On the asymptotic behavior of solutions to Einstein's vacuum equations in wave coordinates

Abstract

We give asymptotics for Einstein vacuum equations in wave coordinates with small asymptotically flat data. We show that the behavior is wave like at null infinity and homogeneous towards time like infinity. We use the asymptotics to show that the outgoing null hypersurfaces approach the Schwarzschild ones for the same mass and that the radiated energy is equal to the initial mass.

Cited by in corpus (23)

• Peeling or not peeling -- is that the question ?
• Nonlinear stability in nonlocal gravity
• Stability of Minkowski space and polyhomogeneity of the metric
• The Stability of the Minkowski space for the Einstein-Vlasov system
• Asymptotics for 1D Klein-Gordon equations with variable coefficient quadratic nonlinearities
• The linear stability of the Schwarzschild solution to gravitational perturbations in the generalised wave gauge
• Nonlinear stability of Minkowski spacetime in Nonlocal Gravity
• The Weak Null Condition in Free-evolution Schemes for Numerical Relativity: Dual Foliation GHG with Constraint Damping
• Asymptotic Behavior of the Maxwell-Klein-Gordon system
• A Vector Field Method for Radiating Black Hole Spacetimes
• A local energy estimate for wave equations on metrics asymptotically close to Kerr
• Scattering from Infinity of the Maxwell Klein Gordon Equations in Lorenz Gauge
• Peeling in Generalized Harmonic Gauge
• Global nonlinear stability of large dispersive solutions to the Einstein equations
• The good-bad-ugly system near spatial infinity on flat spacetime
• Optical functions in de Sitter
• Microlocal analysis near null infinity in asymptotically flat spacetimes
• Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition
• The weak null condition on Kerr backgrounds
• On the Global Well-Posedness of the Einstein-Yang-Mills System
• Scattering for the Equivariant U(1) Problem
• Scattering for wave equations with sources close to the lightcone and prescribed radiation fields
• Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition