Fermion absorption cross section of a Schwarzschild black hole
- Astrophysics Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE (United Kingdom)
We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section {sigma} over a range of gravitational couplings Mm/m{sub P}{sup 2} and incident particle energies E. At high couplings, where the Schwarzschild radius R{sub S} is much greater than the particle wavelength {lambda}, we find that {sigma}(E) approaches the classical result for a point particle. At intermediate couplings, where R{sub S}{approx}{lambda}, we find oscillations around the classical limit whose precise form depends on the particle mass. At low couplings, where R{sub S}<<{lambda}, we demonstrate that the minimum-possible cross section approaches {pi}R{sub S}{sup 2}/2. For high incident particle energies, the cross section converges on the geometric-optics value of 27{pi}R{sub S}{sup 2}/4. At low particle energies we find agreement with an approximation derived by Unruh.
- OSTI ID:
- 20709564
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 71, Issue 12; Other Information: DOI: 10.1103/PhysRevD.71.124020; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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