Black hole gravitational waves in the effective field theory of gravity

Abstract

We investigate the propagation of gravitational waves on a black hole background within the low-energy effective field theory of gravity, where effects from heavy fields are captured by higher-dimensional curvature operators. Depending on the spin of the particles integrated out, the speed of gravitational waves at low energy can be either superluminal or subluminal as compared to the causal structure observed by other species. Interestingly, however, gravitational waves are always exactly luminal at the black hole horizon, implying that the horizon is identically defined for all species. We further compute the corrections on quasinormal frequencies caused by the higher-dimensional curvature operators and highlight the corrections arising from the low-energy effective field.

Causality in curved spacetimes: The speed of light and gravity

“…To summarize, when dealing with a gravitational effective theory, superluminal low-energy speeds (with respect to the metric out of which it is constructed) is not only possible, but is sometimes demanded by underlying causality and analyticity criteria. Indeed this has been well known since the work of [33,34] for QED in curved spacetime [35][36][37][38][39][40][41][42], and more recently noted in [45,46] for GWs. Relativistic causality nevertheless remains intact because the causal support of the retarded propagator vanishes outside of the light cone of the metric, defined in the field frame with a well-defined decoupling limit.…”

“…The central result of [45] is that the low-energy refractive index nð0Þ is determined at leading order by C IR 2 , and the sign of the latter directly determines the sub-or superluminality of the low-energy speed of propagation. In situations where the leading curvature squared terms vanish, such as Schwarzschild spacetime, it is the curvature cubed terms which determine the leading effect, as calculated in [45] and considered in detail in [46].…”

“…Typically when the angular speed is subluminal, the radial speed is superluminal, as is the case if we think of this EFT as arising from integrating out a spin-1=2 field. Generically, the radial speed is given in terms of the coupling constants d 9;10 as follows [46] and is superluminal whenever 2d 9 þ d 10 < 0. In the past, these types of arguments have been used to constraint EFTs.…”

“…The previous criterion can sometimes be correct; however, in the canonical case of gravitational effective theories it is not necessarily the case, and indeed demanding c s ≤ 1 for all species can sit in contradiction with those same requirements of causality and analyticity. In two recent papers [45,46] it was pointed out that integrating out matter fields typically leads to curvature operators in the lowenergy EFT of gravity that can lead to a (small) superluminal low-energy speed for GWs. For the low-energy EFT of gravity, constraining the signs of the low-energy operators to be so as to entirely forbid superluminal lowenergy speed, no matter how small, would lead to a criterion in contradiction with known partial high-energy completions and more generally expectations based on analyticity.…”

Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity

“…Whenever the two eigenvalues of the eikonal phase matrix are distinct, a possible violation of causality at small impact parameter arises, as noticed already at tree level in [87]. See also [74,75,[88][89][90][91][92][93] for further discussions an resolutions of this issue in UV-complete theories, [80,87,94,95] for earlier appearances of the eikonal operator and [72,73] for related discussions involving helicity flip and no-flip amplitudes.…”