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Lets make this thought experiment.

I throw a spaceship inside a black hole. Then, this spaceship start its motors and accelerates rotating around the singularity at great speeds. Due to relativist effects, the spaceship would make a greater deformation of space because of its increased momentum (even though it is expelling matter in the opposite direction, but this matter never gets out the black hole).

Should the radius of the black hole increase due to having more energy (like having more mass)? or does conservation of momentum cancel this effect? would it matter at all? (notice that no information, even gravitational deformation/waves escape the black hole)

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    $\begingroup$ Throw a spaceship into a black hole and it no longer exists. $\endgroup$ – user207455 Jun 21 at 20:54
  • $\begingroup$ If the spaceship tries to accelerate inside the black hole, it cannot “rotate the singularity”. $\endgroup$ – G. Smith Jun 21 at 21:11
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    $\begingroup$ @SolarMike Yes. When you cross the event horizon, you are said to be in the black hole because you can’t get out by crossing the horizon in the outward direction. $\endgroup$ – G. Smith Jun 21 at 21:29
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    $\begingroup$ As safesphere says, to a distant observer, nothing is observed to cross the EH (event horizon) in finite time. But anyway, if you drop something into a BH, once it crosses the EH it's out of causal contact with the rest of the universe. You could drop a huge hydrogen bomb into a BH, and it makes no difference whether the bomb detonates or not, the BH assimilates all of the bomb's energy. $\endgroup$ – PM 2Ring Jun 22 at 14:45
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    $\begingroup$ When you say "starts rotating the singularity," do you mean "starts rotating around the singularity?" $\endgroup$ – Ben Crowell Jun 22 at 19:26
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If some or all of the mass of an object inside a black hole is converted to energy, there is no effect at all on its event horizon. The total mass/energy of the BH determines the radius of the event horizon. Also, since momentum of a rocket, including the ejected matter is conserved, any accelertion inside a BH does not change its angular momentum.

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  • $\begingroup$ While your answer is conceptually correct, it may be worth pointing out that most of the exact black hole solutions are vacuum solutions, in which the stress/energy tensor is zero everywhere. These solutions describe how spacetime is curved by the curved spacetime, not by the stress/energy tensor. $\endgroup$ – safesphere Jun 22 at 5:09
  • $\begingroup$ @safesphere, I agree, an actual solution is more complicated, and would likely require a perturbation calculation around the vacuum solution. My main point was conceptual, as you suggested. Total mass/energy of the BH determines the location of the event horizon. I'll edit the answer. $\endgroup$ – amateurAstro Jun 22 at 13:42

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