Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977jpha...10..885h&link_type=abstract
Journal of Physics A - Mathematical and General, vol. 10, June 1977, p. 885-897.
Astronomy and Astrophysics
Astronomy
1
Black Holes (Astronomy), Perturbation Theory, Transformations (Mathematics), Astronomical Models, Differential Equations, Metric Space
Scientific paper
Investigating the three differential equations in normal form of (1) Zerilli, (2) Bardeen and Press, (3) Regge and Wheeler, governing the perturbations of the Schwarzschild black hole, Chandrasekhar has demonstrated the somewhat complicated transformations between these equations. This complication hides the basic nature of the transformations and their mutual connections. The whole scheme can be parametrized, with one condition imposed, yielding for every functional parameter inevitably three potentials of the above types. Any Schroedinger equation in normal form can be similarly treated, but the analogous Bardeen and Press potential is more complicated than the original. Thus an investigation is undertaken as to why the Bardeen and Press potential for the black hole is analytically 'simple'; conditions for this simplicity inevitably lead to this particular potential, and hence to the other two potentials. Every symbol occurring in these three potentials is thereby explained analytically.
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