### References & Citations

# Mathematical Physics

# Title: The Fermionic Signature Operator in the Exterior Schwarzschild Geometry

(Submitted on 5 Dec 2018 (v1), last revised 22 Aug 2019 (this version, v2))

Abstract: The structure of the solution space of the Dirac equation in the exterior Schwarzschild geometry is analyzed. Representing the space-time inner product for families of solutions with variable mass parameter in terms of the respective scalar products, a so-called mass decomposition is derived. This mass decomposition consists of a single mass integral involving the fermionic signature operator as well as a double integral which takes into account the flux of Dirac currents across the event horizon. The spectrum of the fermionic signature operator is computed. The corresponding generalized fermionic projector states are analyzed.

## Submission history

From: Felix Finster [view email]**[v1]**Wed, 5 Dec 2018 14:11:25 GMT (25kb)

**[v2]**Thu, 22 Aug 2019 15:35:51 GMT (27kb)

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