Modern black hole theory annoys me.
Black holes are a construct of Einstein’s GR equations.
Who derived the obvious idea that adding mass to a black hole makes it bigger?
Yes I know that the mass of a BH is proportional to its ‘radius’ but who derived the idea that it would be more massive?
I suspect that it does gain mass and radius but there are only local mass and energy conservation laws from Einstein’s GR equations.
Global conservation does not stem from local conservation; you cannot add the stress-energy tensor here to the one there any more than you can add two vectors from different vector spaces.
Perhaps if you lowered or let fall a spherically symmetric sphere of mass onto a BH you could numerically watch the mass of the BH increase.
I would like to see this calculation.
Spherical accretion is only a 2D calculation.
The spherical symmetry precludes gravitational radiation.
(I think that Dick White and Stirling Colgate did such calculations in the late 60's.
I suppose they were watching for such deficits at least for debugging.
I suppose that if they had gotten surprising results we would have heard.)
<p>If mass is conserved there is probably an important and currently unknown global conservation theorem of some sort.
Perhaps most people don’t seek such a theorem because they think it is obvious.
I don’t know what form it would take.
Perhaps conservation of several quantities in asymptotically flat space.