Perturbation theory calculation of the black hole elastic scattering cross section

Abstract

The differential cross section for scattering of a Dirac particle in a black hole background is found. The result is the gravitational analog of the Mott formula for scattering in a Coulomb background. The equivalence principle is neatly embodied in the cross section, which depends only on the incident velocity, and not the particle mass. The low angle limit agrees with classical calculations based on the geodesic equation. The calculation employs a well-defined iterative scheme which can be extended to higher orders. Repeating the calculation in different gauges shows that our result for the cross section is gauge-invariant and highlights the issues involved in setting up a sensible iterative scheme.

Fermion scattering by a Schwarzschild black hole

“…This problem has been considered in numerous papers [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and books [15][16][17]. Most authors study the massless scalar wave (with spin s 0) for its mathematical simplicity, or massless electromagnetic (s 1) and gravitational (s 2) waves for physical relevance.…”

“…III we describe analytic methods that can be applied to fermion scattering. The perturbation-theory approach introduced by Doran and Lasenby [14] is taken to the next order, which provides a new estimate of the cross section and polarization at low couplings. The glory-scattering approximation of Zhang and DeWitt-Morette [9] is extended to the massive case, employing the classical results of Sec.…”

Partial wave analysis of the Dirac fermions scattered from Schwarzschild black holes

“…The complex problem of the quantum particles scattered from black holes was studied extensively, mainly considering massless scalar [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] or other massless boson fields [17][18][19], since the equations of massive fields cannot be solved analytically in the Schwarzschild geometry. This is one of the reasons why the scattering of massive Dirac fermions by black holes was studied either in particular cases [20,21] or by using combined analytical and numerical methods [22][23][24][25][26].…”

Gauge Gravity and Electroweak Theory

“…The gravitational analog of the Mott formula for Coulomb scattering is derived in [11] for the first time. This is extended to next order in the Born series in [14], where numerical calculations for absorption, scattering cross section and polarization are compared with theoretical expectations.…”

“…These include clarification and simplification of Kerr solutions, [11][12][13][14] new solutions of the Dirac equation in a black hole field, 9,10 and new results from cosmological modeling with conformal GA. [15][16][17][18] A few words are in order to describe what these substantial publications have to offer.…”