Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -