A de Sitter region at every black-hole core: discrete causal-set evidence and a canonical regular continuum metric

Assumes 1–2 courses of background. Domain terms may appear without definition.

In Einstein’s general relativity, black holes contain a singularity at their center—a point where curvature becomes infinite and the theory breaks down. This paper resolves that singularity using a nonlocal quantum gravity theory called Spectral Causal Theory, which modifies gravity at very small distances. The authors work at two complementary levels: a fundamental discrete model of spacetime (causal sets) and a continuous effective description. At the discrete level, they show that a measure of local curvature remains bounded even when probing extremely close to where the classical singularity would be—meaning the singularity simply does not appear in this more fundamental picture. At the continuous level, they derive that the black hole’s interior is described by a regular metric known as the Hayward metric, which features a de Sitter (expanding-universe) core instead of a singularity. Crucially, the size of this core is fixed by the theory’s own parameters (the “fakeon” mass scale), leaving no free constants—only the black hole’s mass and the fundamental cutoff. This regular black hole has two horizons, its central curvature is finite and independent of mass, and it passes all solar-system tests because corrections to Einstein’s predictions appear only far beyond observational reach. The energy conditions are mostly satisfied, with mild violations confined to the inner core. The authors also address an expected instability at the inner horizon (mass inflation) and suggest that the discrete spacetime structure may ultimately regularize it as well. Overall, the work provides a consistent framework in which black hole singularities are replaced by regular, de Sitter-like cores, both at a fundamental discrete level and in the effective continuum theory.

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