High School How does black hole merger cause loss of mass?

[danihel]

I’ve heard that the black holes that merged together and were the source that triggered gravity wave detector, have lost three solar masses.

I understand to a very limited degree the basic notion of energy conversion like is the case in nuclear fusion/fission, annihilation, chemical energy conversion. But until now I thought the only way a black hole can lose mass is by the Hawking radiation.

I don’t even know how to more specifically pose this question as I have no clue by what mechanism collision of these objects, consisting of infinitely small point of infinite mass surrounded by different degree of space time distortion, can cause them to lose mass or just energy conversion of any kind.

 

[Jonathan Scott]

The gravitational energy emitted in the waves was presumably from the kinetic energy lost as the black holes spiralled together.

 

[danihel]

Thanks for the answer. I understand that kinetic energy is a component that increases observed mass but if I'm not wrong it shouldn't add mass to the black holes themselves, meaning the size of a black hole doesn't change with its kinetic energy.
Maybe I got it completely wrong, i just wish to get a clearer idea about this.

 

[Jonathan Scott]

Regardless of whether it's black holes or billiard balls, an object which is moving relative to the reference frame has rest energy which is due to its mass plus kinetic energy which is due to its motion. The kinetic energy is part of the overall energy of the system, and if for example the objects collide and stick together the effective energy of the combined object in the center of mass frame includes the kinetic energy in some form (for example as heat energy, which is essentially microscopic kinetic energy, or energy in changed chemical bonds).

When a pair of black holes come close together, the forces involved mean that they will have huge kinetic energy relative to their combined center of mass frame, which will tend to make them orbit around one another assuming they weren't moving exactly toward each other (which would be very unlikely). However, if they are really close together, the huge gravitational effects effectively stretch and shrink spacetime as they orbit, which causes some energy to be converted to gravitational waves and lost from the orbit, causing them to spiral together. When they collide, the remaining kinetic energy will effectively become part of the total energy of the combined object. However, the merged object will initially still be lumpy and may continue to give off a little more energy as further gravitational waves until it settles to a smoothly rotating shape. The final energy as seen locally is greater than the sum of the rest energy of the two black holes. As seen relative to their original distant state, the final energy is equal to the potential energy they had relative to one another plus their initial kinetic energy plus their rest masses, minus the energy that was emitted in gravitational waves.

 

[Chronos]

There is no free lunch. Gravity waves carry off energy and energy requires a source. A prodigious amount of energy is necessary to generate gravity waves detectable by LIGO. During inspiral the binary black holes gain kinetic energy. This energy is released in the form of gravitational waves. They progressively increase in energy as distance decreases which culminates in an enormous energy release when merger occurs. This energy is extracted at the price of the mass of the binary system. There is no other possible source for such power, which can exceed the EM energy output of the observable universe at merger

 

[Chalnoth]

I understand to a very limited degree the basic notion of energy conversion like is the case in nuclear fusion/fission, annihilation, chemical energy conversion. But until now I thought the only way a black hole can lose mass is by the Hawking radiation.

Neither black hole lost mass. The final black hole was more massive than either of the black holes that collided.

As for precisely why so much energy is emitted in gravitational radiation from a pair of colliding black holes, I couldn't tell you precisely. All I can say is that the specific rule which applies to black holes is that the horizon of a black hole always increases in area (this is similar to the rule that states that entropy always increases).

I don’t even know how to more specifically pose this question as I have no clue by what mechanism collision of these objects, consisting of infinitely small point of infinite mass surrounded by different degree of space time distortion, can cause them to lose mass or just energy conversion of any kind.

That's not the right way to think of a black hole. The singularity at the center is mathematical nonsense and almost certainly an incorrect description. We don't currently know the correct description of the interior of a black hole.

But fortunately, we don't need to. It is possible to describe all of the physics of how a black hole behaves by referring only to the behavior of space-time outside its event horizon. And that description states that colliding black holes end up with much less mass than the two source black holes had summed together.

 

[PeterDonis]

The final black hole was more massive than either of the black holes that collided.

Just to clarify, it was more massive than either one individually, but it was not more massive than both of the original holes put together. It was 3 solar masses less massive. That 3 solar masses is what was emitted as gravitational waves.

I thought the only way a black hole can lose mass is by the Hawking radiation.

More precisely, the only way a single, isolated, non-rotating black hole can lose mass is by Hawking radiation. A single, isolated, rotating black hole can lose mass by the Penrose process, which reduces the hole's spin and also its mass; this is a classical process and doesn't require quantum effects as Hawking radiation does. And a system of multiple black holes can lose mass by having the holes merge and gravitational waves be emitted during the merger process; this is also a classical process and doesn't require quantum effects.

 

[Lord Crc]

So roughly how much of the initial mass of each BH was due to kinetic energy?

 

[PeterDonis]

roughly how much of the initial mass of each BH was due to kinetic energy?

This question does not have a well-defined answer. The "kinetic energy" description is only heuristic, and breaks down if you push it too far. One key limitation of it is that "kinetic energy" is frame-dependent; the description of the merger in which the holes "gain kinetic energy as the spiral inward" implicitly adopts a frame in which the final black hole, after the merger, is at rest. But you could equally well adopt a frame in which, say, initial black hole #1 is at rest; in that frame initial black hole #1 has zero kinetic energy.

Another key limitation of the "kinetic energy" interpretation is that the mass of a black hole is not "stored" locally; black holes are vacuum and don't have matter sitting inside them that is the source of their mass. The mass of a black hole is really a property of the spacetime geometry around it. So what we really have is a complete isolated system, that starts out containing two black holes and ends up containing one, and in the process the total mass of the system decreases by 3 solar masses as gravitational waves carry off that amount of energy. Right before the merger, you could say, heuristically, that that 3 solar masses of energy was "stored" as kinetic energy of the initial holes (here we are again adopting the frame in which the final hole is at rest); but earlier than that, the kinetic energies of the holes were smaller, but the total mass of the system was the same. (In the same frame, we could account for this by saying that there was also "gravitational potential energy" present, but that concept also has limitations.)