$κ$-General-Relativity II: An Astrophysical Observable from a 2-Body system
Daniel Rozental, Ofek Birnholtz
TL;DR
The paper investigates how RL, arising from $ ext{kappa}$-Minkowski NCST, produces a measurable uncertainty in the observed BBH inspiral frequency. By modeling BBHs in a local operator framework and applying covariance/Delta-method analysis, it derives orientation- and distance-dependent RTUs that accumulate over the inspiral, effectively introducing a 1.25PN-like deviation. Face-on binaries yield tiny, distance-independent RTUs, while edge-on configurations exhibit distance-dependent RTUs that scale with observer distance and orbital energy. This work reframes a QG phenomenology as a potentially testable GW observable, emphasizing the need for novel waveform models to constrain quarter-PN deviations with future detectors or PBH-focused scenarios.
Abstract
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.