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The energy of gravitating systems has been an issue since Einstein proposed general relativity: considered to be ill defined, having no proper local density. Energy–momentum is now regarded as quasi-local (associated with a closed 2-surface). We consider the pseudotensor and quasi-local proposals in the Lagrangian–Noether–Hamiltonian formulations. There are two ambiguities: (i) many expressions, (ii) each depends on some nondynamical structure, e.g. a reference frame. The Hamiltonian approach gives a handle on both problems. Our remarkable discovery is that with a 4D isometric Minkowski reference, a large class of expressions — those that agree with the Einstein pseudotensor's Freud superpotential to linear order — give a common quasi-local energy value. With a best-matched reference on the boundary, this value is the nonnegative Wang–Yau mass. [ABSTRACT FROM AUTHOR]

The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether's two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincaré group. The dynamical potentials of the Poincaré gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed, except on a cosmological scale where it could have significant effects. [ABSTRACT FROM AUTHOR]

Our topic concerns a long standing puzzle: The energy of gravitating systems. More precisely we want to consider, for gravitating systems, how to best describe energy-momentum and angular momentum/center-of-mass momentum (CoMM). It is known that these quantities cannot be given by a local density. The modern understanding is that (i) they are quasi-local (associated with a closed 2-surface), (ii) they have no unique formula, (iii) they have no reference frame independent description. In the first part of this work, we review some early history, much of it not so well known, on the subject of gravitational energy in Einstein's general relativity (GR), noting especially Noether's contribution. In the second part, we review (including some new results) much of our covariant Hamiltonian formalism and apply it to Poincaré gauge theories of gravity (PG), with GR as a special case. The key point is that the Hamiltonian boundary term has two roles, it determines the quasi-local quantities, and furthermore, it determines the boundary conditions for the dynamical variables. Energy-momentum and angular momentum/CoMM are associated with the geometric symmetries under Poincaré transformations. They are best described in a local Poincaré gauge theory. The type of spacetime that naturally has this symmetry is Riemann-Cartan spacetime, with a metric compatible connection having, in general, both curvature and torsion. Thus our expression for the energy-momentum of physical systems is obtained via our covariant Hamiltonian formulation applied to the PG. [ABSTRACT FROM AUTHOR]

We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin-0+ and spin-0- modes. To this end we here consider a very appropriate situation - homogeneous-isotropic cosmologies - which is relatively simple, and yet all the modes have nontrivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these models lead to a set of first-order equations that are compatible with those found for the FLRW models and provide a foundation for further investigations. Typical numerical evolution of these equations shows the expected effects of the cross parity coupling. [ABSTRACT FROM AUTHOR]

We examine several higher spin modes of the Poincaré gauge theory (PGT) of gravity using the Hamiltonian analysis. The appearance of certain undesirable effects due to nonlinear constraints in the Hamiltonian analysis are used as a test. We find that the phenomena of field activation and constraint bifurcation both exist in the pure spin i and the pure spin 2 modes. The coupled spin-O[sup -] and spin-2[sup -] modes also fail our test due to the appearance of constraint bifurcation. The "promising" case in the linearized theory of the PGT given by Kuhfuss and Nitsch likewise does not pass. From this analysis of these specific PGT modes we conclude that an examination of such nonlinear constraint effects shows great promise as a strong test for this and other alternate theories of gravity. [ABSTRACT FROM AUTHOR]

The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of nontrivial viable dynamic modes for the Poincaré gauge theory of gravity. Two modes with propagating spin-zero torsion are analyzed. The explicit form of the Hamiltonian is presented. All constraints are obtained and classified. The Lagrange multipliers are derived. It is shown that a massive spin-0[sup -] mode has normal dynamical propagation but the associated massless 0[sup -] is pure gauge. The spin-0[sup +] mode investigated here is also viable in general. Both modes exhibit a simple type of "constraint bifurcation" for certain special field/parameter values. [ABSTRACT FROM AUTHOR]