Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes

Andersson, Lars; Mars, Marc; Simon, Walter

doi:10.4310/atmp.2008.v12.n4.a5

Cited by 168 publications

(464 citation statements)

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“…[12,13,14]). A trapping horizon [11] is (the closure of) a hypersurface H foliated by closed marginally outer trapped surfaces: H = t∈R S t , with θ ( ) = 0.…”

Section: Quasi-local Horizons As Inner Test Screensmentioning

confidence: 99%

“…An even more curious behaviour of H follows from the two following results: i) Foliation uniqueness [19]: the foliation by MOTSs of a dynamical FOTH is unique. ii) Existence of DHs [12,13]: Given a (stable) marginally outer trapped surface S 0 in a Cauchy hypersurface Σ 0 , to each 3+1 spacetime foliation (Σ t ) t∈R containing Σ 0 it corresponds a unique adapted dynamical FOTHs H that contains S 0 and is sliced by marginally outer trapped surfaces {S t } such that S t ⊂ Σ t .…”

Section: Quasi-local Horizons As Inner Test Screensmentioning

confidence: 99%

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Towards a cross-correlation approach to strong-field dynamics in black hole spacetimes

Jaramillo¹,

Macedo²,

Moesta³

et al. 2012

AIP Conference Proceedings

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Abstract. The qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime represents a challenge both at a fundamental level and in astrophysical applications. Recent advances in numerical relativity and in the geometric characterization of black hole horizons open new conceptual and technical avenues into the problem. We discuss here a research methodology in which spacetime dynamics is probed through the cross-correlation of geometric quantities constructed on the black hole horizon and on null infinity. These two hypersurfaces respond to evolving gravitational fields in the bulk, providing canonical "test screens" in a "scattering"-like perspective onto spacetime dynamics. More specifically, we adopt a 3+1 Initial Value Problem approach to the construction of generic spacetimes and discuss the role and properties of dynamical trapping horizons as canonical inner "screens" in this context. We apply these ideas and techniques to the study of the recoil dynamics in post-merger binary black holes, an important issue in supermassive galactic black hole mergers. A CROSS-CORRELATION APPROACH: MOTIVATIONS AND OBJECTIVEThe general problem here discussed is the qualitative and quantitative understanding of near-horizon gravitational dynamics in the strong-field regime of black hole (BH) spacetimes. This represents a challenge both at a fundamental level and in astrophysical applications. The setting of our discussion is that of classical spacetimes in General Relativity (GR), with a focus on astrophysically motivated problems in which we adopt a numerical relativity methodology. A natural strategy to the study of spacetime dynamics consists in extending to the general relativistic setting the Newtonian description of the dynamics of gravitationally interacting bodies, namely celestial mechanics. This has proved extremely successful in unveiling the physics of compact objects. However, such an approach also meets fundamental obstacles in the general dynamical regime of a gravitational theory in which i) a priori rigid structures providing canonical references (such as symmetries or preferred backgrounds) are generically absent, and ii) where global aspects play a crucial role. Here we rather adopt a complementary approach in the spirit of a coarsegrained description of the dynamics in which we renounce to the detailed tracking of the geometry (trajectories) of given compact regions (objects), and rather emphasize the global/quasi-local properties of the relevant dynamical fields. In particular, we aim at arXiv:1205.3902v1 [gr-qc]

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“…[12,13,14]). A trapping horizon [11] is (the closure of) a hypersurface H foliated by closed marginally outer trapped surfaces: H = t∈R S t , with θ ( ) = 0.…”

Section: Quasi-local Horizons As Inner Test Screensmentioning

confidence: 99%

Section: Quasi-local Horizons As Inner Test Screensmentioning

confidence: 99%

Towards a cross-correlation approach to strong-field dynamics in black hole spacetimes

Jaramillo¹,

Macedo²,

Moesta³

et al. 2012

AIP Conference Proceedings

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show abstract

“…It is well-known (see, for instance, [AMS08]) that the operator L is not necessarily selfadjoint, yet its principal eigenvalue λ 1 (L) is real (this follows from the Krein-Rutman theorem). As a result, it makes sense to give the following definition.…”

mentioning

confidence: 99%

“…Despite their non-variational nature, MOTS do have a suitable notion of stability as suggested by Anderrson, Mars and Simon [AMS08]. For minimal submanifolds (say, for simplicity, of codimension one) the Jacobi operator arises both from the second variation of the area functional and from the (pointwise) first variation of the mean curvature: while the former approach is not applicable to MOTS, the latter can easily be extended.…”

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confidence: 99%

Rigidity of Stable Marginally Outer Trapped Surfaces in Initial Data Sets

Carlotto

2016

Ann. Henri Poincaré

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Abstract. In this article we investigate the restrictions imposed by the dominant energy condition (DEC) on the topology and conformal type of possibly non-compact marginally outer trapped surfaces (thus extending Hawking's classical theorem on the topology of black holes). We first prove that an unbounded, stable marginally outer trapped surface in an initial data set (M, g, k) obeying the dominant energy condition is conformally diffeomorphic to either the plane C or to the cylinder A and in the latter case infinitesimal rigidity holds. As a corollary, when the DEC holds strictly this rules out the existence of trapped regions with cylindrical boundary. In the second part of the article, we restrict our attention to asymptotically flat data (M, g, k) and show that, in that setting, the existence of an unbounded, stable marginally outer trapped surface essentially never occurs unless in a very specific case, since it would force an isometric embedding of (M, g, k) into the Minkowski spacetime as a space-like slice.

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“…The following cases may occurs: (1) S is marginally trapped if Θ never vanishes; (2) partly marginally trapped if Θ ≥ 0 or Θ ≤ 0; (3) marginally outer trapped (MOTS) if Θ is arbitrary. The study of these family of surfaces has been quite active in recent years (see for instance [9,10,11,12,13], etc).…”

Section: Introductionmentioning

confidence: 99%

Isotropy and marginally trapped surfaces in a spacetime

Cabrerizo¹,

Fernández

Gómez

2010

Class. Quantum Grav.

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In this note we shall study the notions of isotropic and marginally trapped surface in a spacetime by using a differential geometric approach. We first consider spacelike isotropic surfaces in a Lorentzian manifold and, in particular, in a four-dimensional spacetime, where the isotropy function appears to be determined by the mean curvature vector field of the surface. Explicit examples of isotropic marginally outer trapped surfaces are given in the standard fourdimensional space forms: Minkowski, De Sitter and anti De Sitter spaces. Then we prove ridigity theorems for complete spacelike 0-isotropic surfaces without flat points in these standard space forms. As a consequence, we also obtain characterizations of complete spacelike isotropic marginally trapped surfaces in these backgrounds.

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Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes

Cited by 168 publications

References 41 publications

Towards a cross-correlation approach to strong-field dynamics in black hole spacetimes

Towards a cross-correlation approach to strong-field dynamics in black hole spacetimes

Rigidity of Stable Marginally Outer Trapped Surfaces in Initial Data Sets

Isotropy and marginally trapped surfaces in a spacetime

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