Towards a non-singular paradigm of black hole physics

This paper, “Towards a non-singular paradigm of black hole physics” (J. Cosmology and Astroparticle Physics, 2025), is not a single new theoretical model with a dedicated dataset; rather, it is a structured overview of a research program aimed at replacing the standard general-relativistic picture of black holes—characterized by event horizons and spacetime singularities—with a less idealized, “non-singular” framework. The core research question is: what would it mean, in a physically adequate way, for black hole spacetimes to be non-singular, and what are the most promising theoretical directions and observational strategies to distinguish regular black holes and horizonless “black hole mimickers” from standard black holes?

The motivation matters because the standard picture relies on idealizations tied to infinities. Event horizons are teleological and cannot be directly detected in any finite-time experiment, while singularities signal incomplete understanding of spacetime and matter at extreme conditions (infinite curvature/energy density in classical GR). A non-singular paradigm aims to redefine black holes as metastable, regular bound states of the gravitational field—an idea the authors connect to Hawking’s perspective—so that physical trajectories remain complete and observables remain finite.

Within the field, this work is significant as a synthesis and roadmap. It organizes the landscape of “regular black holes” (spacetimes with trapped regions and outer horizons but no spacetime singularities, typically with regular cores and inner horizons or spacelike wormhole throats) and “black hole mimickers” (horizonless, trapped-region-free ultracompact objects such as traversable wormholes or ultracompact stars). The paper also emphasizes that these categories are not exhaustive, but they provide a useful classification for comparing theoretical consistency, dynamical plausibility, stability, and observational signatures.

Methodologically, the paper uses a conceptual and literature-review approach shaped by a week-long focus program at IFPU in Trieste (Nov 11–15, 2024). Each section corresponds to thematic questions discussed during the program, and the authors draw on prior results across semiclassical gravity, quantum gravity-inspired effective actions, numerical simulations (often in symmetry-reduced settings), and perturbation theory for stability and observational channels. Because it is an overview, there is no sample size, experimental protocol, or statistical inference in the usual sense; instead, the “evidence” is the accumulation of theoretical arguments, partial dynamical studies, and observational constraints from existing instruments.

Key “findings” are therefore presented as consensus-like conclusions and open problems rather than numerical effect sizes. The paper’s most central technical contribution is the articulation of pragmatic criteria for what “non-singular” should mean. The authors propose two necessary conditions for a predictive physical theory: (1) completeness of physical trajectories (no abrupt endings for physical trajectories; they note that spacelike trajectories may be incomplete without necessarily implying pathology), and (2) finiteness of physical observables measured along those trajectories. In practice, they argue that fully identifying the complete set of physical observables can be difficult in quantum-gravity frameworks, so a heuristic approach is to require completeness of metric geodesics and finiteness of scalar curvature invariants.

Using these criteria, the paper contrasts standard black holes (exact solutions of Einstein vacuum/electrovacuum with trapped regions containing singularities and bounded by event horizons) with regular black holes (geometric deformations with trapped regions and outer horizons but no spacetime singularities, replaced by regular cores and often inner horizons or wormhole throats) and with mimickers (horizonless, no trapped region, with a finite-redshift boundary termed a “surface”). The authors stress that once singularities are removed, event horizons are no longer strictly required for predictability, so regular black holes and mimickers can be constructed without invoking event horizons.

The paper then addresses dynamical transitions between these classes. It argues that (i) mimickers can plausibly collapse into standard black holes under accretion if their surface cannot sustain spacelike evolution; and (ii) regular black holes can evolve into mimickers if the trapped region disappears in finite time. The latter is discussed carefully: pushing a classical black hole beyond extremality (overcharging/overspinning) would typically yield naked singularities and violate weak cosmic censorship, but the analogous transition in a regular (non-singular) setting can correspond geometrically to forming a mimicker without necessarily violating cosmic censorship. However, the physical mechanisms and timescales for such transitions remain only partially understood.

