Trapped surfaces on a spherically symmetric initial data set

1992 ◽  
Vol 45 (8) ◽  
pp. 2998-3001 ◽  
Author(s):  
T. Zannias
Keyword(s):  
Initial Data ◽  
Spherically Symmetric ◽  
Data Set ◽  
Trapped Surfaces ◽  
Symmetric Initial Data

scholarly journals Transversely trapping surfaces: Dynamical version

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Hirotaka Yoshino ◽  
Keisuke Izumi ◽  
Tetsuya Shiromizu ◽  
Yoshimune Tomikawa
Keyword(s):  
Initial Data ◽  
Spacelike Hypersurface ◽  
Closed Surface ◽  
Spherically Symmetric ◽  
Trapped Surfaces ◽  
Strong Gravity ◽  
New Concepts ◽  
Gravity Fields ◽  
Trapped Surface ◽  
Symmetric Initial Data

Abstract We propose new concepts, a dynamically transversely trapping surface (DTTS) and a marginally DTTS, as indicators for a strong gravity region. A DTTS is defined as a two-dimensional closed surface on a spacelike hypersurface such that photons emitted from arbitrary points on it in transverse directions are acceleratedly contracted in time, and a marginally DTTS is reduced to the photon sphere in spherically symmetric cases. (Marginally) DTTSs have a close analogy with (marginally) trapped surfaces in many aspects. After preparing the method of solving for a marginally DTTS in the time-symmetric initial data and the momentarily stationary axisymmetric initial data, some examples of marginally DTTSs are numerically constructed for systems of two black holes in the Brill–Lindquist initial data and in the Majumdar–Papapetrou spacetimes. Furthermore, the area of a DTTS is proved to satisfy the Penrose-like inequality $A_0\le 4\pi (3GM)^2$, under some assumptions. Differences and connections between a DTTS and the other two concepts proposed by us previously, a loosely trapped surface [Prog. Theor. Exp. Phys. 2017, 033E01 (2017)] and a static/stationary transversely trapping surface [Prog. Theor. Exp. Phys. 2017, 063E01 (2017)], are also discussed. A (marginally) DTTS provides us with a theoretical tool to significantly advance our understanding of strong gravity fields. Also, since DTTSs are located outside the event horizon, they could possibly be related with future observations of strong gravity regions in dynamical evolutions.

scholarly journals GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL DEFOCUSING NONLINEAR WAVE EQUATION FOR SPHERICALLY SYMMETRIC DATA

2007 ◽  
Vol 04 (02) ◽  
pp. 259-265 ◽  
Author(s):  
TERENCE TAO
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Regularity ◽  
Spherically Symmetric ◽  
Supercritical Regime ◽  
Critical Equation ◽  
Critical Regularity ◽  
Spatial Dimensions ◽  
Symmetric Initial Data ◽  
Supercritical Wave Equation

We establish global regularity for the logarithmically energy-supercritical wave equation □u = u5 log (2 + u2) in three spatial dimensions for spherically symmetric initial data, by modifying an argument of Ginibre, Soffer and Velo for the energy-critical equation. This example demonstrates that critical regularity arguments can penetrate very slightly into the supercritical regime.

scholarly journals FORMATION OF TRAPPED SURFACES FOR THE SPHERICALLY SYMMETRIC EINSTEIN–VLASOV SYSTEM

2010 ◽  
Vol 07 (04) ◽  
pp. 707-731 ◽  
Author(s):  
HÅKAN ANDRÉASSON ◽  
GERHARD REIN
Keyword(s):  
Initial Data ◽  
Event Horizon ◽  
Apparent Horizon ◽  
Cosmic Censorship ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Asymptotically Flat ◽  
Trapped Surfaces ◽  
Matter Model ◽  
Trapped Surface

We consider the spherically symmetric, asymptotically flat, non-vacuum Einstein equations, using as matter model a collisionless gas as described by the Vlasov equation. We find explicit conditions on the initial data which guarantee the formation of a trapped surface in the evolution which in particular implies that weak cosmic censorship holds for these data. We also analyze the evolution of solutions after a trapped surface has formed and we show that the event horizon is future complete. Furthermore we find that the apparent horizon and the event horizon do not coincide. This behavior is analogous to what is found in certain Vaidya spacetimes. The analysis is carried out in Eddington–Finkelstein coordinates.

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