Gravitational Wave Echoes from Saturated Compact Cores: A Variable Compactness Model Based on the Holographic Entropy Bound

The black hole singularity predicted by classical general relativity, signals abreakdown of the theory at high density regions. We propose that the Schwarzschildradius is not an event horizon, but the physical surface of a saturated core, which isa state of mass-energy at the maximum entropy density permitted by the covariantentropy bound (holographic principle). This core eliminates the singularity andfills the interior volume with matter at the saturation limit. A key observableconsequence is the production of gravitational wave echoes: perturbations becometemporarily trapped within the photon sphere, reflecting between the core surfaceand the centrifugal potential barrier. The echo time delay is derived as ∆t ≈4GMc3 ln(1/ϵ), where ϵ ≡ (Rcore − Rs)/Rs parametrizes the core’s proximity to theSchwarzschild radius. Unlike previous exotic compact object models that assumea universal ϵ, the saturation principle implies ϵ may vary with the core’s equationof state, mass, and formation history. This naturally predicts a spectrum of echosignatures across the compact object population, ranging from multiple distinctchirps to single reflections or none-offering a unified framework to interpret theconflicting results of current gravitational wave echo searches.