The stakes of this question are enormous. In 1969, Roger Penrose proposed the cosmic censorship conjecture, arguing that singularities arising from gravitational collapse should always be concealed within event horizons, forever shielded from any external observer. If that conjecture holds, the predictive power of general relativity is preserved, because a naked singularity would be a region where the theory’s equations break down in plain sight, spewing causally connected unpredictability into the observable universe. If it fails, physics as we know it could lose its ability to forecast the future in certain extreme scenarios. Despite decades of effort, no general proof or disproof of cosmic censorship has ever been achieved, and the new study adds a crucial piece to this ongoing investigation.

The central insight of the new research is that the fate of a collapsing matter cloud is governed by the dynamics of the apparent horizon, a surface that marks the boundary of a region where even light cannot escape. Unlike the event horizon, which is defined globally and requires knowledge of the entire future evolution of the spacetime, the apparent horizon is a quasi-local construct: it can be located by examining the geometry of the spacetime at a given moment. Within the apparent horizon lie trapped surfaces, two-dimensional surfaces from which both outgoing and ingoing light rays converge. The authors show that whether the final singularity is visible or hidden depends critically on the relative timing of when these trapped surfaces first form and when the central singularity comes into existence.

Technically, the analysis is carried out for spherically symmetric collapse of what relativists call a type-I matter field, a broad class that includes most physically reasonable forms of matter, such as dust, perfect fluids, and scalar fields, where the energy-momentum tensor has a well-behaved algebraic structure. The authors work with initial data satisfying C-squared regularity, meaning the relevant functions are twice continuously differentiable, and the weak energy condition, which demands that matter has non-negative energy density as measured by any observer. These are the same broad physical assumptions that underpin most rigorous work on collapse in classical general relativity, giving the results considerable generality within the spherical model.

The key diagnostic tool in the study is the behavior of outgoing null geodesics, the trajectories that light rays follow as they emerge from the region near the forming singularity. If families of future-directed outgoing null geodesics can escape from arbitrarily close to the central singularity, then the singularity is locally visible: light signals generated at or near it can reach distant observers, at least for a finite period before the apparent horizon eventually swallows the region. If, on the other hand, the apparent horizon forms early enough in the collapse, before the singularity has a chance to communicate with the outside, then every outgoing light ray is trapped, and the singularity is destined to be hidden within a black hole. The relative timing of these two events, the birth of trapped surfaces and the birth of the singularity, therefore acts as the decisive switch between the two possible end states.

This timing criterion connects the new work to a long lineage of collapse studies stretching back to the foundational models of the 1930s and the numerical analyses of Eardley and Smarr in 1979, which first made explicit how the apparent horizon curve in a collapsing dust cloud determines what external observers can see. Subsequent work by Christodoulou in the 1980s and 1990s demonstrated both violations of cosmic censorship in dust collapse and the instability of certain naked singularities in scalar field collapse, while Joshi and collaborators showed through the 1990s and 2000s that naked singularities arise in inhomogeneous dust, perfect fluid, and scalar field models under wide classes of initial conditions. The new paper synthesizes this tradition by characterizing, in terms of the apparent horizon’s dynamics, precisely when visibility occurs for a general type-I matter field rather than for one specialized equation of state at a time.

Why does the distinction between apparent horizon and event horizon matter so much? The event horizon of a black hole is teleological: its location at any instant depends on the entire future history of the spacetime, including whether collapse will ever end. This makes it useless for real-time diagnostics, both analytically and in numerical simulations. The apparent horizon, by contrast, is determined by the local geometry, specifically by the vanishing of the expansions of both future-directed null congruences emanating from a closed two-surface. Because of this quasi-local character, apparent horizons can be located in numerical relativity codes during dynamical simulations, and they have become the workhorse of modern black hole physics, from modeling binary mergers detected by gravitational-wave observatories to testing general relativity with future detectors such as LISA. Establishing that the apparent horizon’s evolution controls singularity visibility therefore ties an abstract question about censorship to quantities that observers and simulators can actually compute.

The results also carry weight for observational astrophysics. If naked singularities can form in realistic collapse, they would not be mere mathematical curiosities but potential astrophysical objects with distinct observational signatures. Recent theoretical work has explored how accretion flows around naked singularities differ from those around black holes: hydrodynamic and general-relativistic magnetohydrodynamic simulations of accretion onto Reissner-Nordström-type naked singularities and timelike naked singularities reveal outflows and disc properties that differ qualitatively from the black hole case. Earlier studies by Joshi, Malafarina, and Narayan showed that accretion disc profiles can in principle distinguish black holes from naked singularities. A rigorous characterization of when collapse produces visible singularities, grounded in the apparent horizon dynamics, helps identify the parameter regimes in which such exotic objects might plausibly exist and be searched for with X-ray and gravitational-wave facilities.

