I Radiatively efficient accretion onto BHs

[zviz]

It is said that accretion disk around compact objects like black hole can convert up to 40% of the mass of an infalling material into energy.
This means, to my understanding, that if we throw 1kg of matter onto a BH through an accretion disk, during the accretion 0.4kg worth of energy in the form of radiation would be emitted, and the BH would increase its mass by only 0.6kg.

My question is: where did the rest of the mass go? My confusion arises from thinking about the problem in the atomic level. We throw X atoms of hydrogen (totaling 1kg) into the BH. The same X atoms reach the BH, and yet the BH increases its mass by the mass equivalent of only 0.6X atoms of hydrogen. Phrased differently, I wonder what would have happened if I would've stopped the X atoms just before they entered the event horizon, and measured their mass by some experiment, what would I have found? Would the mass be X or 0.6X?

 

[PeterDonis]

It is said

Where? Please give a reference.

 

[PeterDonis]

where did the rest of the mass go?

The term "mass" is confusing you here because it has two different meanings.

The locally measured mass of an individual hydrogen atom, let's say, does not change, whether you measure it far away from the hole, just above the horizon, or inside the hole.

The mass of the hole, OTOH, is a global quantity, not the same kind of thing as a locally measured mass. Objects falling into the hole that emit radiation become more tightly bound gravitationally to the hole; in other words, the gravitational binding energy of the hole + object, considered as a system, becomes more negative, which is another way of saying that the total energy of the hole + object system decreases (by the amount of energy contained in the radiation that is emitted and escapes to infinity).

 

[Dale]

where did the rest of the mass go?

It went out with the radiation.

This is the famous mass deficit. A bound system has less mass than an unbound system with the same constituents. The mass deficit is not attributable to any specific sub-part of the system. It is a deficit of the system as a whole.

My confusion arises from thinking about the problem in the atomic level.

At the atomic level there is nothing to think about here. This feature only exists at the system level.

Measurements made on bound systems cannot identify a specific component where the binding energy came from. It came from the system as a whole, not some specific part of the bound system.

Note, this is not specific to black holes. It applies equally to any bound system. Planets bound to stars, electrons bound to nuclei, protons bound to a nucleus.

 

[PeterDonis]

Thread closed for moderation.

 

[PeterDonis]

Some cleanup has been done. Thread reopened.