# A Kerr Newman metric correction from Einstein-Rosen m

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1. Nov 26, 2016

### Mihai_B

Einstein (+Rosen) came to the conclusion that they have to change the sign for the energy tensor Tik :
"if we had taken the usual sign for Tik, the solution would involve +ε2 instead of -ε2. It would then not be possible, by making a coordinate transformation, to obtain a solution free from singularities."

And they came up with the solution :
c2 ds2 = 1 / ( 1 - rs/r - rq2/r2) dr2 + r2 (dθ2 + sin2θ dΦ2) - (1 - rs/r - rq2/r2) c2 dt2

Now Kerr-Newman solution for a rotating charged mass involves the +rq2/r2 . But since Einstein came with the correction specified above I was wondering if "this" (see below) is how it would look like if it would have been applied to Kerr-Newman metric :

c2 ds2 = - (dr2/Δ + dθ22 + (c dt - a sin2θ dΦ)2Δ/ρ2 - ((r2 - a2) dΦ - a c dt)2 sin2θ/ρ2

rs = 2mG/(rc2)
rq2 = q2G/(4πεc4)

a = J/(mc)
ρ2 = r2 + a2cos2θ

Δ = 1 - rs/r + a2/r2 - rq2/r2

And the correction is inside Δ where instead of + rq2 we use - rq2 in order to make the metric consistent with Einstein-Rosen "derivation".

My question : is it mathematically ok if one would just change the sign of rq2 in Δ ? Will other signs change too ? I couldn't find anything else to change in the metric.

Thanks anyway!

References:
https://en.wikipedia.org/wiki/Kerr–Newman_metric
http://journals.aps.org/pr/abstract/10.1103/PhysRev.48.73

2. Dec 1, 2016