scholarly journals On the Center of Mass of Asymptotically Hyperbolic Initial Data Sets

2015 ◽  
Vol 17 (6) ◽  
pp. 1505-1528 ◽  
Author(s):  
Carla Cederbaum ◽  
Julien Cortier ◽  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Center Of Mass ◽  
Data Sets ◽  
Asymptotically Hyperbolic

scholarly journals Specifying Angular Momentum and Center of Mass for Vacuum Initial Data Sets

2011 ◽  
Vol 306 (3) ◽  
pp. 785-803 ◽  
Author(s):  
Lan-Hsuan Huang ◽  
Richard Schoen ◽  
Mu-Tao Wang
Keyword(s):  
Angular Momentum ◽  
Initial Data ◽  
Center Of Mass ◽  
Data Sets

scholarly journals Spacetime Positive Mass Theorems for Initial Data Sets with Non-Compact Boundary

2020 ◽  
Author(s):  
Sérgio Almaraz ◽  
Levi Lopes de Lima ◽  
Luciano Mari
Keyword(s):  
Initial Data ◽  
Energy Conditions ◽  
Data Sets ◽  
Positive Mass ◽  
Momentum Vector ◽  
Asymptotically Flat ◽  
The Common ◽  
Underlying Manifold ◽  
Asymptotically Hyperbolic ◽  
Compact Boundary

Abstract In this paper, we define an energy-momentum vector at the spatial infinity of either asymptotically flat or asymptotically hyperbolic initial data sets carrying a non-compact boundary. Under suitable dominant energy conditions (DECs) imposed both on the interior and along the boundary, we prove the corresponding positive mass inequalities under the assumption that the underlying manifold is spin. In the asymptotically flat case, we also prove a rigidity statement when the energy-momentum vector is light-like. Our treatment aims to underline both the common features and the differences between the asymptotically Euclidean and hyperbolic settings, especially regarding the boundary DECs.

scholarly journals On center of mass and foliations by constant spacetime mean curvature surfaces for isolated systems in General Relativity

2021 ◽  
Vol 60 (6) ◽  
Author(s):  
Carla Cederbaum ◽  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Mean Curvature ◽  
Evolution Equations ◽  
Center Of Mass ◽  
Point Particle ◽  
Data Sets ◽  
Data Set ◽  
Definition Of ◽  
Isolated Systems ◽  
Invent Math

AbstractWe propose a new foliation of asymptotically Euclidean initial data sets by 2-spheres of constant spacetime mean curvature (STCMC). The leaves of the foliation have the STCMC-property regardless of the initial data set in which the foliation is constructed which asserts that there is a plethora of STCMC 2-spheres in a neighborhood of spatial infinity of any asymptotically flat spacetime. The STCMC-foliation can be understood as a equivariant relativistic generalization of the CMC-foliation suggested by Huisken and Yau (Invent Math 124:281–311, 1996). We show that a unique STCMC-foliation exists near infinity of any asymptotically Euclidean initial data set with non-vanishing energy which allows for the definition of a new notion of total center of mass for isolated systems. This STCMC-center of mass transforms equivariantly under the asymptotic Poincaré group of the ambient spacetime and in particular evolves under the Einstein evolution equations like a point particle in Special Relativity. The new definition also remedies subtle deficiencies in the CMC-approach to defining the total center of mass suggested by Huisken and Yau (Invent Math 124:281–311, 1996) which were described by Cederbaum and Nerz (Ann Henri Poincaré 16:1609–1631, 2015).

scholarly journals The Jang Equation and the Positive Mass Theorem in the Asymptotically Hyperbolic Setting

2021 ◽  
Author(s):  
Anna Sakovich
Keyword(s):  
Initial Data ◽  
Spatial Dimension ◽  
Positive Mass Theorem ◽  
Positive Mass ◽  
Asymptotically Hyperbolic ◽  
Jang Equation

AbstractWe solve the Jang equation with respect to asymptotically hyperbolic “hyperboloidal” initial data. The results are applied to give a non-spinor proof of the positive mass theorem in the asymptotically hyperbolic setting. This work focuses on the case when the spatial dimension is equal to three.

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
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