Nonlinear Ringdown at the Black Hole Horizon.

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order effects are necessary in binary black hole merger simulations to model the gravitational-wave signal observed by a distant observer. Here, we show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of nonlinear modes. Specifically, we identify one quadratic mode for the l=2 shear data, and two quadratic ones for the l=4, 6 data in simulations with varying mass ratio and boost parameter. The quadratic mode amplitudes display a quadratic relationship with the amplitudes of the linear modes that generate them.

What Happens to Apparent Horizons in a Binary Black Hole Merger?

We resolve the fate of the two original apparent horizons during the head-on merger of two nonspinning black holes. We show that, following the appearance of the outer common horizon and subsequent interpenetration of the original horizons, they continue to exist for a finite period of time before they are individually annihilated by unstable marginally outer trapped surfaces (MOTSs). The inner common horizon vanishes in a similar, though independent, way. This completes the understanding of the analog of the event horizon's "pair of pants" diagram for the apparent horizon. Our result is facilitated by a new method for locating MOTSs based on a generalized shooting method. We also discuss the role played by the MOTS stability operator in discerning which among a multitude of MOTSs should be considered as black hole boundaries.

Interior of a Binary Black Hole Merger.

We find strong numerical evidence for a new phenomenon in a binary black hole spacetime, namely, the merger of marginally outer trapped surfaces (MOTSs). By simulating the head-on collision of two nonspinning unequal mass black holes, we observe that the MOTS associated with the final black hole merges with the two initially disjoint surfaces corresponding to the two initial black holes. This yields a connected sequence of MOTSs interpolating between the initial and final state all the way through the nonlinear binary black hole merger process. In addition, we show the existence of a MOTS with self-intersections formed immediately after the merger. This scenario now allows us to track physical quantities (such as mass, angular momentum, higher multipoles, and fluxes) across the merger, which can be potentially compared with the gravitational wave signal in the wave zone, and with observations by gravitational wave detectors. This also suggests a possibility of proving the Penrose inequality mathematically for generic astrophysical binary back hole configurations.