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Fermion scattering by a Schwarzschild black hole
General Relativity and Quantum Cosmology · Submitted 5 May 2006
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.
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The abstract, sentence by sentence
We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. | contribution 0.99 | 0.94 | 0.06 | asserted 0.96 |
| s1 | We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. | contribution 0.52 | 0.91 | 0.05 | asserted 0.99 |
| s2 | We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. | method 0.65 | 0.94 | 0.06 | asserted 0.99 |
| s3 | Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. | method 0.97 | 0.91 | 0.03 | asserted 0.97 |
| s4 | Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations. | result 0.57 | 0.96 | 0.21 | asserted 0.99 |
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The paper
Original abstract
We study the scattering of massive spin-half waves by a Schwarzschild black hole using analytical and numerical methods. We begin by extending a recent perturbation theory calculation to next order to obtain Born series for the differential cross section and Mott polarization, valid at small couplings. We continue by deriving an approximation for glory scattering of massive spinor particles by considering classical timelike geodesics and spin precession. Next, we formulate the Dirac equation on a black hole background, and outline a simple numerical method for finding partial wave series solutions. Finally, we present our numerical calculations of absorption and scattering cross sections and polarization, and compare with theoretical expectations.
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References
How the literature uses it
20 arXiv papers cite this in 35 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 4 papers
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We can simplify the precession equation [ref] by introducing a new variable $χ$ satisfies [ref] rCl χ/φ = E [1+L^2/r(φ)^2]^-1 , and a new function $B[χ(φ)]$ satisfies rCl S̅^φ(φ) = √(1+L^2/r(φ)^2)B[χ(φ)] .
The precession of particle spin in spherical symmetric spacetimes · The solution of the precession equation · 0.97
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In principle, this method could be extended to higher spin $s$, but here we prefer to develop an alternative method based on that introduced in 1954 in Ref. [ref] , and first applied in the BH context in Ref. [ref] (see also Ref. [ref] ), known as the series reduction method.
Series reduction method for scattering of planar waves by Kerr-Newman black holes · Introduction · 0.90
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Since the sum in Eq. [ref] does not converge very quickly, because of the Coulomb characteristic of the problem, we have applied the convergence method first introduced by Yennie et al. [ref] , and first applied to the BH scattering problem by Dolan et al. in Ref. [ref] .
Scattering by regular black holes: Planar massless scalar waves impinging upon a Bardeen black hole · Results · 1.00
Compares with it 1 paper
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This conclusion is in agreement with what has been found in Ref. [ref] .
Neutrino spin oscillation in screening models revisited · Neutrinos deflected by a static spherical gravitational source · 0.88
Cites it as support 1 paper
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The convergence to the geometric-optics value has been established for spin 0 [ref] , spin 1/2 [ref] , and spin 1 [ref] ; hence the simple expression used throughout this study stands on solid theoretical ground.
Primordial Black Hole mass growth from neutrinos during the radiation era · Neutrinos Absorption · 1.00
Cites it as background 16 papers
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Scattering of massive fields by a Schwarzschild black hole was studied (for bosons and fermions) in [ref] .
Absorption of a massive scalar field by a charged black hole · Introduction · 0.98
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A substantial literature has accumulated on black hole scattering, focusing on the canonical scenario of a planar wave of circular frequency $ω$ and spin $s$ [ref] impinging upon a black hole of mass $M$ in vacuum [ref] .
Scattering from compact objects: Regge poles and the complex angular momentum method · Introduction · 1.00
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While the absorption and transmission properties of massless fields [ref] , as well as those of massive scalar [ref] and fermionic fields [ref] , have been extensively studied in the Schwarzschild background, the corresponding scattering problem for the massive spin-1 fields has remained an open challenge difficulties associated with the separability of the field equations.
Absorption cross section of a Schwarzschild black hole for a massive vector field · Conclusion and outlook · 0.95
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