Nonperturbative suppression of beyond-General-Relativity effects in quadratic gravity

Abstract

Quadratic gravity is a well-motivated extension of general relativity~(GR) wherein the Einstein-Hilbert action is augmented by quadratic curvature terms. This theory is equivalent to GR in an effective-field-theory framework, while the two theories are different at the non-perturbative level. As we have recently shown, black holes in quadratic gravity have a rich linear response, including extra scalar, vector, and tensor quasinormal modes that can be excited in physical processes, even when the stationary solution is the same as in GR. Here, by studying the gravitational-wave emission from point particles plunging into a Schwarzschild black hole in quadratic gravity, we show that observable deviations from GR are exponentially suppressed in the GR limit. This provides a nonperturbative realization of the equivalence between quadratic gravity and GR predicted in the effective-field-theory framework.

Figures (8)

• Figure 1: Normalized waveforms for the monopolar perturbations in the highly relativistic limit ($\gamma\gg 1$), for an extraction radius of $r\mu=(10,100)$ and $M\mu=(0.01,0.05,0.1)$. In each panel the amplitude has been rescaled to its maximum value.
• Figure 2: Top: Monopolar energy flux emitted by a relativistic radially infalling particle, for $M\mu\in[0.001,0.3]$. Each curve is normalized to its maximum value. Bottom: Total emitted energy (normalized by its maximum value) as a function of $M\mu$. The total flux vanishes exponentially in the weak-coupling regime (i.e., as $M\mu$ increases): the dashed line corresponds to the fit $c_1 e^{-c_2 \mu M}$ with $c_1\approx 303$ and $c_2\approx -33$. The shaded area denotes the strong-coupling region where black hole solutions are radially unstable. For completeness, in the inset we show the behavior in the strong-coupling regime (i.e., $M\mu\to0$).
• Figure 3: Left: Amplitudes of the massive perturbation functions for $\ell=1$ for $M\mu=[0.01,0.4]$ as a function of the frequency $\omega$, normalized by their peak value for $M\mu=0.01$. Right: Peak values of the amplitudes as a function of the mass $\mu$. In both panels, the log-linear scale makes the exponential suppression evident.
• Figure 4: Same as Fig. \ref{['fig:peak_scaling_l1']} but for $\ell=2$.
• Figure 5: Fundamental ($n=0$) quasinormal modes of a Schwarzschild black hole in quadratic gravity, $\mu\in [0,0.5]$, with $\ell=0,2$, with polar parity, computed using a matrix-valued continued fraction method Pani:2013pma.