On the null-timelike boundary for Maxwell and spin-2 fields in asymptotically flat spaces

2021 ◽  
Vol 18 (02) ◽  
pp. 343-395
Author(s):  
Qing Han ◽  
Lin Zhang
Keyword(s):  
Field Equation ◽  
Initial Data ◽  
Asymptotic Expansions ◽  
Mixed Boundary ◽  
Initial Value ◽  
Null Infinity ◽  
Asymptotically Flat ◽  
Time Estimates ◽  
Lorentzian Metric ◽  
Timelike Hypersurface

We study the Maxwell equation and the spin-2 field equation in Bondi–Sachs coordinates associated with an asymptotically flat Lorentzian metric. We consider the mixed boundary/initial value problem, where the initial data are imposed on a null hypersurface and a boundary value is prescribed on a timelike hypersurface. We establish Sobolev [Formula: see text] space-time estimates for solutions and their asymptotic expansions at the null infinity.

On the existence of analytic null asymptotically flat solutions of Einstein’s vacuum field equations

1982 ◽  
Vol 381 (1781) ◽  
pp. 361-371 ◽  
Keyword(s):  
Initial Value Problem ◽  
Analytic Solutions ◽  
Null Hypersurface ◽  
Vacuum Field ◽  
Field Equations ◽  
Initial Value ◽  
Null Infinity ◽  
Asymptotically Flat ◽  
Asymptotic Characteristic ◽  
Characteristic Initial Value Problem

This paper proves the existence of analytic solutions of the asymptotic characteristic initial value problem for Einstein’s field equations for analytic data on past null infinity and on an incoming null hypersurface.

scholarly journals Hamiltonian charges in the asymptotically de Sitter spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Physical Meaning ◽  
De Sitter ◽  
Killing Vectors ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
The One

Abstract We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.

scholarly journals Nonanalytic solutions of the KdV equation

2004 ◽  
Vol 2004 (6) ◽  
pp. 453-460 ◽  
Author(s):  
Peter Byers ◽  
A. Alexandrou Himonas
Keyword(s):  
Initial Data ◽  
Initial Value Problem ◽  
Kdv Equation ◽  
Initial Value ◽  
The Kdv Equation

We construct nonanalytic solutions to the initial value problem for the KdV equation with analytic initial data in both the periodic and the nonperiodic cases.

Sign in / Sign up

Export Citation Format

Share Document