arXiv subjects

James M. Nester

Publications and source records attributed to James M. Nester.

53 records · Page 3Linked to original sources

arXiv2006

Classical pseudotenors and positivity in small regions

We have studied the famous classical pseudotensors in the small region limit, both inside matter and in vacuum. A recent work [Deser et al.1999 CQG 16, 2815] had found one combination of the Einstein and Landau-Lifshitz expressions which yields the Bel-Robinson tensor in vacuum. Using similar methods we found another independent combination of the Bergmann-Thomson, Papapetrou and Weinberg pseudotensors with the same desired property. Moreover we have constructed an infinite number of additional new holonomic pseudotensors satisfying this important positive energy requirement, all seem quite artificial. On the other hand we found that Moller's 1961 tetrad-teleparallel energy-momentum expression naturally has this Bel-Robinson property.

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arXiv2005

The Hamiltonian boundary term and quasi-local energy flux

The Hamiltonian for a gravitating region includes a boundary term which determines not only the quasi-local values but also, via the boundary variation principle, the boundary conditions. Using our covariant Hamiltonian formalism, we found four particular quasi-local energy-momentum boundary term expressions; each corresponds to a physically distinct and geometrically clear boundary condition. Here, from a consideration of the asymptotics, we show how a fundamental Hamiltonian identity naturally leads to the associated quasi-local energy flux expressions. For electromagnetism one of the four is distinguished: the only one which is gauge invariant; it gives the familiar energy density and Poynting flux. For Einstein's general relativity two different boundary condition choices correspond to quasi-local expressions which asymptotically give the ADM energy, the Trautman-Bondi energy and, moreover, an associated energy flux (both outgoing and incoming). Again there is a distinguished expression: the one which is covariant.

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arXiv2005

Quasi-local energy-momentum and energy flux at null infinity

The null infinity limit of the gravitational energy-momentum and energy flux determined by the covariant Hamiltonian quasi-local expressions is evaluated using the NP spin coefficients. The reference contribution is considered by three different embedding approaches. All of them give the expected Bondi energy and energy flux.

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arXiv2004

Quasilocal Center-of-Mass

Gravitating systems have no well-defined local energy-momentum density. Various quasilocal proposals have been made, however the center-of-mass moment (COM) has generally been overlooked. Asymptotically flat graviating systems have 10 total conserved quantities associated with the Poincar{é} symmetry at infinity. In addition to energy-momentum and angular momentum (associated with translations and rotations) there is the boost quantity: the COM. A complete quasilocal formulation should include this quantity. Getting good values for the COM is a fairly strict requirement, imposing the most restrictive fall off conditions on the variables. We take a covariant Hamiltonian approach, associating Hamiltonian boundary terms with quasilocal quantities and boundary conditions. Unlike several others, our {\it covariant symplectic} quasilocal expressions do have the proper asymptotic form for all 10 quantities.

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arXiv2004

Quasilocal Center-of-Mass for Teleparallel Gravity

Asymptotically flat gravitating systems have 10 conserved quantities, which lack proper local densities. It has been hoped that the teleparallel equivalent of Einstein's GR (TEGR, aka GR${}_{||}$) could solve this gravitational energy-momentum localization problem. Meanwhile a new idea: quasilocal quantities, has come into favor. The earlier quasilocal investigations focused on energy-momentum. Recently we considered quasilocal angular momentum for the teleparallel theory and found that the popular expression (unlike our ``covariant-symplectic'' one) gives the correct result only in a certain frame. We now report that the center-of-mass moment, which has largely been neglected, gives an even stronger requirement. We found (independent of the frame gauge) that our ``covariant symplectic'' Hamiltonian-boundary-term quasilocal expression succeeds for all the quasilocal quantities, while the usual expression cannot give the desired center-of-mass moment. We also conclude, contrary to hopes, that the teleparallel formulation appears to have no advantage over GR with regard to localization.

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arXiv2002

Spinor Formulations for Gravitational Energy-Momentum

We first describe a class of spinor-curvature identities (SCI) which have gravitational applications. Then we sketch the topic of gravitational energy-momentum, its connection with Hamiltonian boundary terms and the issues of positivity and (quasi)localization. Using certain SCIs several spinor expressions for the Hamiltonian have been constructed. One SCI leads to the celebrated Witten positive energy proof and the Dougan-Mason quasilocalization. We found two other SCIs which give alternate positive energy proofs and quasilocalizations. In each case the spinor field has a different role. These neat expressions for gravitational energy-momentum have much appeal. However it seems that such spinor formulations just have no room for angular momentum; which leads us to doubt that spinor formulations can really correctly capture the elusive gravitational energy-momentum.

