Publikace ÚTF

We continue to study the response of black-hole space-times on the presence of additional strong sources
of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of
Einstein’s equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black
holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric
thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants
determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature
(Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the
horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time)
where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being
already distinct on the level of potential and acceleration, this is still more pronounced on the level
of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes
negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been
interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do
not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/