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user1139
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- TL;DR Summary
- Unable to find surface area of Black Hole using Weyl coordinates
Recently, I was tasked to find the surface area of the Schwarzschild Black Hole. I have managed to do so using spherical and prolate spheroidal coordinates. However, my lecturer insists on only using Weyl canonical coordinates to directly calculate the surface area.
The apparent problem arises from the term gzzgφφ due to the presence of the factor ρ2. Upon setting ρ=0, the integrand becomes zero for −M<z<M thus invalidating the surface area integral. I was unsuccessful in my attempts to get rid of the ρ2 factor.
Can someone advise me on how to proceed, if it is at all possible?
The apparent problem arises from the term gzzgφφ due to the presence of the factor ρ2. Upon setting ρ=0, the integrand becomes zero for −M<z<M thus invalidating the surface area integral. I was unsuccessful in my attempts to get rid of the ρ2 factor.
Can someone advise me on how to proceed, if it is at all possible?