BPS

Does not actually stand for brane preserving some supersymmetry, but that's what its doing

Remember the Reissner-Nordstrom metric around a charged black hole. It has two horizons at




Of course the case M

and



Doing a change of basis to this gives instead.





Of course the RHS should be positive. So this gives a bound banning M < Z.

To be continued with actual branes preserving supersymmetry.