Black hole mergers beyond general relativity: a self-force approach

Abstract

Gravitational waves from binary black hole mergers provide a glimpse of gravitational dynamics in its most extreme observable regime, potentially enabling precision tests of general relativity (GR) and of the Kerr description of black holes. However, until recently, numerical simulations of black hole mergers have not been possible in theories beyond GR. While recent breakthroughs have overcome that obstacle, simulations covering the full, interesting range of binary parameters remain unfeasible. Here we present a new first-principles approach to this problem. We show how self-force theory can be used to model the merger and ringdown of black holes in a broad class of gravitational theories, assuming one object is much smaller than the other. We calculate self-force effects on the merger waveform for the first time, and we demonstrate how our formulation allows us to modularly compute beyond-GR effects and readily incorporate them into a fast merger-ringdown waveform model.

Figures (3)

• Figure 1: Penrose diagram illustrating our choice of spacetime slicing (grey dotted lines) and the particle's geodesic-order plunging trajectory (solid blue curve). The dotted red lines indicate the slice on which the particle crosses the zeroth-order light ring at $r_p=3m_1$. Our choice of slicing links the waveform to the particle at all times along $\mathscr{I}^+$, far after the particle passes the light ring.
• Figure 2: Top panel: orbital frequency and rate of change of the orbital radius as a function of the orbital radius itself as the particle plunges from the ISCO at $r_p=6\,m_1$ to the horizon at $r_p=2\,m_1$. Solid curves correspond to 0PG terms in $\Omega$ and $dr_p/dt$; dashed curves, to 1PG corrections. Bottom panel: the regular field $\varphi^{\rm R}_{(1,1)}$ as a function of $r_p$.
• Figure 3: Top panel: $(2,2)$ mode of the merger-ringdown waveform in GR and beyond GR, with mass ratio $\varepsilon=1/5$ and charge-to-mass ratio $\lambda=1/8$. The two waveforms, which are aligned in time and phase at the peak of $|h_{22}|$, are indistinguishable on this scale. Bottom panel: the difference $\delta h_{22}$ between the GR and beyond-GR waveforms (black curve) and the $\varepsilon^2\lambda^2$ term in the fundamental QNM (red dashed curve).