On a quantum mechanical model of a black hole

Details On a quantum mechanical model of a black hole On a quantum mechanical model of a black hole

May 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990phlb..241..194b&link_type=abstract

Physics Letters B, Volume 241, Issue 2, p. 194-200.

Physics

25

Scientific paper

A quantum mechanical model of a Schwarzschild black hole is constructed. This model is based on the simplest classical model, namely, a spherical thin dust shell as a source for a black hole mass. Such a mechanical system has only one degree of freedom which is quantized. The Klein-Gordon-type equation obtained exhibits some interesting features. This equation is an equation in finite differences and not a differential equation. There are nonlocalities near the singularities (r = 0) and at the horizon. For the large black holes this equation can be approximated by an ordinary differential equation, which has one solution in the interior regions of a black hole. This is an ingoing wave in the collapse region and an outgoing wave in the anticollapse regions. An approximate expression for the bound states is obtained.

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