Black holes, input compared to output

[Phil Fargaze]

I am interested to know the balance of the amount of matter and energy that a black hole absorbs compared to the energy that a black hole gives off.

In other words, do they behave according to the conservation of energy law? Is it even possible to predict an answer?

[DH88]

Are you referring to the accretion disc formed when matter 'falls into' the black hole?

[JulianO]

What energy are you talking about? I'm pretty sure things add up ok.

As matter enters the black hole it gives it more energy and the size expands and it cools. It has more gravity now.

As it loses energy by Hawking radiation it shrinks. This also heats it up, which means it loses mass more quickly.

[Phil Fargaze]

Sorry bit of a vague question, I would say that it does involve the accretion disc. I can see now that more matter equals more gravity etc.

I understand that to an observer an object takes an infinite time to reach the event horizon, but would that mean that the object would not add to the mass of the black hole (from the observers point of view)?

[Tiki]

I understand that to an observer an object takes an infinite time to reach the event horizon, but would that mean that the object would not add to the mass of the black hole (from the observers point of view)?

Your conclusion is correctly drawn from an untrue hypothesis. In general, matter accreting onto a black-hole does so in a finite time.

The Hawking radiation mentioned by JulianO is particularly interesting. The lifetimes for non-accreting black-holes varies massively for bh's of different initial masses. The formula for Hawking radiation is particularly beautiful (and simple), well worth checking out.

[acey]

A black hole has mass (evidenced by its gravitational field, e.g. the speed at which objects orbit around it). When a black hole absorbs matter its mass increases, so mass-energy is conserved. Ultimately the energy is released as Hawking radiation. More controversial is the question whether "information" is conserved or lost in black holes - this was the subject of a famous bet made by Stephen Hawking, Kip Thorne and John Preskill in the 1990s. Hawking paid up in 2004 but it's still not fully settled.

http://en.wikipedia.org/wiki/Black_hole_information_paradox