There are also connections to quantum gravity and to the critical phenomena discovered by Choptuik in 1993, where scalar field collapse exhibits universal scaling behavior near the threshold of black hole formation, with naked singularities appearing exactly at the critical point. The authors’ own recent research program has extended this picture, examining universality and criticality in massless scalar field collapse and the possible formation of primordial naked singularities in the early universe. If tiny naked singularities were produced in the primordial cosmos, their subsequent quantum evaporation, a possibility explored by Goswami, Joshi, and Singh in 2006, could have left observable imprints. The new timing criterion provides a framework for assessing whether such scenarios are dynamically permitted under generic, physically reasonable initial data.

Of course, important caveats remain. The analysis is restricted to spherical symmetry, and the cosmic censorship question in full generality, with rotation, gravitational radiation, and arbitrary asymmetries, remains open. Numerical studies of nonspherical collapse, from Shapiro and Teukolsky’s rotating spheroids to modern binary black hole simulations, continue to probe whether censorship holds beyond the symmetric idealization. Nevertheless, by reducing the visibility question to the concrete, computable dynamics of the apparent horizon and trapped surfaces, and by establishing the result for general type-I matter under standard energy and regularity assumptions, Koushiki and Joshi have converted a famously intractable conjecture into a sharply posed dynamical problem. The race between trapped surfaces and the singularity, it turns out, is the whole story, and knowing the rules of that race brings physicists one step closer to deciding whether the universe’s most violent endings are always hidden from view.

Subject of Research: Visibility of spacetime singularities and apparent horizon dynamics in spherical gravitational collapse

Article Title: Apparent horizon and causal structure of spacetime singularities

Article References: Koushiki, & Joshi, P. S. (2026). Apparent horizon and causal structure of spacetime singularities. General Relativity and Gravitation, 58(10), Article 114. https://doi.org/10.1007/s10714-026-03618-y

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03618-y

Keywords: general relativity, gravitational collapse, spacetime singularities, apparent horizon, trapped surfaces, naked singularity, cosmic censorship, black holes, null geodesics, event horizon, type-I matter field, weak energy condition

Among the most consequential topics at the meeting was the so-called Hubble tension, the statistically significant discrepancy between independent measurements of the present-day expansion rate of the universe. Distance-ladder determinations anchored by Type Ia supernovae calibrated with Cepheid variables yield values of the Hubble constant that differ substantially from those inferred from the temperature anisotropies of the Cosmic Microwave Background within the standard Lambda-CDM framework. The tension now stands at roughly five sigma, and its resolution may reflect uncharacterized systematics in one or both measurement chains, or a genuine breakdown of the standard cosmological model. Michael S. Turner delivered a critical status report on Lambda-CDM, framed as a sequel to his talk at the inaugural 2017 Lemaître meeting, focusing on the DESI Collaboration’s evidence from its first two data releases for a time-evolving dark-energy equation of state in the w0–wa parametrization. The most provocative feature of that evidence is a dark-energy density sharply peaked around redshift z of roughly 0.5, rather than the constant value predicted by a cosmological constant. Joseph Silk, meanwhile, opened from the observation that modern cosmology effectively began with Georges Lemaître in 1927, and proposed a strikingly concrete response to the field’s observational limits: a sustained scientific presence on the lunar far side, whose radio silence, seismic quietness and lack of atmosphere make it uniquely suited to several genuinely guaranteed measurements. Participants also emphasized how data from the James Webb Space Telescope have already tested the robustness of Lambda-CDM at high redshift.

Inflationary cosmology, the leading account of the early universe’s homogeneity, isotropy, flatness and the origin of the primordial density fluctuations that seeded cosmic structure, received a thorough technical audit. Michele Cicoli presented recent progress on inflation and dark energy within type IIB string compactifications, centering on the Loop Blow-up Inflation scenario, in which a blow-up Kähler modulus with an approximate shift symmetry drives slow-roll inflation through a potential generated by string-loop corrections. The model yields sharp, falsifiable predictions: a scalar spectral index in the narrow range between about 0.9757 and 0.9765, and a tensor-to-scalar ratio of roughly two times ten to the minus five, in excellent agreement with current CMB and baryon-acoustic-oscillation data. On dark energy, Cicoli surveyed the difficulty of realizing quintessence in a UV-complete setting, presenting a two-axion hilltop model exploiting poly-instanton suppression as the most promising route to a phenomenologically viable, string-derived dynamical dark energy. Renata Kallosh and Andrei Linde reviewed inflation from the perspective of supergravity, highlighting the predictive successes of attractor models while stressing the open challenge of embedding inflation in a UV-complete framework.

