Geometry of deformed black holes. I. Majumdar-Papapetrou binary

Abstract

Although black holes are eminent manifestations of very strong gravity, the geometry of spacetime around and even inside them can be significantly affected by additional bodies present in their surroundings. We study such an influence within static and axially symmetric (electro-)vacuum space-times described by exact solutions of Einstein's equations, considering astrophysically motivated configurations (such as black holes surrounded by rings) as well as those of pure academic interest (such as specifically "tuned" systems of multiple black holes). The geometry is represented by the simplest invariants determined by the metric (the lapse function) and its gradient (gravitational acceleration), with special emphasis given to curvature (the Kretschmann and Ricci-square scalars). These quantities are analyzed and their level surfaces plotted both above and below the black-hole horizons, in particular near the central singularities. Estimating that the black hole could be most strongly affected by the other black hole, we focus, in this first paper, on the MajumdarPapapetrou solution for a binary black hole and compare the deformation caused by "the other" hole (and the electrostatic field) with that induced by rotational dragging in the well-known Kerr and Kerr-Newman solutions.

Scattering of uncharged particles in the field of two extremely charged black holes

“…The properties of some associated curvature as well as electromagnetic invariants have been recently studied in Ref. [24].…”

Schwarzschild binary supported by an Appell ring

“…With the aim to study the geometry of black holes surrounded by other strong sources of gravity, we first [1] considered the Majumdar-Papapetrou binary made of two extremely charged black holes and found that the horizon interior is not much deformed within this class of solutions. Therefore, in the second paper [2], we tried to distort a black hole which is far from being extreme (actually the Schwarzschild one), surrounding it by a concentric static and axisymmetric thin ring (described by the aged Bach-Weyl solution).…”

“…In such coordinates, the metric reads ds 2 = −N 2 dt 2 + ρ 2 N 2 dφ 2 + e 2λ N 2 dρ 2 + dz 2 and only contains two unknown functions N ≡ e ν and λ of ρ and z, of which ν, representing the Newtonian potential, is given by solution of Laplace equation, so it superposes linearly when the field of multiple sources is being seeked. 1 For the Weyl-type metric, the above invariants N , κ and K are given by…”

“…We do not repeat the whole basics on Weyl space-times, please see for example the first paper[1] of this series, including references.…”

Extremally charged line

“…The two-hole MP spacetime can also be obtained as the extreme limit of the double RN solution [7]. Recently, MP spacetimes were used to study the influence of external sources on black holes since one expects that the most powerful effect is to be expected from an additional black hole [8].…”