So black holes are created by certain dying stars and when the star runs out of nuclear energy gravity wins out and the star implodes. An entire star’s mass collapses down into a smaller and smaller volume of space. Which then creates a black hole, so my question is, do black holes actually have energy to create that type of vacuum to suck light in?

If a black hole was created by a huge star running out of fuel and then collapsing in on it self, would the black hole have energy and if so where would it come from, or is it just like the vacuum in space with no energy at all?

(Please correct me if I said anything wrong about the black holes as I am very young and don't quiet grasp the concept of it yet.)

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An isolated black hole is a vacuum solution of general relativity, so in a very direct sense it does not contain any energy anywhere in spacetime. But perhaps somewhat counter-intuitively, that does not imply that such a black hole has no energy.

Defining the total amount of energy is usually very problematic in general relativity, but in some special cases it is possible. In particular, the usual black hole solutions are all asymptotically flat, i.e., spacetime is just the usual flat Minkowski when far away from the black hole.

Here (or in general when we have a prescribed asymptotic form of the spacetime), we can calculate the total energy-momentum, by essentially measuring the gravitational field of the black hole at infinity. The energy just be one component of energy-momentum.

There are actually two relevant different kinds of 'infinity' here: spatial infinity and null (lightlike) infinity, depending on whether we are 'far away' from the black hole in a spacelike or lightlike direction. There's also timelike infinity, but that just corresponds to waiting an arbitrarily long time, so it's not relevant here. The two different infinities beget different definitions of energy-momentum, giving the the ADM energy and the Bondi energy, respectively. In a vacuum, the intuitive difference between the two is that Bondi energy excludes gravitational waves.

So the short answer is 'yes', with the caveat that in a more complicated situation, where we can't attribute everything to the black hole itself, the answer to how much energy is due to the black hole may be ambiguous or ill-defined.

Note that the ADM and Bondi energy-momenta also define their corresponding measures of mass, as the norm of those energy-momenta ($m^2 = E^2-p^2$), but for a black hole we can also define mass more operationally in terms of orbits around the black hole. There are also other alternatives for addressing mass specifically.

In outer space, a vacuum isn't what sucks in matter to a black hole. That may be the case for your household vacuum cleaner, but everywhere in outer space is essentially a vacuum. Instead, it's the black hole's powerful gravitational pull.

However, black hole can have energy. One type that comes to mind is angular kinetic energy. This is the energy that a spinning object has - in this case, a rotating black hole (see also Kerr black hole and Kerr-Newman black hole). Black holes can also have translational kinetic energy - the energy of an object in motion. Also black holes have gravitational potential energy - potential energy due to gravity - and black holes with electric charge can have electric potential energy.

So black holes do have energy, although perhaps not in the form you thought.

Keep asking good questions!

I hope this helps.

The only way we can detect black holes is through the effect that their gravitating mass has on objects outside the event horizon. These objects can gain energy from the black hole, as they fall into the potential well they heat up and radiate (often in the X-ray region of the spectrum). So black holes have gravitational energy from their mass. A black hole could also have charge, but this is rare in the universe which is largely neutral. Many black holes probably rotate, and these also have rotational energy.

The principle of conservation of energy tells us that the amount of energy in the universe is constant. Therefore we can conclude the energy that once made up a star that turned into a black hole cannot be destroyed. So yes according to the principle of conservation of energy a black hole contains energy.

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    Conservation of energy on a universal scale is not a given and is not required by General relativity. – Rob Jeffries Mar 31 '16 at 10:41

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