A conservative solution to the Singularity Problem in Classical GR

TL;DR

The paper addresses the black hole singularity problem by proposing a conservative interior regularization within classical GR plus semiclassical QFT, replacing the singular interior with a null hypersurface $\Sigma$ and a conformally flat bubble manifold. The SRPT is triggered as the exterior spacetime approaches algebraic speciality, with a curvature–dependent mass term $m_{\rm eff}^2 = m_0^2 - \xi_{\Delta} |\Delta|^{1/6}$ that nucleates a domain wall and transfers ADM data onto $\Sigma$ via Barrabes-Israel junction conditions. Ingoing Hawking radiation provides an isotropic energy influx that seeds an almost FLRW interior without inflation; anisotropy growth then drives the interior to acquire nonzero Weyl curvature inside the bubble. The exterior geometry remains, to leading order, the standard Schwarzschild/Kerr/Reissner–Nordström solution, while a covariant flux-balance law and the generalized entropy $S_{gen}$ (defined as the area term plus exterior entropy) ensure the second-law-like behavior along $\Sigma$. Altogether, the framework preserves familiar black hole observables at leading order while offering a mechanism to resolve singularities and seed a cosmology-like interior, with future work on wall dynamics, stability, and potential observational footprints.

Abstract

We present a conservative approach to the black hole singularity problem that remains within the framework of classical General Relativity (GR) supplemented by semiclassical quantum field theory (QFT). Our construction replaces the singular interior of a black hole with a null characteristic hypersurface that carries the exterior ADM data. The excised singular interior is replaced by a conformally flat bubble manifold. We assume the characteristic data on $Σ$ are shear-quiet (vanishing Bondi news and shear to leading order) so that the initial development is conformally flat (Weyl = 0) over an early epoch. We further posit that the ingoing Hawking radiation flux provides statistically isotropic initial conditions on the bubble boundary, seeding a nearly FLRW-like epoch without first undergoing exponential inflation. The overall framework is consistent with the generalized second law of thermodynamics and offers a possible resolution of the singularity problem without invoking a full theory of quantum gravity.

Figures (1)

• Figure 1: Penrose diagram of our universe, the bubble manifold and their extensions. The red dotted boundary around the bubble manifold is the boundary of the manifold where the geometry is the same as our manifold. The green dotted boundary is the null hypersurface with initial data for the bubble manifold and has an internal geometry with higher degree of symmetry. The blue path (including blue dotted path) represents a possible trajectory of a field/particle.