Laetitia Martel | Searcharxiv

arXiv2026

Critical and extremal gravitational collapse of a spherical charged scalar field in 4+1 spacetime dimensions

We numerically investigate the gravitational collapse of a charged scalar field coupled to the Einstein and Maxwell equations in spherical symmetry, in 4+1 spacetime dimensions. At the threshold of collapse we find type-II critical phenomena very similar to what is seen in 3+1 dimensions, including self-similarity of the critical solution and power-law scaling of the black hole mass and charge. Well inside the collapse region, we also identify initial data that collapse to an extremal black hole. By varying all parameters of the initial data by up to $\sim0.5\%$, we give evidence that there is a small neighbourhood in the space of initial data where an exactly extremal charged black hole is formed in the evolution of a codimension-1 set of initial data. We believe this is the first such evidence for scalar field collapse from regular initial data.

gr-qc↗

arXiv2026

Simulations of gravitational collapse in null coordinates IV: evolving through the event horizon, with an application to the spherical charged scalar field

We consider line elements of the form $-2G\,du\,(dx+B\,du) + R^2(...)$, where $(...)$ does not contain $dx$. Surfaces of constant $u$ are then null surfaces, and their affinely parameterised generators have tangent vector $G^{-1}\partial_x$. Considering $u$ as the time coordinate, we can evolve either $R$ or $G$, with the other one found by solving the Raychaudhuri equation along the null generators, or we can evolve both. This choice of {\em formulation} is independent from the remaining {\em gauge} choice $x\to x'(u,x,...)$ in the line element above, which is fixed incrementally by the choice of $B$. For example, we can evolve $G$, in order to be able to evolve through an event horizon, and use $B$ to adapt the coordinates to type-II critical collapse. As a demonstration of these ideas, we consider a charged scalar field in spherical symmetry. We consider two settings: a domain where the outgoing null cones emanate from a regular centre $R=0$, and a domain where they emanate from an ingoing-null boundary. In both settings, we demonstrate convergence with resolution, within each formulation and between the three formulations. As testbeds, we compute the critical exponents and periodic fine-structures of the black hole charge and mass scaling laws in a one-parameter family of charged regular initial data, and examples of perturbed extremal Reissner-Nordström solutions.

gr-qc↗