The problem of singularities and event horizons in classical black holes motivates the search for alternatives: regular black holes retain the horizon but remove the singularity, while horizonless mimickers such as gravastars lack both. Previous work in the archive has examined the properties of gravastars, their distinction from black holes via gravitational waves and electromagnetic radiation, and the birth of black holes without singularities during a cosmic bounce. However, the dynamical formation of a gravastar from collapsing matter remained unsolved: earlier studies were limited to static solutions or shell collapse. This paper fills that gap by proposing the first explicit mechanism for gravastar birth within general relativity, without invoking higher-curvature corrections.
The starting point is the Oppenheimer–Snyder collapse: a homogeneous dust sphere described by the Friedmann–Lemaître–Robertson–Walker solution, matched to an exterior Schwarzschild solution. An expanding de Sitter bubble with negative pressure, initially of zero size, is introduced inside the collapsing dust. Spacetime is divided into three regions: an inner de Sitter region, an intermediate dust region, and an outer Schwarzschild region. Matching conditions at the boundaries ensure continuity of the induced metric, and at the de Sitter boundary a surface tension and surface energy density arise. Instead of simulating forward from initial conditions, the authors integrate the equations backward in time from the final gravastar state, which reveals the required fine-tuning of parameters. Numerical integration is performed using an implicit fifth-order Runge–Kutta scheme.
It is shown that with fine-tuning of the initial energy density and spatial curvature in the de Sitter region, the bubble expands, slows down near the Schwarzschild radius, and meets the surface of the collapsing dust, forming a static gravastar. The parameter space is divided by a separatrix: below it, collapse leads to a black hole; above it, to a non-equilibrium configuration; and exactly on the line, to a gravastar. Each point on the separatrix corresponds to infinitely fine tuning, but there are infinitely many such points, giving an infinite family of initial conditions for gravastar birth. A compactness limit is found: for successful gravastar formation, the initial compactness of the dust sphere must satisfy C = M/R̄₂ ≤ 3/8 = 0.375, which is only slightly less than the Buchdahl limit of 4/9 ≈ 0.444. For higher compactness, collapse inevitably ends in a black hole. In the limit of low de Sitter energy density, the solution reduces to the Milne solution, corresponding to flat Minkowski space in hyper-spherical coordinates.
This work demonstrates for the first time that within classical general relativity, without higher-curvature terms or quantum corrections, a collapse can occur that ends neither in a singularity nor an event horizon. This differs from neighboring works, where the formation of horizonless objects was either postulated or required modified gravity. Here, the minimal extension of the Oppenheimer–Snyder collapse by adding a de Sitter bubble makes the model transparent and testable. The result raises the question of how realistic the fine-tuning required for gravastar birth is, and whether it could arise naturally, for instance from quantum fluctuations or a conformal anomaly.
Future work should verify the stability of the resulting gravastars against non-radial perturbations and deviations from spherical symmetry. It is also important to investigate more realistic equations of state for the collapsing matter instead of idealized dust. The fine-tuning might prove less stringent when quantum effects are included, such as nucleation of the de Sitter bubble due to a conformal anomaly or instabilities in anti-de Sitter space. An open question remains: which initial conditions in real collapse are more likely, those leading to a black hole or those leading to a gravastar?
The results are important for the astrophysics of compact objects, as they offer a concrete scenario for the birth of gravastars, which could be candidates for observed supermassive objects. This also affects the interpretation of gravitational-wave signals and shadow images, since gravastars can mimic black holes.
The next step should be to model the collapse with a more realistic equation of state and to study the stability of the gravastar shell. It is also important to investigate whether the nucleation of the de Sitter bubble can occur naturally, without artificial fine-tuning.
The work is directly related to the cosmic censorship problem and the nature of singularities in general relativity. It shows that a singularity is not an inevitable outcome of gravitational collapse, challenging the Penrose and Hawking theorems in the context of realistic initial data. The question remains open how generic such a scenario is and whether it can occur in nature without exotic matter.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The paper constructs a model of the collapse of a homogeneous dust sphere with a de Sitter bubble forming inside, which halts the contraction at the Schwarzschild radius, producing a gravastar. The authors integrate the equations backward from the final state and find an infinite family of finely tuned initial parameters, as well as a compactness limit of C ≤ 3/8.
Where its strength is
The strength of the work lies in an explicit dynamical mechanism for the birth of a gravastar within general relativity, without higher-curvature terms, featuring a clearly identified separatrix in the parameter space and a quantitative compactness limit.
Where it could go next
Worth trying
Why this may matter
The proposed mechanism fills the gap between static gravastar solutions and black hole collapse, providing a concrete criterion for when collapse can halt, which is important for identifying observational differences of horizonless objects.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.55, against a usual 0.64. It looks like few have drilled nearby.
The compactness limit of 3/8 for gravastar birth is surprisingly close to the Buchdahl limit of 4/9 for stable stars, even though it arises from completely different considerations: causality rather than stability.