Revisiting event horizon finders

Abstract

Event horizons are the defining physical features of black hole spacetimes, and are of considerable interest in studying black hole dynamics. Here, we reconsider three techniques to find event horizons in numerical spacetimes: integrating geodesics, integrating a surface, and integrating a levelset of surfaces over a volume. We implement the first two techniques and find that straightforward integration of geodesics backward in time is most robust. We find that the exponential rate of approach of a null surface towards the event horizon of a spinning black hole equals the surface gravity of the black hole. In head-on mergers we are able to track quasi-normal ringing of the merged black hole through seven oscillations, covering a dynamic range of about 10 5 . Both at late times (when the final black hole has settled down) and at early times (before the merger), the apparent horizon is found to be an excellent approximation of the event horizon. In the head-on binary black hole merger, only some of the future null generators of the horizon are found to start from past null infinity; the others approach the event horizons of the individual black holes at times far before merger.

Final remnant of binary black hole mergers: Multipolar analysis

“…10-13 for the current multipoles show similar agreement, but are omitted here because they look essentially the same. Incidentally, similar (though less detailed) agreement with quasinormal ringing frequencies was noted in the oscillation of the area of spatial slices of the event horizon in other recent simulations using the SpEC code [46].…”

“…The work here depends heavily on the formalism of dynamical horizons [25], which are dependent on the slicing of spacetime (or, from a different viewpoint, are themselves invariantly defined yet carry unique foliations into apparent horizons that are compatible with the foliation of spacetime only in certain time slicings). Use of a unique and invariantly defined horizon such as the event horizon may be of interest (and is possible in the SpEC code [46]), however it would not alleviate the problem of slicing dependence, as a slicing must be chosen at some point to break the three-dimensional horizon worldtube into two-dimensional surfaces on which the spherical harmonic projections are taken.…”

Event horizon deformations in extreme mass-ratio black hole mergers

“…A general operational way to obtain the event horizon, e.g., for the binary black-hole merger spacetime, is to first go to the final state of the spacetime, in which a final, nearly quiescent, black hole exists, with an easily identifiable, late portion of the event horizon. Null rays on that horizon can be propagated backwards in time, and trace out the entire event horizon [13][14][15].…”

Naked singularity formation in $${f({\mathcal R})}$$ gravity

“…Thus the regions of extreme curvatures and densities are concealed from the outside observers. The event horizon or surface of a black hole is defined as the boundary of the spacetime that is causally connected to future null infinity [28], or in other word the boundary between events from which light rays emitted inside this boundary surface can not escape to future infinity while those emitted outside in a suitable direction can. Both event and apparent horizons coincide in stationary spacetimes, however this case is not generally true in dynamical ones.…”