Effective Lagrangian for Quantum Black Holes

Details Effective Lagrangian for Quantum Black Holes Effective Lagrangian for Quantum Black Holes

1995-04-14

arxiv.org/abs/gr-qc/9504020v2

Nucl.Phys.B451:677-698,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

24 pages, Latex, Nucl. Phys. B, to appear

Scientific paper

10.1016/0550-3213(95)00351-R

We discuss the most general effective Lagrangian obtained from the assumption that the degrees of freedom to be quantized, in a black hole, are on the horizon. The effective Lagrangian depends only on the induced metric and the extrinsic curvature of the (fluctuating) horizon, and the possible operators can be arranged in an expansion in powers of $\mpl/M$, where $\mpl$ is the Planck mass and $M$ the black hole mass. We perform a semiclassical expansion of the action with a formalism which preserves general covariance explicitly. Quantum fluctuations over the classical solutions are described by a single scalar field living in the 2+1 dimensional world-volume swept by the horizon, with a given coupling to the background geometry. We discuss the resulting field theory and we compute the black hole entropy with our formalism.

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