The Swampland programme, which seeks to identify which effective low-energy theories can be consistently completed into quantum gravity, featured prominently. Hirosi Ooguri reviewed Swampland-type constraints in asymptotically anti-de Sitter spacetimes, where they can be rigorously tested via the AdS/CFT correspondence. He summarized, in particular, a proof with Daniel Harlow that any exact global symmetry in a bulk gravitational theory is incompatible with the consistency of the dual boundary conformal field theory, and a further result establishing universal bounds on the exponential decay rate governing the Distance Conjecture in two-dimensional CFTs dual to AdS3 gravity. Cumrun Vafa combined the Distance Conjecture, the associated species scale, the de Sitter Conjecture and the TransPlanckian Censorship Conjecture to derive increasingly sharp bounds on inflationary potentials. Imposing the TCC, he argued, renders standard slow-roll inflation viable only in a strongly fine-tuned corner of parameter space with an essentially unobservable tensor-to-scalar ratio. Applied to the present epoch, the same reasoning implies that our universe, if presently in a metastable de Sitter phase, cannot remain so for much longer than of order two trillion years, a bound Vafa frames as string theory’s answer to the question posed by the very title of Lemaître’s 1927 paper, now viewed from the vantage of the universe’s future rather than its origin.

Thomas Hertog returned most directly to Lemaître’s own 1931 Nature letter on the primeval atom, reading it as an early and remarkably prescient statement that the origin of the universe should be a proper object of physical, rather than merely metaphysical, inquiry. Tracing a conceptual line from Lemaître’s primeval quantum through the Hartle–Hawking no-boundary wave function to the modern “top-down” reformulation of quantum cosmology, Hertog confronted a long-standing embarrassment of the no-boundary proposal: taken at face value, it overwhelmingly favors nearly empty histories incompatible with the existence of observers. He showed that once an observer is treated as a genuine quantum subsystem within the theory, modeled concretely via the information content of a CMB temperature map, the resulting conditional probability distribution can undergo a Page-like transition, in which the dominant saddle point shifts abruptly from a low-inflation history to one beginning deep in the eternal-inflation regime for sufficiently detailed observational situations. The past, on this view, is contingent on the question being asked of the wave function, a striking modern echo of Lemaître’s insistence at the 1958 Solvay Council that any information on the state of matter must be inferred from the condition that the actual universe has been able to evolve from it.

The nature of spacetime singularities, whether at the Big Bang or in the deep interior of black holes, remains one of the most profound unresolved problems in theoretical physics, and two contributions took Lemaître’s own 1933 dust model as their explicit point of departure. Claus Kiefer and Hamid Mohaddes asked what happens to the classical singularity of Lemaître’s model under canonical quantization. Working first with a thin null dust shell and then with the full Lemaître–Tolman–Bondi cloud, reduced shell by shell to a self-adjoint Hamiltonian for the outermost layer, they constructed exact, normalizable wave-packet solutions whose unitary evolution forces the collapsing packet to bounce at a minimal radius and re-expand rather than terminate. This picture persists in the homogeneous Oppenheimer–Snyder limit under affine coherent-state quantization, though the authors remain open about whether the bounce timescale is compatible with observation and whether the method extends beyond spherical symmetry. Alexander Kamenshchik revisited the problem of singularity crossing, showing that a Big Bang–Big Crunch singularity in the Jordan frame can correspond to a perfectly regular geometry in the Einstein conformal frame, allowing the crossing to be described unambiguously. The idea, first worked out for isotropic Friedmann–Lemaître universes, has since been extended to anisotropic Bianchi-I and Kantowski–Sachs cosmologies, and in the quantum cosmology of soft future singularities such as the “Big Brake,” the wave function can vanish at the singularity while the correctly normalized probability density does not.

Gabriele Veneziano presented progress on the central open problem of the Pre-Big-Bang scenario he proposed with Maurizio Gasperini over three decades ago: whether the singularity separating the inflationary pre-bang branch from the decelerating post-bang branch can be tamed by higher-order alpha-prime corrections consistent with the O(d,d) duality symmetry of classical string cosmology. Building on the all-order reformulation by Hohm and Zwiebach, a Hamiltonian approach reduces the existence of regular bouncing solutions to a simple analytic criterion, yielding explicit bounces and, with a non-perturbative dilaton potential, late-time attractors of Minkowski, metastable-vacuum or de Sitter type. Roberto Casadio questioned the common assumption that quantum gravity is relevant only at the Planck length, arguing that this conflates the Compton length governing scattering with the very different scales governing bound states. Proposing that quantum effects become important for any self-gravitating system whose compactness approaches unity, he built a many-body ground state for a dust ball from a hierarchy of quantized shells obeying hydrogen-atom-like radial equations, finding a core radius of order the gravitational radius, with the ground-state occupation number reproducing the Bekenstein area scaling. The resulting interior has finite tidal forces and no inner Cauchy horizon, replacing the point singularity with what Casadio calls an integrable singularity. Misao Sasaki reviewed the formation of primordial black holes from rare, large-amplitude curvature perturbations, with non-minimally coupled curvaton models capable of producing primordial black hole dark matter in the asteroid-mass window of roughly 10^18 to 10^22 grams together with a scalar-induced gravitational-wave background within reach of forthcoming detectors such as LISA. Gia Dvali proposed a microscopic, string-theoretic account of de Sitter horizon entropy via open–closed string duality, showing that at a critical coupling the species entropy of open-string degrees of freedom in a D9–anti-D9 brane construction exactly reproduces the closed-string Gibbons–Hawking entropy.

