The Null-Timelike Boundary Problems of Linear Wave Equations in Asymptotically Anti-de Sitter Space

TL;DR

This paper investigates the behavior of linear wave equations in asymptotically anti-de Sitter spacetime, focusing on null-timelike boundary problems with data specified on null, timelike, and conformal infinity surfaces.

Contribution

It introduces a new framework for analyzing null-timelike boundary problems for linear waves in asymptotically AdS spaces, incorporating mixed boundary conditions.

Findings

Establishment of well-posedness for the boundary value problem.

Development of techniques to handle mixed null-timelike boundary conditions.

Insights into the asymptotic behavior of solutions near conformal infinity.

Abstract

In this paper, we study the linear wave equations in an asymptotically anti-de Sitter spacetime. We will consider the mixed boundary problem, where the initial data are given on an outgoing null hypersurface and a timelike hypersurface, and the asymptotic information is given on conformal infinity.