[Paper Review] Geometries with integrable singularity -- black/white holes and astrogenic universes

V. N. Lukash, Vladimir Strokov|arXiv (Cornell University)|Sep 13, 2011

Cosmology and Gravitation Theories3 references3 citations

TL;DR

This paper proposes a cosmogenesis paradigm in which collapsing astrophysical objects generate geodesically complete black/white hole geometries with integrable singularities at r=0, enabling continuous spacetime extension into expanding white-hole regions. These regions host cosmological flows driven by effective matter and inflation, suggesting that universes may form inside black holes via quantum-gravity-induced particle creation and momentum transfer from collapsing matter.

ABSTRACT

We briefly review the problem of generating cosmological flows of matter in GR (the genesis of universes), analyze models' shortcomings and their basic assumptions yet to be justified in physical cosmology. We propose a paradigm of cosmogenesis based on the class of spherically symmetric solutions with {\it integrable} singularity $r=0$. They allow for geodesically complete geometries of black/white holes, which may comprise space-time regions with properties of cosmological flows.

Motivation & Objective

• To address the initial value problem in cosmology by proposing a physical mechanism for generating expanding cosmological flows within general relativity.
• To overcome the limitations of existing cosmogenesis models that rely on exotic matter or unverified quantum-gravitational effects.
• To demonstrate that geodesically complete spacetimes with integrable singularities (r=0) can support continuous evolution from black hole collapse to white hole expansion.
• To explore the role of effective matter with negative pressure in T-regions of black/white holes as a source of cosmological flow.
• To propose a physical mechanism—particle creation and momentum transfer at high curvature—for launching expanding universes from collapsing astrophysical objects.

Proposed method

• Analyzes spherically symmetric solutions of Einstein's equations with a 2+2 spacetime split, focusing on integrable singularities at r=0.
• Uses geodesic completeness as a criterion to extend spacetime beyond r=0, enabling transition from black hole to white hole regions.
• Introduces effective energy-momentum tensors with moderate (integrable) divergence at r=0 to model quantum-gravitational effects phenomenologically.
• Constructs a toy model invariant under r → -r to simulate symmetric black/white hole geometries and study T-region dynamics.
• Applies the weak, strong, and dominant energy conditions to assess physical viability, noting that violations may be acceptable in quantum-gravity regimes.
• Models particle creation and momentum transfer at high curvature near r=0, linking collapsing matter to the launch of cosmological expansion.

Experimental results

Research questions

• RQ1 Can spacetime geodesics be extended through the r=0 singularity in spherically symmetric solutions, enabling a continuous transition from black hole to white hole regions?
• RQ2 What physical conditions—specifically effective matter properties—are required to sustain expanding cosmological flows in the T-regions of black/white holes?
• RQ3 How can the initial momentum for cosmological expansion be generated without violating energy-momentum conservation, and what role does tidal gravity play?
• RQ4 To what extent can quantum-gravitational effects be modeled phenomenologically via effective energy-momentum tensors with integrable singularities?
• RQ5 Can the collapse of astrophysical objects naturally trigger the formation of new, expanding universes via particle creation and spacetime extension?

Key findings

• Geodesically complete black/white hole solutions exist for a class of spherically symmetric spacetimes with integrable singularity at r=0, allowing continuous extension of radial geodesics into the white-hole region.
• The T-regions of such solutions contain expanding, homogeneous matter flows with spatial symmetry ℝ×𝕊², resembling cosmological flows.
• Effective matter with negative longitudinal pressure (p < 0) is required to source the eternal black/white hole geometry and sustain the white-hole region.
• The momentum from the collapsing matter is transferred via long-range tidal forces to the effective matter in the T-region, launching the expansion of the white-hole universe.
• Inflation in the T-region can grow the cosmological flow to quasi-Hubble scales, making it observationally plausible as a model for our universe.
• The paradigm differs from bouncing or baby-universe models by linking cosmogenesis to the collapse of real astrophysical objects and quantum-gravitational particle creation, not initial conditions or symmetry assumptions.