The following are a selection of movies from some recent numerical simulations that I have performed using the Spectral Einstein Code (SpEC) as part of my research in collarboation with the Simulating eXtreme Spacetimes (SXS) collaboration. For more, please see the SXS Collaboration's YouTube channel.

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Advanced LIGO saw gravitational waves from two black holes that merged over a billion light years from Earth. This computer simulation shows (in slow motion) what this would look like up close.  If this movie were played back in real time, it would last for about one third of a second.
In this movie, the black holes are near us, in front of a sky filled with stars and gas and dust. The black regions are the shadows of the two black holes: no light would reach us from these areas.  Light from each star or bit of gas or dust travels to our eyes along paths (light rays) that are greatly bent by the holes' gravity and by their warped spacetime. This is called "gravitational lensing."  Because of this gravitational lensing, the pattern of stellar and gas/dust images changes in fascinating ways, as the black holes orbit each other, then collide and merge.
The ring around the black holes, known as an "Einstein ring," arises from all the stars in a small region directly behind the holes; gravitational lensing smears their images into the shape of a ring.
The gravitational waves themselves would not be seen by a human near the black holes (though they would be felt!) and so do not show in this video, with one important exception: The gravitational waves that are traveling outward toward the small region behind the black holes disturb that region’s stellar images in the Einstein ring, causing them to slosh around in the ring, even long after the collision. The gravitational waves traveling in other directions cause weaker, and shorter-lived sloshing, everywhere outside the Einstein ring.
Credit: SXS Lensing


A computer simulation of the gravitational waves from the merging black holes that LIGO observed. Our three-dimensional space is shown as a two-dimensional surface, with one dimension removed. The black holes’ strong gravity curves the space near them into funnel shapes. As the black holes spiral together and merge into one, gravitational waves ripple outward. The movie is shown in slow motion, about 40 times slower than real time.



This movie shows two black holes that are spinning very rapidly (about 97% of the theoretical maximum) as they spiral together and merge. The simulation was published in Geoffrey Lovelace, Michael Boyle, Mark A. Scheel, and Bela Szilagyi, Class. Quantum Grav. 29, 045003 (2012) (, and the movie was rendered by Cornell undergraduate researcher Robert McGehee, Jr.

The holes trace out their orbits as cyan and magenta lines, and their spins point along the white arrows. The colored surfaces are the holes' apparent horizons, shaded by the horizon vorticity (i.e., by how much an observer's body, oriented perpendicular to the horizon, would be twisted by the hole as it spins).
The black holes’ spins and the orbital angular momentum point in the same direction. Consequently, the holes experience an “orbital hangup” effect previously seen in simulations with lower spins: the holes merge much more slowly (after many more orbits) than if the spins were pointing in the opposite direction. This gives the system time to radiate enough angular momentum so that the final black hole will have a spin less than the theoretical maximum (the final hole ends up with about 95% of the maximum in this case). The initial holes have the highest spins of all binary-black-hole simulations to date.




Merging black holes are among the most promising sources of gravitational waves for the Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO). Accurate predictions of the gravitational waves emitted by merging black holes---necessary both for detecting the waves in LIGO data and for estimating the properties of the binaries that generated those waves---can only be constructed using numerical simulations. In this talk, I will review recent progress and discuss current challenges in numerical simulations of merging, spinning black holes. After summarizing recent results (including the effects of black-hole spin on the holes' motion, the remnant hole's mass and spin, and the emitted gravitational waveforms), I will discuss the significant challenges that simulations of spinning binary black holes must still overcome. In particular, I will discuss the challenges of constructing and applying simulated waveforms to gravitational-wave data analysis, particularly when the spins are misaligned (causing orbital and spin precession) and when the holes are spinning near the theoretical maximum.