  The recent direct observation of gravitational waves (GW) from merging black
holes opens up the possibility of exploring the theory of gravity in the strong
regime at an unprecedented level. It is therefore interesting to explore which
extensions to General Relativity (GR) could be detected. We construct an
Effective Field Theory (EFT) satisfying the following requirements. It is
testable with GW observations; it is consistent with other experiments,
including short distance tests of GR; it agrees with widely accepted principles
of physics, such as locality, causality and unitarity; and it does not involve
new light degrees of freedom. The most general theory satisfying these
requirements corresponds to adding to the GR Lagrangian operators constructed
out of powers of the Riemann tensor, suppressed by a scale comparable to the
curvature of the observed merging binaries. The presence of these operators
modifies the gravitational potential between the compact objects, as well as
their effective mass and current quadrupoles, ultimately correcting the
waveform of the emitted GW.
