# New boundary variables for classical and quantum gravity on a null surface

## TL;DR

This paper introduces new boundary variables for classical and quantum gravity on null surfaces, providing a framework that generalizes black-hole thermodynamics and has implications for non-perturbative quantum gravity.

## Contribution

It presents novel canonical variables at null boundaries in the covariant Hamiltonian formulation of gravity, extending the understanding of boundary geometry and symmetries.

## Key findings

- New spinor and two-form variables encode null surface geometry.
- Derived quasi-local expressions for boundary symmetry generators.
- Generalized the first law of black-hole thermodynamics for null surfaces.

## Abstract

The covariant Hamiltonian formulation for general relativity is studied in terms of self-dual variables on a manifold with an internal and lightlike boundary. At this inner boundary, new canonical variables appear: a spinor and a spinor-valued two-form that encode the entire intrinsic geometry of the null surface. At a two-dimensional cross-section of the boundary, quasi-local expressions for the generators of two-dimensional diffeomorphisms, time translations, and dilatations of the null normal are introduced and written in terms of the new boundary variables. In addition, a generalisation of the first-law of black-hole thermodynamics for arbitrary null surfaces is found, and the relevance of the framework for non-perturbative quantum gravity is stressed and explained.