A major theme is whether “geometrodynamics” (continuum differential-geometry-based field theories) can generically cure singularities. The authors note two caveats: a theory might resolve singularities only for some initial conditions, and some physically relevant regimes might require discrete geometry or topology change. They point to action-principle-based proposals that bypass these caveats, but emphasize that realistic non-singular evolution—through collapse and mergers—still lacks a fully developed dynamical framework.

For formation, the paper surveys mechanisms that introduce new physics near horizon formation or at Planckian densities. Examples include gravastar-like phase transitions, fuzzball-inspired horizon avoidance, and semiclassical/quantum-gravity effects that effectively violate energy conditions or modify the gravitational dynamics via higher-curvature terms. The authors also highlight that many arguments are currently based on idealized static or spherically symmetric settings, leaving open dynamical questions, especially beyond spherical symmetry.

For instabilities, the paper provides a structured taxonomy of how different spacetime features behave under perturbations. It emphasizes that instabilities are not merely shortcomings; they can be informative, indicating transient phases in collapse and helping select viable long-lived configurations. The paper lists: Hawking-radiation-driven instability of event/outer horizons (or Hawking meta-stability for macroscopic objects), mass inflation instability at Cauchy/inner horizons (including semiclassical effects when horizon surface gravities mismatch), Aretakis instability for extremal horizons, accretion-driven instability of mimicker “surfaces,” ergoregion instability for horizonless rotating objects, and slow-decay behavior near stable light rings with possible nonlinear consequences. It also notes that wormhole throats rely on topology change, which introduces conceptual challenges for purely geometrodynamic theories.

Observationally, the paper identifies channels sensitive to replacing event horizons and singularities: gravitational and electromagnetic wave windows, black hole imaging (shadow and photon rings), and gravitational-wave phenomena such as echoes. The authors argue that long-lived outer horizons can mimic event-horizon phenomenology for arbitrarily long times, so the key observational differences may come from trapped-region closure and radiation release (potentially quasi-periodic bursts). For mimickers, the absence of trapped regions allows waves to propagate into the interior, motivating photon-ring modifications, thermal emission from heated surfaces, and gravitational-wave echoes or tidal heating.

A crucial practical point is that many observational signatures are currently limited by incomplete knowledge of nonlinear dynamics beyond GR and by astrophysical uncertainties. For gravitational waves, uncertainties include eccentricity, spin precession, tides, microlensing, and viscosity; for images, uncertainties are dominated by accretion-disk physics (magnetization, non-thermal emission, ray-tracing limitations). The paper discusses strategies to mitigate degeneracies, including focusing on photon rings of sufficiently high order (e.g., where emission details become less relevant) and using “lensing bands” to marginalize over astrophysical effects: if lensing bands of a given photon-ring order do not overlap for two spacetimes, detecting that ring order can rule out one spacetime.

Limitations are acknowledged implicitly and explicitly throughout. The authors repeatedly note that dynamical understanding is the missing link: stability and observational predictions often rely on linearized or test-field approximations, while nonlinear evolution and timescales are poorly known for most regular black hole and mimicker models. They also emphasize that many formation studies are restricted to symmetry-reduced scenarios, and that observational constraints can be degenerate with environmental effects. Finally, because the paper is an overview, it does not provide new quantitative constraints or statistical results; its “limitations” are those of the broader literature it synthesizes.

Practically, the paper is aimed at theorists and model-builders who need a coherent definition of non-singularity, a map of dynamical and stability obstacles, and a set of observational discriminants. It is also relevant to observationalists and data analysts planning tests with current and next-generation facilities (LIGO/Virgo/KAGRA, EHT, and future instruments like LISA, Einstein Telescope, Cosmic Explorer, and proposed EHT successors). The authors’ overarching implication is that progress will require coupling improved theoretical dynamics (especially nonlinear waveforms and accretion/merger modeling) with robust observational “null tests” that can break degeneracies between spacetime physics and astrophysical systematics.

Overall, the paper argues that the conceptual motivation for a non-singular paradigm is strong and that the mathematical machinery and phenomenological opportunities are maturing, but that the field’s decisive bottleneck is dynamics: understanding how regular black holes and mimickers form, evolve, and remain stable on physically relevant timescales, and then predicting observables that survive astrophysical uncertainties.