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In lecture notes that I have about black holes and space-time metrics it says:

The Schwarzschild solution, which is appropriate outside a spherical, non-spinning mass distribution, was discovered in 1916. It was not until 1963 that a solution corresponding to spinning black holes was discovered by New Zealander Roy Kerr. This solution leads to the possible existence of a family of rotating, deformed black holes that are called Kerr black holes.

Angular momentum is complicated: In Newtonian gravity rotation produces centrifugal effects but does not influence the gravitational field directly. But angular momentum implies rotational energy, so in general relativity rotation of a gravitational field is itself a source for the field.

I understand that in Newtonian mechanics rotation invokes a centrifugal force, how to reconciliation this in the case of gravity is something I hope somebody could elaborate here. thank you!

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  • $\begingroup$ Is there maybe a translation issue here? Is the original in English? Is the lecturer a native English speaker? I can't make much sense of that sentence (and not just because of the minor error of a missing article after "of"). I'm guessing it means to say something more like a rotating gravitational field is a source for the field — which I suppose could be considered true in the sense that (for example) a black-hole binary stirs up gravitational waves as it rotates. Is there any more context? $\endgroup$ – Mike Jan 20 '18 at 15:41
  • $\begingroup$ Which lecture notes? $\endgroup$ – Qmechanic Jan 20 '18 at 16:24
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The source of the gravitational field is the stress-energy tensor, which measures mass-energy, momentum, pressure, and shear stress. Gravitational fields themselves have properties such as energy and momentum, and therefore the gravitational field acts as its own source (couples to itself). This is why the Einstein field equations are nonlinear.

A rotating material body such as the earth has a gravitational field that differs from that of a nonrotating body. This was verified experimentally by Gravity Probe B.

A black hole that has angular momentum has a far field that is very similar to the earth's external field.

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