Gravity in the 3+1-Split Formalism I: Holography as an Initial Value Problem

TL;DR

This paper explores the 3+1-split formalism of gravity with a cosmological constant, revealing how holography relates to the initial value problem and how divergence subtraction methods correspond to transformations of canonical variables.

Contribution

It demonstrates the connection between holography and the initial value formulation of gravity through the 3+1-split formalism, linking divergence subtraction to canonical variable transformations.

Findings

Holographic subtraction methods correspond to transformations of canonical variables.

The initial value problem is properly set at the boundary in this formalism.

The boundary energy momentum tensor is a component of the Weyl tensor.

Abstract

We present a detailed analysis of the 3+1-split formalism of gravity in the presence of a cosmological constant. The formalism helps revealing the intimate connection between holography and the initial value formulation of gravity. We show that the various methods of holographic subtraction of divergences correspond just to different transformations of the canonical variables, such that the initial value problem is properly set up at the boundary. The renormalized boundary energy momentum tensor is a component of the Weyl tensor.