February 28, 2024
Null infinity (Scri) arises as a boundary of the Penrose conformal completion of an asymptotically flat physical space-time. We first note that Scri is a weakly isolated horizon (WIH), and then show that its familiar properties can be derived from the general WIH framework. This seems quite surprising because physics associated with black hole (and cosmological) WIHs is very different from that extracted at Scri. We show that these differences can be directly traced back to t...
July 12, 2006
We derive from Einstein equation an evolution law for the area of a trapping or dynamical horizon. The solutions to this differential equation show a causal behavior. Moreover, in a viscous fluid analogy, the equation can be interpreted as an energy balance law, yielding to a positive bulk viscosity. These two features contrast with the event horizon case, where the non-causal evolution of the area and the negative bulk viscosity require teleological boundary conditions. This...
October 4, 2017
We initiate a series of works where we study the interior of dynamical rotating vacuum black holes without symmetry. In the present paper, we take up the problem starting from appropriate Cauchy data for the Einstein vacuum equations defined on a hypersurface already within the black hole interior, representing the expected geometry just inside the event horizon. We prove that for all such data, the maximal Cauchy evolution can be extended across a non-trivial piece of Cauchy...
December 5, 2024
In recent years there have been many studies on exactly solvable black hole mergers, based on a model by Emparan and Martinez where the mass of one black hole is blown up to infinity. Here we replace the large black hole by a cosmological horizon, and study how it merges with a black hole in the Schwarzschild-de Sitter spacetime by considering an observer positioned at future null infinity. We describe the geometry of the horizon over time, including the role that caustics pl...
October 14, 2021
We prove that if in a spacetime endowed with a merely continuous metric, a complete partial Cauchy hypersurface has nonempty Cauchy horizon, then the horizon is caused by the presence of almost closed causal curves behind it or by the influence of points at infinity. This statement is related to strong cosmic censorship and a conjecture of Wald. In this light, Wald's conjecture can be reformulated as a PDE problem about the location of Cauchyh horizons inside black hole inter...
September 11, 1997
The last seven years has produced a growing body of evidence which concludes that the Cauchy horizon in black hole-de Sitter spacetimes is classically stable when the surface gravity at the cosmological event horizon is greater than that at the Cauchy horizon. That stability persists for a finite, but non-zero, region of the black hole's parameter space, $(M,Q,J,\Lambda)$, suggests that black holes immersed in de Sitter space are counter-examples to the strong cosmic censorsh...
April 1, 2001
Hawking has shown that if black holes were to exist in a universe that expands forever, black holes would completely evaporate, violating unitarity. I argue this means unitarity requires that the universe exist for only a finite future proper time. I develop this argument, showing that unitarity also requires the boundaries of all future sets to be Cauchy surfaces, and so no event horizons can exist. Thus, the null generators of the surfaces of astrophysical black holes must ...
August 2, 2007
It is a well known analytic result in general relativity that the 2-dimensional area of the apparent horizon of a black hole remains invariant regardless of the motion of the observer, and in fact is independent of the $ t=constant $ slice, which can be quite arbitrary in general relativity. Nonetheless the explicit computation of horizon area is often substantially more difficult in some frames (complicated by the coordinate form of the metric), than in other frames. Here we...
September 23, 2008
We investigate whether black holes can be defined without using event horizons. In particular we focus on the thermodynamic properties of event horizons and the alternative, locally defined horizons. We discuss the assumptions and limitations of the proofs of the zeroth, first and second laws of black hole mechanics for both event horizons and trapping horizons. This leads to the possibility that black holes may be more usefully defined in terms of trapping horizons. We also ...
May 26, 2023
We propose a new notion of singularity in General Relativity which complements the usual notions of geodesic incompleteness and curvature singularities. Concretely, we say that a spacetime has a volume singularity if there exist points whose future or past has arbitrarily small spacetime volume: In particular, smaller than a Planck volume. From a cosmological perspective, we show that the (geodesic) singularities predicted by Hawking's theorem are also volume singularities. I...