15 research outputs found
Stability of marginally outer trapped surfaces and symmetries
We study properties of stable, strictly stable and locally outermost
marginally outer trapped surfaces in spacelike hypersurfaces of spacetimes
possessing certain symmetries such as isometries, homotheties and conformal
Killings. We first obtain results for general diffeomorphisms in terms of the
so-called metric deformation tensor and then particularize to different types
of symmetries. In particular, we find restrictions at the surfaces on the
vector field generating the symmetry. Some consequences are discussed. As an
application we present a result on non-existence of stable marginally outer
trapped surfaces in slices of FLRW.Comment: 23 pages, 3 figure
Where are the trapped surfaces?
We discuss the boundary of the spacetime region through each point of which a
trapped surface passes, first in some simple soluble examples, and then in the
self-similar Vaidya solution. For the latter the boundary must lie strictly
inside the event horizon. We present a class of closed trapped surfaces
extending strictly outside the apparent horizon.Comment: 6 pages, 1 figure; talk at the Spanish Relativity Meeting ERE09 in
Bilba
Fundamental properties and applications of quasi-local black hole horizons
The traditional description of black holes in terms of event horizons is
inadequate for many physical applications, especially when studying black holes
in non-stationary spacetimes. In these cases, it is often more useful to use
the quasi-local notions of trapped and marginally trapped surfaces, which lead
naturally to the framework of trapping, isolated, and dynamical horizons. This
framework allows us to analyze diverse facets of black holes in a unified
manner and to significantly generalize several results in black hole physics.
It also leads to a number of applications in mathematical general relativity,
numerical relativity, astrophysics, and quantum gravity. In this review, I will
discuss the basic ideas and recent developments in this framework, and
summarize some of its applications with an emphasis on numerical relativity.Comment: 14 pages, 2 figures. Based on a talk presented at the 18th
International Conference on General Relativity and Gravitation, 8-13 July
2007, Sydney, Australi
Uniqueness theorems for static spacetimes containing marginally outer trapped surfaces
Marginally outer trapped surfaces are widely considered as the best
quasi-local replacements for event horizons of black holes in General
Relativity. However, this equivalence is far from being proved, even in
stationary and static situations. In this paper we study an important aspect of
this equivalence, namely whether classic uniqueness theorems of static black
holes can be extended to static spacetimes containing weakly outer trapped
surfaces or not. Our main theorem states that, under reasonable hypotheses, a
static spacetime satisfying the null energy condition and containing an
asymptotically flat initial data set, possibly with boundary, which possesses a
bounding weakly outer trapped surface is a unique spacetime. A related result
to this theorem was given in arXiv:0711.1299, where we proved that no bounding
weakly outer trapped surface can penetrate into the exterior region of the
initial data where the static Killing vector is timelike. In this paper, we
also fill some gaps in arXiv:0711.1299 and extend this confinement result to
initial data sets with boundary.Comment: 30 pages, 9 figure
From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity
This article reviews some aspects in the current relationship between
mathematical and numerical General Relativity. Focus is placed on the
description of isolated systems, with a particular emphasis on recent
developments in the study of black holes. Ideas concerning asymptotic flatness,
the initial value problem, the constraint equations, evolution formalisms,
geometric inequalities and quasi-local black hole horizons are discussed on the
light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity.
Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24
November, 2006), part of the "General Relativity Trimester" at the Institut
Henri Poincare (Fall 2006). Comments and references added. Typos corrected.
Submitted to Classical and Quantum Gravit
Marginally outer trapped surfaces in stationary initial data
We present two results for bounding marginally
outer trapped surfaces (MOTSs) in Killing initial data satisfying the null
energy condition and containing an untrapped barrier.
The first one applies to the stationary case and
states that no bounding MOTS
lying in the
exterior region where the stationary Killing vector is causal and
penetrating into the timelike region can exist.
The second result applies to the static case
and shows that no bounding MOTS can
penetrate into the exterior region where
the static Killing vector is timelike.
These results extend an interesting theorem by P. Miao (Miao 2005)
Additive and interactive effects of spatial attention and expectation on perceptual decisions
Spatial attention and expectation are two critical top-down mechanisms controlling perceptual inference. Based on previous research it remains unclear whether their influence on perceptual decisions is additive or interactive. We developed a novel multisensory approach that orthogonally manipulated spatial attention (i.e. task-relevance) and expectation (i.e. signal probability) selectively in audition and evaluated their effects on observers’ responses in vision. Critically, while experiment 1 manipulated expectation directly via the probability of task-relevant auditory targets across hemifields, experiment 2 manipulated it indirectly via task-irrelevant auditory non-targets. Surprisingly, our results demonstrate that spatial attention and signal probability influence perceptual decisions either additively or interactively. These seemingly contradictory results can be explained parsimoniously by a model that combines spatial attention, general and spatially selective response probabilities as predictors with no direct influence of signal probability. Our model provides a novel perspective on how spatial attention and expectation facilitate effective interactions with the environment