# Does the mass distribution matter in (Schwarzschild) black holes?

Is it possible that from the same initial mass different black hole radius will be created due to different mass distribution during black hole creation? If mass is concentrated more on the outside bigger event horizon will be created? If mass is concentrated more in the center smaller black hole will be created?

No, it is not possible.

This is the whole essence of the so-called no-hair theorem: that all previous details concerning the object from which the black hole formed has no bearing whatsoever on the properties of the final object, except for mass, electric charge and angular momentum. And also, that these quantities enter only as global values, not with their initial distributions.

Notice that the impact of the theorem is even wider than you seem to imply: not only it does not matter which initial distribution these three quantities had (for instance, you might have some matter corotating while some fraction of matter is counterrotating, but it does not matter so long as you have the same total angular momentum), but also matter might be made of leptons or baryons, charged could be made of different number of positively or negatively charged particles, or of mostly neutral particles plus only one sign of charge.

Also, the no-hair theorem states that this property is not the result of some special assumption or of highly symmetrical initial conditions, but that instead it is the necessary outcome of any history of the matter going into the black hole, regardless of any parameter save for the global values of M, Q, J.

• So is event horizon always created spherical even if it is created during collision of two heading from opposite direction massive stars? Aug 13, 2014 at 22:53
• @PawelWelsberg Yes, because the total angular momentum vanishes. If the total angular momentum is not zero, the event horizon is flattened at the poles. Aug 13, 2014 at 23:02
• And, yet, there is a non-trivial discussion about the black hole information paradox as raised by Bekenstein, I believe. Is it truly lost, as the classical equations predict, or does quantum gravity save the day, and black holes do have microscopic degrees of freedom (fuzzball?), as string theory seems to predict? Aug 13, 2014 at 23:03
• Too many questions in too little space. My reply dealt with GR. As for quantum effects, though many interesting discussions are present, there is of course no definite prediction about any of these topics because of the well-known lack of a suitable theory. Aug 13, 2014 at 23:10
• The distribution of matter will affect how much energy is lost to gravitational radiation during formation of the hole, and in that sense will affect its mass and radius, though this doesn't seem to be the sort of effect the original question had in mind. Aug 14, 2014 at 5:06

Going out on a limb here, if string theory is right, and one can make microscopic black holes in an accelerator, there should be gravitational analogs of Stern-Gerlach (and more general spin polarization) experiments for these microscopic black holes. They could also have measurable excited states leading to decay spectra.

For macroscopic black holes, of course, the thermalization timescale would be unmeasurably short, and they will, just like MariusMatutiae said, not return any useful information about their past beyond these mentioned conserved quantities. That, of course, is no different from nuclei, atoms and molecules.