EinsteinProcaScalar Gravity with Dynamical Renormalisation Group Flow

Abstract We present a novel extension of general relativity in which the renormalisation group scale is promoted to a dynamical scalar field λ(x), modifying the gravitational coupling G(λ). While motivated by theoretical requirements for horizon-avoidant collapse, the primary contribution of this work is the computational realisation of this theory as a production-grade numerical instrument. Drawing on the discrete-time geometry framework developed in Geometric Chronon Field Theory [1], we derive the system from a covariant variational principle and prove its strong hyperbolicity via a first-order reduction and a block-diagonal principal symbol analysis. Beyond the theoretical framework, we provide a complete, exascale-ready implementation architecture featuring: a finite-volume MUSCL-HLL flux-conservative solver with Z4c constraint damping; an integrated Cauchy-Characteristic Extraction (CCE) pipeline for high-fidelity waveform propagation to future null infinity I+; and a fault-tolerant, asynchronous master execution loop designed for HPC environments. This framework enables direct prediction of observable signatures such as RG-corrected ringdown modes and horizon-avoidant bounce phenomena.