constraint to be satisfied for a finite loop size. We assign a spin with torsion in each area bit and entanglement entropy of a black hole is computed in terms of the entanglement entropy of this spin system. We have derived the Bekenstein-Hawking entropy along with a logarithmic correction term with a specific coefficient. Also we have shown that the Bekenstein-Hawking entropy can be formulated in terms of the Noether charge associated with a diffeomorphism invariant Lagrangian.


Quantum geometry Entanglement entropy Black hole 


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsHiralal Mazumdar Memorial College for WomenDakshineswar, KolkataIndia
  2. 2.Physics and Applied Mathematics UnitIndian Statistical InstituteKolkataIndia

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