Can Black Holes Increase Their Mass According to Remote Observers?

[hellfire]

A remote observer describes a black hole with Schwarzschild coordinates. These have a coordinate singularity at the horizon, which implies that the distante between any spacetime point and the horizon is infinite. My question is whether a remote observer is allowed to claim that a black hole may increase its mass (objects falling into the black hole), since any object needs of infinite time to reach the horizon. (Example: we as remote observers of the supermassive black hole in the centre of the Milky Way).

Regards.

 

[yogi]

Interesting question - I have wondered myself whether the frozen time concept is applicable to the rate at which black holes accrete additional matter - these issues always seem to not go away easily because they involve different interpretations of SR and GR - is time really stopped at the Swartzchild radius - or is the slow down ajectival. Seems the black hole would have to dilate to embrace a greater mass as its density diminishes. Ed Harrison gives this account: "The free falling particle's own spacetime is always flat and the same as that for ordinary SR, and therefore the particle passes smoothly into the black hole without realizing that anything unusual has happened. If we are measuring its own intervals of time, it reaches the singularity after entering the black hole in a time equal to the Schwartzchild radius divided by the speed of light. To the distant observer, however, the particle takes an infinite time to enter the black hole." I wonder then how the size of the black hole at the center of our Milkyway would appear in different epochs - it must have grown to reach its present size - but it takes infinite time to change ---something bothersome here.

 

[Stingray]

Very good question. Its somewhat hard to talk about the gravitational field, so think about the electric one instead. A charge all by itself will have electric field lines radially pointing out of it. Put it near an uncharged black hole, and those lines will be bent.If you put it very near the horizon, the lines appear to come out of the center of the black hole, not the charge! To an external observer, it looks like the charge fell into hole, even though it didn't.

There is no functional difference between the singularity+horizon viewpoint, and the one that a black hole is a star frozen in collapse with "near infinite" redshift (at least in spherical symmetry).

 

[kurious]

Does a black hole increase its mass if its speed relative to the Earth increases? And if it does, does this mean its temperature drops too?
And what about the scwarzschild horizon - does that get smaller by lorentz contraction?

 

[Stingray]

Does a black hole increase its mass if its speed relative to the Earth increases? And if it does, does this mean its temperature drops too?
And what about the scwarzschild horizon - does that get smaller by lorentz contraction?

Mass doesn't increase when moving. Mass (when defineable) is independent of the frame of reference. I know popular books and freshman textbooks often say that mass increases with speed, but this is poor terminology. Mass is almost always taken to mean proper mass in relativity, which stays the same.

The temperature will look different for one observer or another due to a redshift or blueshift.

The horizon can be made to look distorted by a moving observer. Its area looks the same to everyone though.

 

[kurious]

Mass is almost always taken to mean proper mass in relativity, which stays the same.
What happens to proper mass when GR breaks down at the time of the big bang -
did the universe have a different mass then?

 

[hellfire]

I was trying to find an answer to my question reading chapter 7 of Sean Carroll's Lecture Notes on General Relativity (http://arxiv.org/gr-qc/9712019 ) and my impression is that there exists a coordinate system called Eddington-Finkelstein coordinates, which is adequate for remote observers and does allow crossing of the event horizon. Is this correct?

Regards.

 

[Stingray]

Mass is almost always taken to mean proper mass in relativity, which stays the same.
What happens to proper mass when GR breaks down at the time of the big bang -
did the universe have a different mass then?

Nobody knows what happens when GR breaks down.

Actually, my original statement wasn't completely correct. Mass cannot even be defined consistently in GR in many contexts. Cosmology is one of those examples. Measuring mass requires that the spacetime be asymptotically flat (at least as far as anyone can tell).

 

[Stingray]

I was trying to find an answer to my question reading chapter 7 of Sean Carroll's Lecture Notes on General Relativity (http://arxiv.org/gr-qc/9712019 ) and my impression is that there exists a coordinate system called Eddington-Finkelstein coordinates, which is adequate for remote observers and does allow crossing of the event horizon. Is this correct?

Regards.

I looked at the section you're talking about. The part important to this discussion is (p 189)

"The fact that we never see the infalling astronauts reach r=2M is a meaningful statement, but the fact that their trajectory in the t-r plane never reaches there is not."

To translate, external observers never see anything fall into a black hole, but that doesn't mean that things don't fall in. Particles will fall in in a finite amount of *proper* time, but someone sitting outside the hole won't ever see it.

This might have little to do with reality. I suspect that it is taking the Schwarzschild solution too far. In real life, there is matter (Schwarzschild assumes a perfect vacuum everywhere), there is time dependence, and there is an external universe. Intuitively, each of these things could invalidate any results on passing through horizons. I don't know the answer, but its interesting to think about.

If you can find it, I'd recommend a book called "Black Holes: The Membrane Paradigm," edited by Kip Thorne, Price, and Macdonald. It gives a much more astrophysically-motivated conceptualization of black holes than the standard one.