Edward Witten presented progress toward a background-independent algebraic formulation of quantum gravity, constructing an algebra of observables, fields gravitationally dressed to the worldline of an observer with bounded-below energy, defined without reference to any particular background spacetime and becoming background-dependent only once a Hilbert-space representation is chosen. Specialized to a geodesic observer in empty de Sitter space, the algebra acquires a genuine trace, and the thermal Bunch–Davies state of maximum entropy reproduces, via its vanishing relative entropy, Bousso’s intuition that the late-time empty static patch is the entropically preferred state. Raphael Bousso and Sami Kaya extended the notion of a generalized entanglement wedge from AdS/CFT boundary regions to arbitrary gravitating regions, yielding a full complementarity theorem for holograms and showing that any spacetime containing a Big Bang or Big Crunch is trivially reconstructible, an information-theoretic counterpart to Lemaître’s intuition that a genuine cosmological beginning renders any pre-existence of the universe causally inaccessible. Batoul Banihashemi and Ted Jacobson argued that the Gibbons–Hawking derivation of the Bekenstein–Hawking entropy A/4G from the Euclidean gravitational path integral rests on shaky foundations, since the Euclidean Einstein–Hilbert action is unbounded below and the correct integration contour is unknown, and showed how a Lorentzian version of the Gauss–Bonnet theorem combined with a Regge-calculus treatment of the horizon’s deficit angle can reproduce the Bekenstein–Hawking result. On the foundational side, Rosa-Laura Lechuga-Solis and Daniel Sudarsky examined the routine identification of quantum uncertainties with genuine stochastic fluctuations in inflationary cosmology, deriving modified power spectra with a substantially suppressed tensor-to-scalar signal using spontaneous collapse dynamics, while Lajos Diósi formulated a stochastic semiclassical dynamics based on spontaneous quantum monitoring that reduces in the Newtonian limit to a modified Schrödinger–Newton equation free of Born-rule violations.

The collection was completed by Dominique Lambert’s historical and epistemological reconstruction of the genesis of Lemaître’s 1931 primeval-atom hypothesis, tracing its roots to Lemaître’s engagement with cosmic-ray physics, his 1930–1931 work on quantum theory, and his response to Eddington’s philosophical rejection of a cosmic beginning, while carefully distinguishing the shifting ontological status the hypothesis held across his career and his explicit theological separation of a physical “natural beginning” from metaphysical creation. The conference, co-sponsored by the Vatican Observatory and the Istituto Nazionale di Fisica Nucleare, achieved its principal goal of fostering productive interaction between theory and observation. As the editors note, progress on the Hubble tension will require improved observational precision and theoretical creativity in exploring extensions of and alternatives to Lambda-CDM; the resolution of spacetime singularities awaits a formulation of a quantum theory of gravity; and the relationship between quantum mechanics, measurement and gravity remains one of the deepest open problems in theoretical physics. The enduring example of Georges Lemaître, a scientist who combined mathematical rigor, physical intuition, philosophical sophistication and intellectual courage, serves as an inspiration for all of these endeavors.

Subject of Research: A topical collection from the Lemaître Conference 2024 presenting research on black holes, gravitational waves, spacetime singularities, cosmology and quantum gravity.

Article Title: Black holes, gravitational waves and space-time singularities (Lemaître Conference 2024)

Article References: Bianchi, M., Cacciatori, S. L., Galaverni, M., Gionti S.J., G., & Scardigli, F. (2026). Black holes, gravitational waves and space-time singularities (Lemaître Conference 2024). General Relativity and Gravitation, 58(9), Article 108. https://doi.org/10.1007/s10714-026-03608-0

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03608-0

Keywords: black holes, gravitational waves, spacetime singularities, Hubble tension, Lambda-CDM, inflation, quantum gravity, string theory, primordial black holes, horizon thermodynamics, Georges Lemaître, cosmology