Goursat's Problem and the Holographic Principle
Enrique Alvarez, Jorge Conde, Lorenzo Hernandez
TL;DR
This paper explores the Goursat problem in the context of Ricci flat Lorentzian spaces, connecting it to the holographic principle and boundary data determining bulk physics.
Contribution
It investigates the Goursat (characteristic) problem for Ricci flat spaces, extending the holographic principle to Lorentzian signature in this setting.
Findings
Analysis of the Goursat problem for Ricci flat spaces.
Connection established between boundary data and bulk physics.
Extension of holographic ideas to Lorentzian characteristic problems.
Abstract
The whole idea of holography as put forward by Gerard 't Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing cosmological constant.
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