Extended Extreme Multiple Reissner Nordstrom Black holes

[keithdow]

I have a question about equation 10.21 in "Exact Space-times in Einstein's General Relativity" by Griffiths and Podolski. The equation is the well know standard metric for multiple extreme Reissner Nordstrom black holes.
It has the below term:

(1+ sigma(mi/ri))

The point ri = 0 is of course the surface of the hole. My questions is the book states "The analytically extended
region inside this horizon has a metric similar to "10.21" but with a negative sign in the corresponding term in the sum, ... " They don't give a reference. Does anyone know how to I derive the above result?

Thanks.

 

[George Jones]

Equations (10.20) and (9.21) have (roughly) the same form. The sentence before the sentence that includes (10.20) states "As shown by Hartle and Hawking (1972)". There is open-access to this paper at

http://projecteuclid.org/euclid.cmp/1103858037

A 1966 paper by Carter might also be useful.

 

[keithdow]

Thank you sir. You are correct. I am reading it now.