Scaling Limit of the Noncommutative Black Hole

Details Scaling Limit of the Noncommutative Black Hole Scaling Limit of the Noncommutative Black Hole

2010-09-27

arxiv.org/abs/1009.5406v1

J.Phys.Conf.Ser.284:012003,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, 3 figures with several pdf graphics

Scientific paper

10.1088/1742-6596/284/1/012003

We show that the recent `quantum' black hole wave operator in the $\kappa$-Minkowski or bicrossproduct model quantum spacetime has a natural scaling limit $\lambda_p\to 0$ at the event horizon. Here $\lambda_p$ is the Planck time and the geometry at the event horizon in Planck length is maintained at the same time as the limit is taken, resulting in a classical theory with quantum gravity remnants. Among the features is a frequency-dependent `skin' of some $\omega\over\nu$ Planck lengths just inside the event horizon for $\omega>0$ and just outside for $\omega<0$, where $\nu$ is the frequency associated to the Schwarzschild radius. We use bessel and hypergeometric functions to analyse propagation through the event horizon and skin in both directions. The analysis confirms a finite redshift at the horizon for positive frequency modes in the exterior.

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