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We recast the tools of `global causal analysis' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization… (More)

We study Ricci flows on R, n ≥ 3, that evolve from rotationally symmetric, asymptotically flat initial data containing no embedded minimal hyperspheres. We show that in this case the flow is… (More)

For any asymptotically flat spacetime with a suitable causal structure obeying (a weak form of) Penrose's cosmic censorship conjecture and satisfying conditions guaranteeing focusing of complete null… (More)

By a simple modification of Hawking's well known topology theorems for black hole horizons, we find lower bounds for the areas of smooth apparent horizons and smooth cross sections of stationary… (More)

Abstract We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma… (More)

A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that… (More)

Motivated by recent interest in black holes whose asymptotic geometry approaches that of anti‐de Sitter spacetime, we give a proof of topological censorship applicable to spacetimes with such… (More)

B List has recently studied a geometric flow whose fixed points correspond to static Ricci flat spacetimes. It is now known that this flow is in fact Ricci flow modulo pullback by a certain… (More)

We study the evolution of the renormalized volume functional for asymptotically Poincare-Einstein metrics (M,g) which are evolving by normalized Ricci flow. In particular, we prove that the time… (More)

Assuming certain asymptotic conditions, we prove a general theorem on the non-existence of static regular black holes in spacetimes with a negative cosmological constant, given that the fundamental… (More)