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A physicist who uses numerical relativity to study strong gravitational fields, especially curvature singularities and gravitational collapse. His simulations test how the Einstein field equations behave close to a singularity, including whether the behavior found in symmetric models survives when symmetry restrictions are removed.^[ref]

With José M. Martín Senovilla, he reviewed how the Penrose singularity theorem connects gravitational collapse with geodesic incompleteness.^[ref]

A physicist working on the mathematical structure of general relativity. His review with David Garfinkle explains why the Penrose singularity theorem changed the understanding of gravitational collapse: a trapped surface, together with the theorem’s causal and energy assumptions, forces geodesic incompleteness. The conclusion does not depend on choosing an exactly spherical model of a collapsing star. Their account distinguishes the theorem’s precise mathematical conclusion from an informal claim that a particular curvature quantity must diverge.^[ref]

The Penrose singularity theorem states that a globally hyperbolic spacetime with a noncompact Cauchy hypersurface, a closed trapped surface, and the null convergence condition is future null-geodesically incomplete. Time reversal replaces the trapped surface by an anti-trapped surface and gives past incompleteness.

In his 1965 paper Gravitational Collapse and Space-Time Singularities, Roger Penrose used trapped surfaces and global causal structure to address whether nonspherical perturbations could avert a breakdown during gravitational collapse. Quasars supplied the opening astrophysical motivation. The paper used metric signature $(+,-,-,-)$ and a stronger timelike local-energy assumption; the statement above uses the modern null convergence condition.^[ref]

For this version, take a smooth connected four-dimensional spacetime with a time orientation. A Cauchy hypersurface meets every inextendible causal curve exactly once; its existence expresses global hyperbolicity. The hypersurface must be noncompact, meaning not compact; this is a global spatial condition, not an assumption about the size of the collapsing body. The null convergence condition is $R_{ab}{k}^a{k}^b\ge 0$ for every null vector $k$. Through the Einstein field equations it follows from the null energy condition; a cosmological constant drops out of the null contraction.^[ref]

The conclusion is that at least one future-inextendible null geodesic has a finite upper endpoint of its affine parameter. It neither asserts infinite mass density or divergent curvature at every endpoint, nor says that such an endpoint is visible. Locating an event horizon requires additional global information; the theorem is not a horizon-finding rule for arbitrary spacetimes. Weak cosmic censorship conjecture is an additional issue.^[ref]

The supermassive black hole account describes the motivating observational evidence from stellar orbits at the Galactic centre. Such measurements infer a compact gravitating mass. They do not observe a trapped surface, measure a geodesic's complete future, or experimentally prove the Penrose singularity theorem.