# Effective mass of a black hole?

Suppose a black hole forms from a given mass of particles such as the core of a star going supernova. The black hole formed will have an effective mass due to the curvature of space time induced. Such a mass is presumably the inferred mass deduced from the effect of the black hole on the motion of nearby bodies. How does this effective mass compare with the original mass of particles all of which ended up "in the black hole"? Is the effective mass less greater or the same as the formation mass?

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In general relativity, mass/energy of any system is conserved from the point of view of a distant observer (I forget the name of this theorem). We use this mass when we talk about how heavy a black hole is because we are (very) far away.

If you start with particles that are stationary, the total mass of the system is slightly less than the mass of the particles (because of gravitational binding energy). When they fall toward each-other to make a hole, additional (a few % typically) energy is released as gravitational waves (and light rays, neutrinos, etc). Due to conservation of energy, this means less mass for the final hole. In fact, asymmetric radiation of gravitational waves also can create a recoil effect that ejects the hole formed (although this case is for two black holes merging):