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When a black hole absorbs matter is it destroying that mass, thereby destroying energy, therefore violating the first law of thermodynamics?

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    $\begingroup$ The premise of your question is broken. Where did you hear that black holes "destroy energy", whatever that means? $\endgroup$ – Lightness Races in Orbit Sep 4 '15 at 18:25
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Do black holes violate the first law of thermodynamics?

No. See Wikipedia re the first law of thermodynamics: "The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems. The law of conservation of energy states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed". If you throw a one-kilogram object into a zillion-kilogram black hole, the black hole mass increases by one kilogram. The object might get destroyed, but you can't destroy energy. Or create it. There are no perpetual motion machines. Energy is fundamental. Everything is made of it, including light and matter, and black holes.

When a black hole absorbs matter is it destroying that mass, thereby destroying energy, therefore violating the first law of thermodynamics?

No. It destroys the matter, but the total mass stays the same, as does the total energy. In the scenario above, you start with one zillion and one kilograms, and you end up with with one zillion and one kilograms. The black hole's gravitational field increases a little because you increased its mass-energy by one kilogram.

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    $\begingroup$ Small note: I don't think it has been established that black holes destroy matter that falls into it. What does destroy even mean in this context? Perhaps this could be addressed as well. Otherwise a good answer. $\endgroup$ – Danu Sep 4 '15 at 15:07
  • $\begingroup$ Thanks @Danu. I guess nobody knows for sure, but one hears about spaghettification and firewalls and GRBs, and we can read Kip Thorne saying this: "The matter of which a star is made, the atoms of which a star is made, are destroyed at the center of a black hole, when the black hole is created. The matter is gone, but the mass, in the sense of mass and energy being equivalent, has gone into the warped space-time of the black hole." $\endgroup$ – John Duffield Sep 4 '15 at 16:16
  • $\begingroup$ @JohnDuffield Note that the "birth" of a black hole is something different from it absorbing outside matter, so the quote does not apply; I'm pretty sure most physicists wouldn't dare claim that infalling matter is really destroyed at the Schwarzschild radius. The singularity itself is a different issue, but when we talk about matter being absorbed by black holes, we talk about it passing the Schwarzschild radius (or an analogous boundary in more general black holes). $\endgroup$ – Danu Sep 4 '15 at 17:03
  • $\begingroup$ @Danu : some physicists claim the infalling matter is destroyed before it gets to the Schwarzschild radius! But IMHO we need a separate question on that. $\endgroup$ – John Duffield Sep 4 '15 at 17:17
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No, it does not.

If it did, then it would not curve spacetime and it would not be a black hole.

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    $\begingroup$ This doesn't really answer the question, or at least it doesn't explain why the energy doesn't disappear. $\endgroup$ – Javier Sep 3 '15 at 21:33
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    $\begingroup$ @Javier It is a 100% valid answer to say "if it worked that way, then general relativity wouldn't be correct," because the contrapositive of that statement is "General relativity implies that it doesn't work that way." It is perhaps not very respectable if you are looking for low-level kinematics, but that's a huge can of worms that is not needed to answer this question. $\endgroup$ – CR Drost Sep 3 '15 at 21:39
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    $\begingroup$ I know, but the point is that it doesn't improve the OP's understanding of physics. Your answer doesn't say what happens to the energy nor does it show the connection between "black holes curve spacetime" and "black holes don't destroy energy". $\endgroup$ – Javier Sep 3 '15 at 21:47
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    $\begingroup$ On those counts I'm guilty as charged, although it more or less stands to reason that if a black hole doesn't destroy inbound mass-energy then that mass-energy goes inside the black hole. $\endgroup$ – CR Drost Sep 3 '15 at 21:50
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Yes, a black hole can violate conservation of energy. According to JamelS' answer at Energy conservation and General Relativity, energy is not necessarily conserved in general relativity. According to my answer at Energy conservation and General Relativity, the electric field of a charged black hole can accelerate a charged particle but an electric field can't accelerate a charged black hole. If you have two charged black holes orbiting each other, they will accelerate each other only with their gravitational field and not with their electric field so total of their gravitational potential energy and the energy of their gravitational waves will remain constant but their electric potential energy will keep changing as they spiral into each other.

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    $\begingroup$ Energy is not conserved in general relativity, but it is conserved in asymptotically flat spacetimes, which means that it's conserved for the purpose of the present discussion. $\endgroup$ – Ben Crowell Nov 24 '17 at 21:42

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