Surface Charges Toolkit for Gravity

TL;DR

This paper provides a comprehensive catalog of surface charge formulas for various gravity theories, clarifying methods to compute quasi-local charges and extending existing literature with new results and practical examples.

Contribution

It offers a detailed, unified review and extension of surface charge formulas across multiple gravity theories and variables, including new computational examples.

Findings

Extended catalog of surface charge formulas for gravity theories.

Clarified methods for computing quasi-local surface charges.

Provided practical notebooks demonstrating the methods.

Abstract

These notes provide a detailed catalog of surface charge formulas for different classes of gravity theories. The present catalog reviews and extends the existing literature on the topic. Part of the focus is on reviewing the method to compute quasi-local surface charges for gauge theories in order to clarify conceptual issues and their range of applicability. Many surface charge formulas for gravity theories are expressed in metric, tetrads-connection, Chern-Simons connection, and even BF variables. For most of them, the language of differential forms is exploited and contrasted with the more popular metric components language. The gravity theory is coupled with matter fields as scalar, Maxwell, Skyrme, Yang-Mills, and spinors. Furthermore, three examples with ready-to-download notebook codes, show the method in full action. Several new results are highlighted through the notes.