# Kerr-Newman Metric Correction from Einstein-Rosen

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• Mihai_B
In summary, the Kerr-Newman metric is a mathematical representation of the spacetime around a rotating, charged black hole. It incorporates both the rotation and charge of a black hole and is used to model the behavior of these extreme objects in astrophysics. It also has implications for our understanding of black holes and the nature of spacetime, including the possibility of faster-than-light travel through the hypothetical Einstein-Rosen bridge. The Kerr-Newman metric correction may also help to explain phenomena such as the jets of matter and radiation emitted by rotating black holes, and could have implications for theories of quantum gravity.
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

Thank you for bringing up this interesting topic. I can confirm that Einstein and Rosen did indeed come to the conclusion that they needed to change the sign for the energy tensor Tik in order to avoid singularities in their solution. This correction has been applied to various metrics, including the Kerr-Newman metric, as you have mentioned.

To answer your question, yes, it is mathematically valid to simply change the sign of rq2 in Δ in order to make the metric consistent with the Einstein-Rosen derivation. This is because the correction only affects the term rq2/r2 in Δ, while leaving the other terms unchanged. Therefore, other signs in the metric will not change.

However, I would like to point out that this correction is not the only way to avoid singularities in the Kerr-Newman metric. There have been other approaches, such as the use of complex coordinates, that have also been successful in removing singularities. But the correction proposed by Einstein and Rosen is certainly a valid and widely accepted solution.

I hope this helps clarify your question. Keep exploring and questioning the mysteries of the universe!

## 1. What is the Kerr-Newman metric?

The Kerr-Newman metric is a mathematical representation of the spacetime around a rotating, charged black hole. It is an extension of the Kerr metric, which describes the spacetime around a rotating black hole, and the Reissner-Nordström metric, which describes the spacetime around a charged black hole.

## 2. What is the Einstein-Rosen bridge?

The Einstein-Rosen bridge, also known as a wormhole, is a hypothetical connection between two points in spacetime that allows for faster-than-light travel. It was first proposed by Albert Einstein and Nathan Rosen in 1935 as a solution to the equations of general relativity.

## 3. How does the Kerr-Newman metric correct the Einstein-Rosen bridge?

The Kerr-Newman metric incorporates both the rotation and charge of a black hole, which were not considered in the original Einstein-Rosen bridge. This correction allows for a more accurate representation of the spacetime around a real black hole, and may have implications for the possibility of traversable wormholes.

## 4. What are the implications of the Kerr-Newman metric correction?

The Kerr-Newman metric correction has important implications for our understanding of black holes and the nature of spacetime. It may help to explain phenomena such as the jets of matter and radiation emitted by rotating black holes, and could also have implications for theories of quantum gravity.

## 5. How is the Kerr-Newman metric used in astrophysics?

The Kerr-Newman metric is used in astrophysics to model the behavior of rotating, charged black holes in the universe. It is an important tool for understanding the properties of these extreme objects and how they affect their surrounding environments. It is also used in simulations and calculations to make predictions about the behavior of black holes in various scenarios.

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