A new point of view on the solutions to the Einstein constraint equations with arbitrary mean curvature and small TT-tensor

DOI10.1088/0264-9381/31/19/195014zbMath1304.83006arXiv1403.5655OpenAlexW2963578382MaRDI QIDQ2930680

Publication date: 19 November 2014

Published in: Classical and Quantum Gravity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5655

zbMATH Keywords

mean curvature Yamabe invariant TT-tensor conformal method Einstein constraint equation

Mathematics Subject Classification ID

Applications of differential geometry to physics (53Z05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Gravitational energy and conservation laws; groups of motions (83C40) Exact solutions to problems in general relativity and gravitational theory (83C15)

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The general relativistic constraint equations ⋮ Solutions to the Einstein-scalar field constraint equations with a small TT-tensor ⋮ On the backward stability of the Schwarzschild black hole singularity ⋮ Limit equation for vacuum Einstein constraints with a translational Killing vector field in the compact hyperbolic case ⋮ Existence of solutions to the Lichnerowicz equation: A new proof ⋮ Einstein-type elliptic systems ⋮ On the Sampson Laplacian ⋮ Construction of vacuum initial data by the conformally covariant split system ⋮ Solutions to the Einstein constraint equations with a small TT-tensor and vanishing Yamabe invariant ⋮ Applications of fixed point theorems to the vacuum Einstein constraint equations with non-constant mean curvature ⋮ The emergence of gravitational wave science: 100 years of development of mathematical theory, detectors, numerical algorithms, and data analysis tools ⋮ Progress on nonuniqueness of solutions to the vacuum Einstein conformal constraint equations with positive Yamabe invariant

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