<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>κ</mml:mi></mml:math>-general relativity II: An astrophysical observable from a two-body system

We examine gravitational waves (GWs) from Binary Black Holes (BBH) as possible suitable systems for investigating the physical validity of theories predicting the Relative Locality (RL) effect, an effect arising in the kappa-Minkowski non-commutative spacetime, a central property in theories of Quantum Gravity (QG) Phenomenology. Hence, we are taking a step towards realizing the purpose of the phenomenological effort of having observational evidence to put constraints on QG approaches. In particular, we show that the RL effect induces an uncertainty in the observed rotational frequency omega during the inspiral phase. This uncertainty becomes stronger with increasing observational distance. It also increases with decreasing orbital radius, and it statistically accumulates as an increasing variance of omega over successive cycles. In terms of the post-Newtonian deviations, the uncertainty contributes at 1.25th order, an order that has not yet been directly constrained in GW analyses.