Mass conservation in black holes

[Ranku]

Is the mass of gravitationally collapsed matter conserved in a black hole?

 

[Ibix]

Depends what you mean.

Classically, gravitational collapse leads to a singularity. There isn't any matter inside the hole once the collapse completes, so whether its mass is conserved or not isn't a necessarily a meaningful question.

If the initial state was spherically symmetric and non-rotating then the gravitational field outside the hole is Schwarzschild with the same mass parameter before and after the collapse (assuming no matter was ejected before crossing the horizon). That might be what you mean.

If the black hole is spinning then you can trade between mass and angular momentum, within limits. That may not match what you mean. Also, as far as I'm aware, nobody has proved that the spacetime around a rotating mass that isn't a black hole is Kerr (and I rather suspect it isn't exactly). So it's at least possible that the mass parameter in the spacetime around the black hole is not the same as the one around the original star, even allowing for mass loss.

 

[PeterDonis]

Is the mass of gravitationally collapsed matter conserved in a black hole?

In an idealized collapse where nothing is emitted (no matter or radiation or gravitational waves), the mass of the spacetime, i.e., the geometric property (for example, the mass you would get by putting a test object in orbit and measuring its orbital parameters) is conserved.

Of course no real collapse occurs with nothing being emitted. But there are still ways to define the mass that's emitted such that the total mass (what's emitted plus what remains in the black hole) is conserved. ("Mass" is not the usual expression for the quantities involved, "energy" is, since rest mass is not the only contribution to it.)

 

[PeterDonis]

If the black hole is spinning then you can trade between mass and angular momentum, within limits.

Even in this case, I believe there is a way to capture the exchange so that the mass and the angular momentum of the overall spacetime are conserved.

 

[liuzilu]

Does energy conservation hold when matter approaches the event horizon of a black hole and its mass becomes infinite?

 

[Ibix]

Does energy conservation hold when matter approaches the event horizon of a black hole and its mass becomes infinite?

The mass of matter doesn't become infinite as it approaches the event horizon. Where did you get the idea that it does?

 

[liuzilu]

The mass of matter doesn't become infinite as it approaches the event horizon. Where did you get the idea that it does?

For example, as a photon approaches the event horizon, its frequency becomes infinitely high. Doesn't that mean its energy (mass) becomes infinite as well?

 

[phinds]

For example, as a photon approaches the event horizon, its frequency becomes infinitely high. Doesn't that mean its energy (mass) becomes infinite as well?

Huh? Where did you get THAT idea?

 

[Ibix]

For example, as a photon approaches the event horizon, its frequency becomes infinitely high.

No it doesn't - where did you get that idea?