# GW190521 black hole merger total mass calculation and missing mass, how does this happen?

I have just read an article about that black hole merge event (it's in Italian):

What made me curious is that the article tell that a 66 solar mass black hole merge with a 85 solar mass black hole to form a 142 solar mass black hole. If the datas are correct, that suggests to me that during a merge event, matter inside a black hole is ejected (66+85=151).

Is that (mass ejection) possible? I have always thought that escape form the inside of a black hole is impossible.

I suppose it is somewhat possible if we think about Hawking radiation, but due my amateur knowledge level I have not been able to dig into this very much.

I remember the first time I'd read about a gravitational wave detection and the resulting mass I also stopped when I realized the numbers didn't add up. At first it's shocking. While we might be aware that very tiny changes in mass are associated with huge amounts of energy release, it's absolutely amazing to think of a mass the size of our Sun radiated as energy!

But that's exactly what happens in the mergers of black holes. The fraction of mass converted to energy is much smaller when two normal stars merge, gravitational waves are produced but are small in comparison. But when the objects are extremely dense so that they can orbit very close before the merger, as in the case of neutron stars and black holes, those gravitational waves are powerful and a significant fraction of that mass will radiate away as ripples in space itself.

Answer(s) to Fraction of initial mass lost (radiated) by neutron star mergers compared to black hole mergers? indicate that this fraction can be up to several percent in these cases.

We can convert an absurdly tiny amount of those distortion waves back into other forms of energy as a thought experiment, though not practical. For more on that, see answers to

• Amazing, i have never thought that grvitational wave could carry so much energy Commented Sep 5, 2020 at 19:26

This is not "mass ejection". This is the release of gravitational potential energy (as gravitational waves)

When the two black holes fall towards each other they release Energy as gravitational waves. Energy is mass (by E=mc²). This mass must come from somewhere, so the combined mass of the merged black holes must be less than the sum of the masses of the individual black holes.

In fact the same thing happens when any two masses fall together. It is just that the amount of mass lost when a football is dropped to the ground is so small that it is undetected. But when black holes fall together, the mass lost is significant.

• A spherical collapse results in a change in gravitational potential energy, but no gravitational waves. Commented Sep 5, 2020 at 7:33