Gravitational Energy-Momentum in MAG

TL;DR

This paper explores the Hamiltonian formulation of energy-momentum in Metric-Affine Gravity, emphasizing boundary terms and their role in defining quasilocal and total conserved quantities, with applications to black hole thermodynamics.

Contribution

It introduces a Hamiltonian approach to gravitational energy-momentum in MAG, highlighting boundary term choices and their implications for defining conserved quantities and black hole entropy.

Findings

Different boundary term choices lead to various energy-momentum definitions.

A general expression for black hole entropy is derived.

Quasilocal energy-momentum values are computed for specific solutions.

Abstract

Energy-momentum (and angular momentum) for the Metric-Affine Gravity theory is considered from a Hamiltonian perspective (linked with the Noether approach). The important roles of the Hamiltonian boundary term and the many choices involved in its selection-which give rise to many different definitions-are emphasized. For each choice one obtains specific boundary conditions along with a value for the quasilocal, and (with suitable asymptotic behavior) total (Bondi and ADM) energy-momentum and angular momentum. Applications include the first law of black hole thermodynamics-which identifies a general expression for the entropy. Prospects for a positive energy proof are considered and quasilocal values for some solutions are presented.