Geodesic motion around a distorted static black hole

Abstract

In this paper we study geodesic motion around a distorted Schwarzschild black hole. We consider both timelike and null geodesics which are confined to the black hole's equatorial plane. Such geodesics generically exist if the distortion field has only even interior multipole moments and so the field is symmetric with respect to the equatorial plane. We specialize to the case of distortions defined by a quadrupole Weyl moment. An analysis of the effective potential for equatorial timelike geodesics shows that finite stable orbits outside the black hole are possible only for q ∈ (qmin, qmax], where qmin ≈ −0.0210 and qmax ≈ 2.7086 × 10 −4 , while for null equatorial geodesics a finite stable orbit outside the black hole is possible only for q ∈ [qmin, 0). Moreover, the innermost stable circular orbits (ISCOs) are closer to the distorted black hole horizon than those of an undistorted Schwarzschild black hole for q ∈ (qmin, 0) and a null ISCO exists for q = qmin. These results shows that an external distortion of a negative and sufficiently small quadrupole moment tends to stabilize motion of massive particles and light.

Metamorphoses of a photon sphere

“…In accordance with the study of the equatorial null geodesics around a distorted Schwarzschild black hole [52], where it was shown that null circular orbits in the black hole equatorial plane exist only if q ≥ q min , where q min = 1 − 2 cos(π/9) 24 cos 2 (π/9) + 20 cos(π/9) + 2 ≃ −0.020944533 ,…”

“…The next term is the quadrupole, which is defined by a quadrupole moment a 2 . It defines the most dominant, nontrivial distortion field that allows for equatorial null geodesics [52], and it also captures the structure of many celestial objects that are nearly symmetric with respect to their equatorial plane. Here we shall consider only the quadrupole distortion and neglect the higher-order multipole moments.…”

“…Here we consider a quadrupole distortion. This type of distortion allows for equatorial null geodesics that were studied in [52]. Moreover, many celestial objects, such as stars, star clusters, and galaxies, are nearly symmetric with respect to their equatorial plane.…”

Self-gravitating perfect-fluid tori around black holes: Bifurcations, ergoregions, and geometrical properties

“…Investigating the geodesic motion around distorted black holes is a natural and active field of research, and focusing on the location of the ISCO is motivated by the astrophysical context. An example of a quite general, recent analysis in this direction is given in [23].…”

Geometry and topology of the Kerr photon region in the phase space

“…For static spacetimes, trapping of light has turned out to be a useful tool to prove uniqueness theorems; a static, asymptotically flat vacuum spacetime with a photon sphere as its inner boundary has to be a Schwarzschild spacetime [1,3]; analogous results holds for some cases with matter [2,25,26,27], and for one case even perturbative uniqueness was established [28], see also [20,21].…”