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Tortoiselike coordinate transform for interior metric 
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#1
Apr311, 06:39 PM

P: 481

Hello!
When using the Schwarzschild exterior metric in the kleingordon equation one can perform the standard tortoise(EF) coordinate transform to yield a wave equation which has a well defined potential that is independent of the energy term. My understanding is that the motivation for this coordinate transform was the removal of the coordinate singularity at the horizon of this metric. If one wanted to generate a wave equation from an INTERIOR metric, say the Schwarzschild interior, that also had a well defined potential independent of energy, on what premise would one start, given that if we want to consider a fluid sphere there is no singularity at the horizon? Certainly i can take the wave equation and put it in a Schrodingerlike form but this yields an effective potential with the energy term coupled to coordinate terms which I must admit i don't know how to transform away without reinstating the first derivative (ie no longer in schrodinger form). Hope that makes sense! 


#2
Apr511, 02:12 PM

Sci Advisor
Thanks
P: 4,160

Don't know if it's what you want, but one way of arriving at EddingtonFinkelstein coordinates is to find a retarded time that serves to eliminate the dr^{2} term in the metric. This can be done in general. For
ds2 = A(r)^{2} dt^{2}  B(r)^{2} dr^{2} + ... just let u = t ± integral(B/A dr) 


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