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Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons

Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons,10.1103/PhysRevD.82.044050,Physical Review D,Jonathan Engle,Karim

Black hole entropy from the SU(2)-invariant formulation of type I isolated horizons   (Citations: 5)
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A detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2) invariant formulation where the (effective) horizon degrees of freedom are described by an SU(2) Chern-Simons theory. This leads to a more transparent description of the quantum theory in the context of loop quantum gravity and modifications of the form of the horizon entropy.
Journal: Physical Review D - PHYS REV D , vol. 82, no. 4, 2010
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    • ...More precisely, in the passage from Palatini-like variables to connection variables that is necessary for the description of the horizon degrees of freedom in terms of Chern-Simons theory (central for the quantization), an ambiguity parameter arises [9, 10]...
    • ...In [9, 10], we have shown that the level k and the area a can be considered as independent variables...
    • ...This paper has been devoted to the calculation of leading and sub-leading terms of the SU(2) black hole entropy in Loop Quantum Gravity when the black hole is spherically symmetric [8, 9] and when it is distorted [10]...
    • ...To reach this aim, we derived first, by means of the recoupling theory of the quantum group Uq(su(2)), a new integral formula, resulting to be very useful, for the dimension of the Hilbert space of SU(2) Chern-Simons theory on a punctured two-sphere, which enters the definition of the Hilbert space of the SU(2) spherically symmetric and distorted black hole as derived in [9, 10]...

    J. Engleet al. The SU(2) black hole entropy revisited

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