Absorption cross sections of a Schwarzschild black hole

Details Absorption cross sections of a Schwarzschild black hole Absorption cross sections of a Schwarzschild black hole

Jul 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cqgra...1..403f&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 1, July 11, 1984, p. 403-405.

Astronomy and Astrophysics

Astronomy

1

Absorption Cross Sections, Black Holes (Astronomy), Quantum Mechanics, Schwarzschild Metric, Klein-Gordon Equation, Nonrelativistic Mechanics, Perturbation Theory, Relativistic Particles, Space-Time Functions, Wave Functions

Scientific paper

The absorption of nonrelativistic particles by a small Schwarzschild black hole is investigated theoretically, accounting for quantum-mechanical effects. The Klein-Gordon equation in curved space-time and the metric tensor of a Schwarzschild space-time in Finkelstein coordinates are combined to derive the equation for the stationary wavefunction in the nonrelativistic approximation. The exact solution under the Newtonian potential is taken as the zero-order wavefunction, with the black hole potential corrections as perturbation terms in the Hamiltonian, in obtaining an explicit expression for the absorption cross section in first-order perturbation. The 1/v dependence of the cross section for a small black hole indicates that a particle bound by a black hole is absorbed by it.

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