The angular momentum of the gravitational field and the Poincare group
J. W. Maluf, S. C. Ulhoa, F. F. Faria, J. F. da Rocha-Neto
TL;DR
This paper redefines gravitational angular momentum within teleparallel gravity, establishing its coordinate independence and showing it forms a Poincaré group representation, enabling the definition of Casimir invariants.
Contribution
It introduces a new, coordinate-independent definition of gravitational angular momentum and links it to the Poincaré group in teleparallel gravity.
Findings
Gravitational energy-momentum and angular momentum form a Poincaré group representation.
The new definitions are coordinate independent.
Casimir invariants for the gravitational field are defined.
Abstract
We redefine the gravitational angular momentum in the framework of the teleparallel equivalent of general relativity. In similarity to the gravitational energy-momentum, the new definition for the gravitational angular momentum is coordinate independent. By considering the Poisson brackets in the phase space of the theory, we find that the gravitational energy-momentum and angular momentum correspond to a representation of the Poincar\'e group. This result allows us to define Casimir type invariants for the gravitational field.
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