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Dirac equation is solved in the near horizon limit geometry of an extremeKerr black hole. We decouple equations first as usual, into an axial andangular part. The axial equation turns out to be independent of the mass and issolved exactly. The angular equation reduces, in the massless case, to aconfluent Heun equation. In general for nonzero mass, the angular equation isexpressible at best, as a set of coupled first order differential equations aptfor numerical investigation. The axial potentials corresponding to theassociated Schrodinger-type equations and their conserved currents are found.Finally, based on our solution, we verify in a similar way the absence ofsuperradiance for Dirac particles in the near horizon, a result which iswell-known within the context of general Kerr background.Comment: 20 pages, no figure, to be appeared in Phys.Rev.

Solution of the Dirac equation in the near horizon geometry of an extreme Kerr black hole