Marginally outer trapped surfaces in the Schwarzschild spacetime: Multiple self-intersections and extreme mass ratio mergers

Booth, Ivan; Hennigar, Robie A.; Mondal, Saikat

doi:10.1103/physrevd.102.044031

Cited by 14 publications

(43 citation statements)

References 25 publications

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“…We go on to present a derivation of the equations defining MOTSs in these spacetimes, along with a discussion of the stability operator. Our main results begin with a discussion of the Schwarzschild spacetime, reviewing the self-intersecting surfaces first found in [26], and showing that these surfaces are generic within a large family of PG-like slicings. We then consider black holes with inner (Cauchy) horizons, focusing on two examples: the Reissner-Nordström black hole, and the black hole of four-dimensional Gauss-Bonnet gravity [28][29][30][31].…”

Section: Introductionmentioning

confidence: 91%

“…In [26], PG coordinates were used to study the axisymmetric interior MOTSs of the Schwarzschild black hole. The aim of that work was to draw a connection between recent advances in understanding the interior of a black hole merger [19] and the exact description of the event horizon of a merger that is possible in the extreme mass ratio limit [27].…”

Section: A Generalizing Painlevé-gullstrand Coordinatesmentioning

confidence: 99%

“…It was found that the interior of the Schwarzschild spacetime contains an infinite number of MOTSs that possess self-intersections, like those found in [19], providing exact solution examples of this feature of a black hole merger. Our work here will build on the foundation of [26], seeking to better understand the exotic MOTSs present in the interiors of black holes. To do so, we will continue to use a generalization of PG coordinates.…”

Section: A Generalizing Painlevé-gullstrand Coordinatesmentioning

confidence: 99%

“…We first look at the Schwarzschild solution in generalized Painlevé-Gullstrand coordinates. It was shown in [26] that standard PG time slices of the Schwarzschild black hole each contain an infinite number of closed, selfintersecting MOTSs inside the event horizon. Here we will show that this feature persists -and is qualitatively identical -in generalized PG coordinate systems for several choices of constant p, thereby showing that the result is robust, at least within this family of slicings.…”

Section: The Schwarzschild Spacetimementioning

confidence: 99%

“…In [19] a novel geometrical property of unstable MOTSs was pointed out when it was shown that the inner common MOTS present in a binary merger ultimately develops self-intersections. It was then shown that MOTSs possessing self-intersections are, in fact, quite common: an apparently infinite number of such surfaces were found in the interior of the Schwarzschild spacetime in a Painlevé-Gullstrand (PG) slicing [26]. It was also argued in that work that such surfaces may be relevant to understanding the interior dynamics of black hole mergers in the extreme mass ratio limit framework of [27].…”

Section: Introductionmentioning

confidence: 99%

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The Interior MOTSs of Spherically Symmetric Black Holes

Hennigar¹,

Billy²,

Liam³

et al. 2021

Preprint

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There are notable similarities between the marginally outer trapped surfaces (MOTSs) present in the interior of a binary black hole merger and those present in the interior of the Schwarzschild black hole. Here we study the existence and properties of MOTSs with self-intersections in the interior of more general static and spherically symmetric black holes and coordinate systems. Our analysis is carried out in a parametrized family of Painlevé-Gullstrand-like coordinates that we introduce. First, for the Schwarzschild spacetime, we study the existence of these surfaces for various slicings of the spacetime finding them to be generic within the family of coordinate systems we investigate. Then, we study how an inner horizon affects the existence and properties of these surfaces by exploring examples: the Reissner-Nordström black hole and the four-dimensional Gauss-Bonnet black hole. We find that an inner horizon results in a finite number of self-intersecting MOTSs, but their properties depend sensitively on the interior structure of the black hole. By analyzing the spectrum of the stability operator, we show that our results for two-horizon black holes provide exact-solution examples of recently observed properties of unstable MOTSs present in the interior of a binary black hole merger, such as the sequence of bifurcations/annihilations that lead to the disappearance of apparent horizons.

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Section: Introductionmentioning

confidence: 91%

Section: A Generalizing Painlevé-gullstrand Coordinatesmentioning

confidence: 99%

Section: A Generalizing Painlevé-gullstrand Coordinatesmentioning

confidence: 99%

Section: The Schwarzschild Spacetimementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Interior MOTSs of Spherically Symmetric Black Holes

Hennigar¹,

Billy²,

Liam³

et al. 2021

Preprint

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Horizon area bound and MOTS stability in locally rotationally symmetric solutions

Sherif¹,

Dunsby²

2023

Class. Quantum Grav.

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In this paper, we study the stability of marginally outer trapped surfaces (MOTS), foliating horizons of the form $r=X(\tau)$, embedded in locally rotationally symmetric class II perfect fluid spacetimes. An upper bound on the area of stable MOTS is obtained. It is shown that any stable MOTS of the types considered in these spacetimes must be strictly stably outermost, that is, there are no MOTS ``outside" of and homologous to $\mathcal{S}$. Aspects of the topology of the MOTS, as well as the case when an extension is made to imperfect fluids, are discussed. Some non-existence results are also obtained. Finally, the ``growth" of certain matter and curvature quantities on certain unstable MOTS are provided under specified conditions.

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Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension

Booth

Billy

Hennigar

et al. 2023

Class. Quantum Grav.

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The recently developed MOTSodesic method for locating marginally outer trapped surfaces was eﬀectively restricted to non-rotating spacetimes. In this paper we extend the method to include (multi-)axisymmetric time slices of (multi-)axisymmetric spacetimes of any dimension. We then apply this method to study marginally outer trapped surfaces (MOTSs) in the BTZ, Kerr and Myers-Perry black holes. While there are many similarities between the MOTSs observed in these spacetimes and those seen in Schwarzschild and Reissner-Nordström, details of the more complicated geometries also introduce some new, previously unseen, behaviours.

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Marginally outer trapped surfaces in the Schwarzschild spacetime: Multiple self-intersections and extreme mass ratio mergers

Cited by 14 publications

References 25 publications

The Interior MOTSs of Spherically Symmetric Black Holes

The Interior MOTSs of Spherically Symmetric Black Holes

Horizon area bound and MOTS stability in locally rotationally symmetric solutions

Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension

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