Nils Siemonsen

Nonlinear treatment of a black hole mimicker ringdown

In this reference, we perform the first nonlinear and self-consistent study of the merger and ringdown of a black hole mimicking object with stable light rings. To that end, we numerically solve the full Einstein-Klein-Gordon equations governing the head-on collisions of a series of binary boson stars in the large-mass-ratio regime resulting in spinning horizonless remnants with stable light rings. We broadly confirm the appearance of features in the extracted gravitational waveforms expected based on perturbative methods: the signal from the prompt response of the remnants approaches that of a Kerr black hole in the large-compactness limit, and the subsequent emissions contain periodically appearing bursts akin to so-called gravitational wave echoes. However, these bursts occur at high frequencies and are sourced by perturbations of the remnant’s internal degrees of freedom. Furthermore, the emitted waveforms also contain a large-amplitude and long-lived component comparable in frequency to black hole quasi-normal modes. We further characterize the emissions, obtain basic scaling relations of relevant timescales, and compute the energy emitted in gravitational waves.

In this figure, we show (left panels) the ℓ = 2 (top) and ℓ = 8 (bottom) components of the gravitational waves emitted after the merger of the sequence of four binary boson stars compared with that of the black hole-boson star binary (labelled “Kerr”). The waveforms are aligned in time as in Figure 1. (central panels) Close-ups of the first bursts in each of the two polar modes. See Appendix B for details on uncertainties of these waveforms. (right panels) The Fourier transform of the full C = 0.38 signal as function of angular frequency ω, focusing only on dominant radiation components in each mode: the long-lived component in the ℓ = 2 mode (top) and the burst-like high-frequency component in the ℓ = 8 mode (bottom).

The state of the C = 0.38 binary system at selected coordinate times during the plunge, merger, and ringdown. The main plots show the Newman-Penrose scalar Ψ4 at coordinate radii r > 3M0, which qualitatively shows the local gravitational waves. We indicate the initial production and subsequent propagation of the high-frequency component of the prompt response as “PR” together with a dotted white circle (roughly corresponding to the propagating wavefronts). Similarly, the first two gravitational wave bursts are labelled 1st and 2nd. In the region r < 3M0, we show two (black and gray) surfaces of constant scalar field magnitude |Φ| (with a close-up in the insets); recall, spinning boson stars are toroidally shaped. Arrows in the insets indicate the motion of the largest perturbation of |Φ| between snapshots. The symmetry axis is at x = 0.