Abstract
We consider the behavior of the innermost stable circular orbit (ISCO) in the magnetic field near "dirty" (surrounded by matter) axially-symmetric black holes. The cases of near-extremal, extremal and nonextremal black holes are analyzed. For nonrotating black holes, in the strong magnetic field ISCO approaches the horizon (when backreaction of the field on geometry is neglected). Rotation destroys this phenomenon. The angular momentum and radius of ISCO look model-independent in the main approximation. We also study the collisions between two particles that results in the ultra-high energy $E_{c.m.}$ in the centre of mass frame. Two scenarios are considered - when one particle moves on the near-horizon ISCO or when collision occurs on the horizon, one particle having the energy and angular momentum typical of ISCO. If the magnetic field is strong enough and a black hole is slow rotating, $E_{c.m.}$ can become arbitrarily large. Kinematics of high-energy collision is discussed. As an example, we consider the magnetized Schwarzschild black hole for an arbitrary strength of the field (the Ernst solution). It is shown that backreaction of the magnetic field on the geometry can bound the growth of $E_{c.m.}$.
Highlights
The motion of particles in the vicinity of black holes is a subject that has been continuing to attract interest until recently
It is the proximity to the horizon that enables us to describe some properties of innermost stable circular orbit (ISCO), even not specifying the metric and even with a magnetic field
We took into account both factors, so generalized the previous results for the case when both matter and magnetic field are present
Summary
A new circumstance came into play that makes the properties of ISCO important in a new context. It is the ISCO that turns out to be a natural venue for the realization of the so-called BSW effect Several years ago, it was shown by Bañados, Silk, and West that if two particles collide near the black hole horizon of the extremal Kerr metric, their energy Ec.m. in the center-of-mass (CM) frame can grow unboundedly [10]. It is the proximity to the horizon that enables us to describe some properties of ISCO, even not specifying the metric (so we work in a model-independent way) and even with a magnetic field This can be considered as one manifestation of universality of black hole physics. 12, the exact solution of the Einstein–Maxwell equations (static Ernst black hole) is chosen as a background for collisions This enables us to evaluate the role of backreaction of the magnetic field on Ec.m. In Sect.
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