The Schwarzschild metric describes spacetime around a spherically symmetric neutral object and, as such, it is considered as a vacuum solution, with zero contribution from the energy-momentum tensor that otherwise influences the space in the region 0<r<2GM.(adsbygoogle = window.adsbygoogle || []).push({});

The Schwarzschild metric can be analytically extended to cover the region beyond the horizon, obviously, but this remains a vacuum solution.

I was wondering why the Reissner-Nostrom metric, being the solution AROUND a spherically symmetric charged object, is not considered a vacuum solution as well.

What I mean is: aren't the actions of the gravitational field and of the electromagnetic field qualitatively the same? If the electromagnetic field can be "felt" outside the horizon (so that the metric outside [itex]r_{+}[/itex] is influenced by it), shouldn't it be the same for the gravitational field of the pointlike mass at the origin of the Schwarzschild solution, thus causing the latter to be influenced by some non-vanishing stress-energy tensor?

In the same way "there's no mass" outside the Schwarzschild radius, there is no charge outside [itex]r_{+}[/itex].

I'm sure I'm mistaken somewhere, but can't see why.

Thanks

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# Charged Black Holes

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