Trapped surfaces in nonspherical initial data sets and the hoop conjecture

1992 ◽  
Vol 46 (4) ◽  
pp. 1429-1439 ◽  
Author(s):  
Eanna Flanagan
Keyword(s):  
Initial Data ◽  
Data Sets ◽  
Trapped Surfaces ◽  
Hoop Conjecture

scholarly journals Formation of dynamically transversely trapping surfaces and the stretched hoop conjecture

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Hirotaka Yoshino ◽  
Keisuke Izumi ◽  
Tetsuya Shiromizu ◽  
Yoshimune Tomikawa
Keyword(s):  
Black Holes ◽  
Initial Data ◽  
Apparent Horizon ◽  
Ring System ◽  
Conformally Flat ◽  
Trapped Surfaces ◽  
Marginally Trapped Surface ◽  
Spherical Topology ◽  
Hoop Conjecture ◽  
Trapped Surface

Abstract A dynamically transversely trapping surface (DTTS) is a new concept for an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $\mathcal{C}\lesssim 6\pi GM$ describes the condition for the DTTS formation well, where $\mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.

scholarly journals Initial data sets for the Schwarzschild spacetime

2007 ◽  
Vol 75 (2) ◽  
Author(s):  
Alfonso García-Parrado Gómez-Lobo ◽  
Juan A. Valiente Kroon
Keyword(s):  
Initial Data ◽  
Data Sets ◽  
Schwarzschild Spacetime

Gluing Initial Data Sets for General Relativity

2004 ◽  
Vol 93 (8) ◽  
Author(s):  
Piotr T. Chruściel ◽  
James Isenberg ◽  
Daniel Pollack
Keyword(s):  
General Relativity ◽  
Initial Data ◽  
Data Sets

scholarly journals A NOTE ON THE CYLINDRICAL COLLAPSE OF COUNTER-ROTATING DUST

2002 ◽  
Vol 11 (09) ◽  
pp. 1469-1477 ◽  
Author(s):  
SÉRGIO M. C. V. GONÇALVES ◽  
SANJAY JHINGAN
Keyword(s):  
Cylindrical Shell ◽  
Initial Data ◽  
Analytical Solutions ◽  
Curvature Singularity ◽  
Apparent Horizons ◽  
Long Cylindrical Shell ◽  
Hoop Conjecture ◽  
Cylindrical Collapse

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that — for the classes of solutions discussed herein — from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.

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