Results 1  10
of
37
Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes
, 2008
"... ..."
(Show Context)
The area of horizons and the trapped region
, 2007
"... This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the ..."
Abstract

Cited by 37 (2 self)
 Add to MetaCart
This paper considers some fundamental questions concerning marginally trapped surfaces, or apparent horizons, in Cauchy data sets for the Einstein equation. An area estimate for outermost marginally trapped surfaces is proved. The proof makes use of an existence result for marginal surfaces, in the presence of barriers, curvature estimates, together with a novel surgery construction for marginal surfaces. These results are applied to characterize the boundary of the trapped region.
Black hole boundaries
"... Abstract: Classical black holes and event horizons are highly nonlocal objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and numerical relativity. These include apparent, killing ..."
Abstract

Cited by 26 (1 self)
 Add to MetaCart
(Show Context)
Abstract: Classical black holes and event horizons are highly nonlocal objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and numerical relativity. These include apparent, killing, trapping, isolated, dynamical, and slowly evolving horizons. All of these
MATHEMATICAL GENERAL RELATIVITY: A SAMPLER
, 2010
"... We provide an introduction to selected recent advances in the mathematical understanding of Einstein’s theory of gravitation. ..."
Abstract

Cited by 24 (2 self)
 Add to MetaCart
(Show Context)
We provide an introduction to selected recent advances in the mathematical understanding of Einstein’s theory of gravitation.
Present Status of the Penrose Inequality
 CLASSICAL AND QUANTUM GRAVITY
, 2009
"... The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the area of suitable surfaces that represent black holes. Its validity is supported by the cosmic censorship conjecture and therefore its proof (or disproof) is an important problem in relation with gravitationa ..."
Abstract

Cited by 19 (2 self)
 Add to MetaCart
The Penrose inequality gives a lower bound for the total mass of a spacetime in terms of the area of suitable surfaces that represent black holes. Its validity is supported by the cosmic censorship conjecture and therefore its proof (or disproof) is an important problem in relation with gravitational collapse. The Penrose inequality is a very challenging problem in mathematical relativity and it has received continuous attention since its formulation by Penrose in the early seventies. Important breakthroughs have been made in the last decade or so, with the complete resolution of the socalled Riemannian Penrose inequality and a very interesting proposal to address the general case by Bray and Khuri. In this paper, the most important results on this field will be discussed and the main ideas behind their proofs will be summarized, with the aim of presenting what is the status of our present knowledge in this topic.
Event and apparent horizon finders for 3+1 numerical relativity
 Living Rev. Rel
, 2007
"... Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numericallycomputed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event h ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numericallycomputed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptoticallyflat spacetime is the boundary between those events from which a futurepointing null geodesic can reach future null infinity, and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time: it’s a global property of the entire spacetime, and must be found in a separate postprocessing phase after (part of) the spacetime has been numerically computed. There are 3 basic algorithms for finding event horizons, based respectively on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a
Production and decay of evolving horizons
 CLASS. QUANTUM GRAV. 23 (2006) 4637–4658
, 2006
"... We consider a simple physical model for an evolving horizon that is strongly interacting with its environment, exchanging arbitrarily large quantities of matter with its environment in the form of both infalling material and outgoing Hawking radiation. We permit fluxes of both lightlike and timelike ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
We consider a simple physical model for an evolving horizon that is strongly interacting with its environment, exchanging arbitrarily large quantities of matter with its environment in the form of both infalling material and outgoing Hawking radiation. We permit fluxes of both lightlike and timelike particles to cross the horizon, and ask how the horizon grows and shrinks in response to such flows. We place a premium on providing a clear and straightforward exposition with simple formulae. To be able to handle such a highly dynamical situation in a simple manner we make one significant physical restriction—that of spherical symmetry—and two technical mathematical restrictions: (1) we choose to slice the spacetime in such a way that the spacetime foliations (and hence the horizons) are always spherically symmetric. (2) Furthermore, we adopt Painlevé–Gullstrand coordinates (which are well suited to the problem because they are nonsingular at the horizon) in order to simplify the relevant calculations. Of course physics results are ultimately independent of the choice
Asymptotic Behavior of Spherically Symmetric Marginally Trapped Tubes
"... Abstract. We give conditions on a general stressenergy tensor Tαβ in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event ..."
Abstract

Cited by 14 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We give conditions on a general stressenergy tensor Tαβ in a spherically symmetric black hole spacetime which are sufficient to guarantee that the black hole will contain a (spherically symmetric) marginally trapped tube which is eventually achronal, connected, and asymptotic to the event horizon. Price law decay per se is not required for this asymptotic result, and in this general setting, such decay only implies that the marginally trapped tube has finite length with respect to the induced metric. We do, however, impose a smallness condition (B1) which one may obtain in practice by imposing decay on the Tvv component of the stressenergy tensor. We give two applications of the theorem to selfgravitating Higgs field spacetimes, one using weak Price law decay, the other certain strong smallness and monotonicity assumptions. 1.