Gravitational Corner Conditions in Holography

TL;DR

This paper reveals the existence of infinite corner conditions in asymptotically anti-de Sitter gravitational solutions, which are crucial for correctly setting initial data in holographic contexts, challenging previous assumptions.

Contribution

It clarifies the role of corner conditions in holography, providing a simple explanation and illustrating their importance with an example, thus broadening understanding of boundary constraints.

Findings

Infinite corner conditions are essential for asymptotically AdS solutions.

These conditions influence the initial data setup in holography.

Implications for holographic theories are discussed.

Abstract

Contrary to popular belief, asymptotically anti-de Sitter solutions of gravitational theories cannot be obtained by taking initial data (satisfying the constraints) on a spacelike surface, and choosing an arbitrary conformal metric on the timelike boundary at infinity. There are an infinite number of corner conditions that also must be satisfied where the initial data surface hits the boundary. These are well known to mathematical relativists, but to make them more widely known we give a simple explanation of why these conditions exist and discuss some of their consequences. An example is given which illustrates their power. Some implications for holography are also mentioned.