Daniel Rozental | Searcharxiv

arXiv2025

$κ$-General-Relativity I: a Non-Commutative GR Theory with the $κ$-Minkowski Spacetime as its Flat Limit

We employ a twist deformation of infinitesimal diffeomorphisms to construct a modification of General Relativity on a non-commutative spacetime extending the local kappa-Minkowski geometry. This spacetime arises in Deformed Special Relativity (DSR) models, where a fundamental length scale is incorporated into Special Relativity as an effective description of quantum gravitational effects. To avoid the mathematical and physical inconsistencies associated with twisting the Poincare group, we instead deform the dilatation-enlarged IGL(3,1) group, constructing a covariant and explicitly consistent gravitational theory (distinct from Weyl gravity). The relativistic consistency of the twisted kappa-Minkowski spacetime is demonstrated, including deformed transformations and differential structures. A physically motivated Inonu-Wigner (IW) contraction procedure is suggested to enable a well-defined classical limit, addressing the correspondence issue. This framework provides a consistent foundation for a dynamical sector of DSR and allows, in future treatment, explicit computations that could advance phenomenological predictions.

gr-qc↗

arXiv2025

$κ$-General-Relativity II: An Astrophysical Observable from a 2-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.

gr-qc↗