The famous three parameter family of BH solutions
(i.e. (
)
Kerr-Newman solution)
is believed to describe the final fate of any sufficiently
massive configuration of matter which cannot support itself in
a hydrostatic equilibrium.
All other characteristics of matter (such as scalar charge or,
which is more understandable,
deviations from spherical symmetry not related to rotation)
must radiate away or ``fall into the BH'' according to this belief.
But the only reason why this family of solutions is separated from
other possible ones is because (according to various ``no-hair''
theorems [12], [11])
it is the only family of (stationary) BH solutions
with non-singular horizons.
Look at these ``no-hair'' theorems from another perspective. What they basically say is that a generic solution in GR does contain singularities not covered by horizons. Then what is the reason for neglecting all these singular solutions? Well, it has been speculated (the so called Cosmic Censorship Conjecture) that ``physically reasonable matter configurations'' would never evolve to naked singularities starting from non-singular initial conditions. But this conjecture is now known to be false (see [13] for a discussion of the known counterexamples and further references).
What is the meaning of the scalar solution which is basically indistinguishable from Schwarzschild BH, but is not a BH and rather describes a naked singularity (analogous to electric field of a point charge in electrodynamics)? Yes, it is unstable. And it is reasonable, because scalar charge can radiate (unlike mass, electric charge and angular momentum, which makes (exterior of) the Kerr-Newman solution stable). But for arbitrarily small scalar charge the scalar solution is still singularly different from Schwarzschild and is not a BH! In [10] it is shown that the horizon in scalar field collapse must form asymptotically (in time), and it is exactly what happens here when scalar charge radiates, but still the horizon does not really form, there is only approach to it (and numerical calculations cannot distinguish between these two different possibilities).
And all those static axially symmetrical solutions. What do they tell us? ...
GR is already 85 years old and a lot of research has been done in the field, but even though much is known (e.g. a huge number of solutions to the GR equations have been found), the physical understanding of gravity beyond the Newtonian physics is still on a very low level.