Resolution of the mystery behind Chandrasekhar's black hole transformations

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Abstract
Investigating, in normal form, the three differential equations of (i) Zerilli (1970), (ii) Bardeen and Press (1973), (iii) Regge and Wheeler (1957), 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. It is shown that the whole scheme can be parametrized, with one condition imposed, yielding for every functional parameter three potentials of the above types. 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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