TY - JOUR

T1 - Asymptotics and Hamiltonians in a first-order formalism

AU - Ashtekar, Abhay

AU - Engle, Jonathan

AU - Sloan, David

PY - 2008/4

Y1 - 2008/4

N2 - We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined without the need of infinite counter terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy–momentum and angular momentum of the spacetime. We address the subtle but important problems that arise because of logarithmic translations and super translations both in the Lagrangian and Hamiltonian frameworks. As a forthcoming paper will show, the treatment of higher dimensions is considerably simpler. Our first-order framework also suggests a new direction for generalizing the spectral action of non-commutative geometry.

AB - We consider four-dimensional spacetimes which are asymptotically flat at spatial infinity and show that, in the first-order framework, the action principle for general relativity is well defined without the need of infinite counter terms. It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy–momentum and angular momentum of the spacetime. We address the subtle but important problems that arise because of logarithmic translations and super translations both in the Lagrangian and Hamiltonian frameworks. As a forthcoming paper will show, the treatment of higher dimensions is considerably simpler. Our first-order framework also suggests a new direction for generalizing the spectral action of non-commutative geometry.

U2 - 10.1088/0264-9381/25/9/095020

DO - 10.1088/0264-9381/25/9/095020

M3 - Journal article

VL - 25

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 9

M1 - 095020

ER -