# Embeddings of dynamical event horizons

Event horizons are distorted by tidal stresses that arise from a binary companion. Studying and quantifying these distortions has been the main Ph.D. project of Stephen O’Sullivan. On this page, we show videos illustrating situations in which a black hole’s horizon distortions vary dynamically, following the dynamics of the applied tide which itself follows the dynamics of the binary’s orbit. These videos are specifically designed to match up to Section V of the final chapter of Stephen’s thesis; when the paper based on this chapter is posted to the arXiv, we will link it here.

We begin with a simple case: A circular orbit of a Schwarzschild black hole. The orbit is at

*r*= 6

*M*(the smallest radius stable Schwarzschild orbit), and inclined with respect to our chosen equatorial plane by 60 degrees. For Schwarzschild, orbital inclination doesn’t mean much: The hole is spherically symmetric, and any orbital plane is equivalent to any other. We see this here by the fact that the horizon’s distortion moves in perfect lockstep with the orbit. If we rode along with the orbiting body, the event horizon would look static; all of its dynamics are perfectly locked to those of the orbit.

(Double click on the frame below to begin the animation.)

We next examine a more interesting case: A circular orbit of radius

*r*= 6

*M*inclined at 60 degrees around a Kerr black hole with spin

*a*= 0.6

*M*. Orbital inclination is very important here; the black hole’s spin axis picks out a preferred direction, and the black hole is not spherically symmetric. Even though this orbit is of constant radius, the tidal field that acts on the horizon varies over the course of the orbit. We see “bending” dynamics for the black hole as the orbit proceeds in this case; the bulge’s behavior is not “locked” to the orbit in the same way that we saw in the Schwarzschild case. The rotating axes seen in this case (and the next two as well) are tied to the black hole’s rotation; they rotate at the horizon spin frequency,

*a*/(2

*M r*H), where

*r*H is the coordinate radius of the event horizon.

(Double click on the frame below to begin the animation.)

Now, move away from circular orbits. Our next case is a black hole with spin

*a*= 0.85

*M*. The orbit is confined to the equatorial plane; it has eccentricity

*e*= 0.7, and semi-latus rectum

*p*= 4

*M*. This means the orbital radius varies from

*r*= 2.35

*M*to

*r*= 13.33

*M*over an orbit. The tidal field (which varies as one over

*r*cubed) thus varies by a factor of about 182 over an orbit! We see this here in that the horizon’s distortion varies from essentially undistorted at large radius to highly distorted as the orbit passes near its closest approach.

(Double click on the frame below to begin the animation.)

The final case we examine here combines all of these features: As in the previous case, the black hole spin is again

*a*= 0.85

*M*, the orbit has eccentricity

*e*= 0.7, and semi-latus rectum

*p*= 4

*M*. Now, we incline orbit 30 degrees above the equatorial plane. We again the large-scale variation in horizon geometry as the orbit varies from minimum to maximum radius and back; in addition to this, we see the interesting “bending” dynamics associated with the smaller body’s orbital motion above and below the equatorial plane.

(Double click on the frame below to begin the animation.)