# Is energy conserved when things fall into a black hole?

1. We all know in physics, the law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another. What happens when said energy ie planets, stars, light etc..enter a black hole?

2. Does it simply change form or does it disappear from this universe into another?

3. I know many physicists have said all laws start to break down once something enters a black hole but are there any new theories on this? Is it possible it simply turns the energy into a new form like dark matter?

• Related: physics.stackexchange.com/q/204099/2451 and links therein. Jul 26 '16 at 13:10
• See also The Black Hole War by Leonard Susskind. He and Stephen Hawking had a long standing disagreement about questions like these which is documented in the book. Jul 26 '16 at 14:13
• Well, as one of the chapter titles in A Brief History of Time states, "black holes ain't so black". Entropy is conserved by Hawking Radiation. Jul 26 '16 at 15:42

Energy (in any form) falling into a black hole contributes to the mass of the hole, and mass is one of the many forms that energy can take, using the usual conversion factor: $E = mc^2$.

• That becks the question. How can you add mass to something that is already infinitely dense? In the centre of a black hole is a gravitational singularity, a one-dimensional point which contains a huge mass in an infinitely small space, where density and gravity become infinite and space-time curves infinitely.
– Noah
Jul 26 '16 at 4:02
• @Killer066 The basic framework of nature is quantum mechanical. Quantum mechanics has no singularities. For example the hydrogen atom: with the 1/r electric potential there is a singularity at r=0. Quantum mechanics solves it by quantizing the energy. The singularity of the original big bang model has been avoided by assuming an effective quantization of gravity for the beginning of the universe. Analogously an effective quantization of a black hole will get rid of the singularity, though one does not talk about it , it is the reason the infinite density etc do not disturb cosmological models Jul 26 '16 at 5:13
• @dmckee This isn't obvious in light of issues defining energy conservation in GR. Jul 26 '16 at 7:58
• @Killer066 The singularity inside a black hole is infinitely dense because its volume is 0, but its mass is finite. So you can add mass to it and its density will always be infinite. Jul 26 '16 at 8:13
• @annav To do a little nitpicking, the singularity in $r=0$ for the hydrogen atom isn't solved by quantising the energy. It is solved by choosing a priori a class of wave functions such that $\int dr\, f(r)/r$ converges; those would represent the "physical" states on which the energy eigenvalues make sense. This said, there might indeed still be singularities in GR and QFT, especially when it comes to black holes and degenerate metrics. Jul 26 '16 at 8:32

To expand on @dmckee's answer, if we have a speacetime that has the matter concentrated in a central area, we can definte an overall conserved energy-momentum vector called the ADM energy. It can be further shown that the ADM energy does not change when the matter falls into the black hole.

• Do BHs satisfy all conservation laws when you throw things into them? I've heard people say it could break global symmetries. Jul 26 '16 at 8:01
• @innisfree: it's a subtle question. Stuff like the ADM energy is defined for the whole spacetime, at its boundary, the question you asked is, usually interpreted in terms of local conservation laws, and coordinate invariance makes local conservation somewhat tricky. Jul 26 '16 at 15:06
• @innisfree In a nutshell, an isolated black hole lives in an "asymptotically flat" spacetime, and so we can unambiguously define a time direction at infinity, and so all the usual Noetherian stuff holds. Another way of looking at it is that accounting for the gravitational redshift factor is well defined and independent of the way in which you move material around as far as the normal observer at infinity cares.
– user10851
Jul 27 '16 at 18:36
• @ChrisWhite: The ADM energy is a bit stronger than just the Noetherian stuff -- because the ADM Hamiltonian is identically zero minus boundary terms, the value of the ADM energy is, literally, the exact value of the Hamiltonian. Sep 5 '16 at 17:24
1. It loses organization, e.g. matter changes into pure energy or some such thing. It's not entirely clear what form there is (some suggest there is no form at all, but it's obvious that it doesn't follow Pauli's exclusion principle). This is nothing special, it happens all the time - when you burn carbon, for example, you get a bit of disorganised energy (heat) and a molecule of carbon dioxide that has the energy of the free carbon and oxygen molecule, minus the lost heat.
2. There's no reason to believe that the matter is lost - for one, the mass of the black hole is exactly the same as of the matter that formed the black hole, so both the mass and energy must still be there. Second, we have good reasons to believe that black holes emit radiation and "evaporate" over time - for microscopic black holes, this is so important that they don't exist for very long. This is lucky for us, since we have pretty good evidence that microscopic black holes are created all the time in Earth's upper atmosphere. EDIT: My fault, this isn't actually true. String theory predicts that this might be true, but it seems we don't have solid evidence of this yet. When they evaporate, all the trapped energy is released back into our environment. If the universe gets cold enough, this will eventually happen to all black holes, even those gigantic ones in the center of galaxies - but it's going to take a long, long time, and even then only if the universe keeps expanding.
3. Laws don't break, and there's little reason to believe they would. What breaks is some models - but most physicist you ask will tell you that when the model breaks down, it's a problem of the model, not of reality. We know black holes are real, therefore any model that breaks down when describing a black hole is wrong. That doesn't mean the model is useless - it just means you can't use it to describe black holes (and presumably other, possibly yet undiscovered phenomena).
• "This is lucky for us, since we have pretty good evidence that microscopic black holes are created all the time in Earth's upper atmosphere." I would enjoy a reference for this. Jul 26 '16 at 16:33
• @TrevorAlexander Oh, my bad. I must have mis-remembered from the time of the LHC scare :) I'll remove that. Jul 26 '16 at 19:51
• No, wait! I actually wanted a source for it, not to rebut anybody. Jul 26 '16 at 21:03