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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 gravitational singularity theorem gives sufficient conditions for geodesic incompleteness: some freely falling worldline or light-ray geodesic cannot continue through an unlimited proper time or affine parameter within the stated spacetime. The conclusion concerns the failure of complete geodesic evolution; it does not by itself establish a curvature singularity.

A typical argument combines a focusing assumption such as the null energy condition, the focusing of a geodesic congruence, and assumptions on the global causal structure. The Penrose singularity theorem uses a trapped surface to show that collapse need not preserve exact spherical symmetry to force null incompleteness under its other hypotheses. This is useful because highly symmetric exact solutions alone cannot establish what happens during generic collapse.^[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 Einstein field equations and the null energy condition imply the null convergence condition:The scalar-curvature and any cosmological constant terms vanish because $U^a{U}_a=0$. For generators of the null hypersurface, the supplied twist-free property gives $\hat{\omega }=0$. The null shear squared is nonnegative on the screen. Thus the Null Raychaudhuri equation impliesStarting from $\theta ({\lambda }_0)={\theta }_0<0$, the null expansion remains negative for as long as the regular congruence exists. HenceBefore the right-hand side reaches zero, inversion of the negative quantities givesSince the inverse of a finite negative null expansion cannot be nonnegative, the regular congruence cannot continue through the proposed upper limit. The null focusing theorem therefore givesProvided the geodesic itself extends this far, the transverse area collapses and $\theta \to -\infty$ at or before this bound. An earlier end of the affine geodesic would instead be geodesic incompleteness. A divergence of the null expansion marks a caustic or a conjugate point to a spacelike surface; it does not by itself establish a curvature singularity.