Advances in Theoretical and Mathematical Physics

Volume 7 (2003)

Number 1

The long-time dynamics of Dirac particles in the Kerr-Newman black hole geometry

Pages: 25 – 52

DOI: http://dx.doi.org/10.4310/ATMP.2003.v7.n1.a2

Authors

Felix Finster

Niky Kamran

Joel Smoller

Shing-Tung Yau

Abstract

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data in Linfinityloc near the event horizon with L2 decay at infinity, the probability of the Dirac particle to be in any compact region of space tends to zero as t goes to infinity. This means that the Dirac particle must either disappear in the black hole or escape to infinity.

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