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arXiv2000

Gravitational Energy-Momentum in MAG

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.

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arXiv2000

Gravitational Energy-Momentum in the Tetrad and Quadratic Spinor Representations of General Relativity

In the Tetrad Representation of General Relativity, the energy-momentum expression, found by Moller in 1961, is a tensor wrt coordinate transformations but is not a tensor wrt local Lorentz frame rotations. This local Lorentz freedom is shown to be the same as the six parameter normalized spinor degrees of freedom in the Quadratic Spinor Representation of General Relativity. From the viewpoint of a gravitational field theory in flat space-time, these extra spinor degrees of freedom allow us to obtain a local energy-momentum density which is a true tensor over both coordinate and local Lorentz frame rotations.

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arXiv2000

A Symplectic Hamiltonian Derivation of Quasilocal Energy-Momentum for GR

The various roles of boundary terms in the gravitational Lagrangian and Hamiltonian are explored. A symplectic Hamiltonian-boundary-term approach is ideally suited for a large class of quasilocal energy-momentum expressions for general relativity. This approach provides a physical interpretation for many of the well-known gravitational energy-momentum expressions including all of the pseudotensors, associating each with unique boundary conditions. From this perspective we find that the pseudotensors of Einstein and Møller (which is closely related to Komar's superpotential) are especially natural, but the latter has certain shortcomings. Among the infinite possibilities, we found that there are really only two Hamiltonian-boundary-term quasilocal expressions which correspond to {\em covariant} boundary conditions; they are respectively of the Dirichlet or Neumann type. Our Dirichlet expression coincides with the expression recently obtained by Katz and coworkers using Noether arguments and a fixed background. A modification of their argument yields our Neumann expression.

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arXiv1999

Energy-Momentum (Quasi-)Localization for Gravitating Systems

Traditional approaches to energy-momentum localization led to reference frame dependent pseudotensors. The more modern idea is quasilocal energy-momentum. We take a Hamiltonian approach. The Hamiltonian boundary term gives not only the quasilocal values but also boundary conditions via the Hamiltonian variation boundary principle. Selecting a Hamiltonian boundary term involves several choices. We found that superpotentials can serve as Hamiltonian boundary terms, consequently pseudotensors are actually quasilocal and legitimate. Various Hamiltonian boundary term quasilocal expressions are considered including some famous pseudotensors, Møller's tetrad-teleparallel ``tensor'', Chen's covariant expressions, the expressions of Katz & coworkers, the expression of Brown & York, and some spinor expressions. We emphasize the need for identifying criteria for a good choice.

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arXiv1999

Hamiltonian analysis of Poincaré gauge theory scalar modes

The Hamiltonian constraint formalism is used to obtain the first explicit complete analysis of non-trivial 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-$0^-$ mode has normal dynamical propagation but the associated massless $0^-$ is pure gauge. The spin-$0^+$ mode investigated here is also viable in general. Both modes exhibit a simple type of ``constraint bifurcation'' for certain special field/parameter values.

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arXiv1995

Quasilocal Energy-Momentum for Geometric Gravity Theories

From a covariant Hamiltonian formulation, using symplectic ideas, we obtain covariant quasilocal energy-momentum boundary expressions for general gravity theories. The expressions depend upon which variables are fixed on the boundary, a reference configuration and a displacement vector field. We consider applications to Einstein's theory, black hole thermodynamics and alternate spinor expressions.

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arXiv1994

Can Galactic Observations Be Explained by a Relativistic Gravity Theory?

We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression for the metric to order $(v/c)^2$. This allows us to compare the predictions of the theory with various experimental data: the Newtonian limit, light deflection and retardation, rotation of galaxies and gravitational lensing. Our general conclusion is that the possibility for any gravity theory to explain the behaviour of galaxies without dark matter is rather improbable.

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arXiv1994

A Quadratic Spinor Lagrangian for General Relativity

We present a new finite action for Einstein gravity in which the Lagrangian is quadratic in the covariant derivative of a spinor field. Via a new spinor-curvature identity, it is related to the standard Einstein-Hilbert Lagrangian by a total differential term. The corresponding Hamiltonian, like the one associated with the Witten positive energy proof is fully four-covariant. It defines quasi-local energy-momentum and can be reduced to the one in our recent positive energy proof. (Fourth Prize, 1994 Gravity Research Foundation Essay.)

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arXiv1994

Some Spinor-Curvature Identities

We describe a class of spinor-curvature identities which exist for Riemannian or Riemann-Cartan geometries. Each identity relates an expression quadratic in the covariant derivative of a spinor field with an expression linear in the curvature plus an exact differential. Certain special cases in 3 and 4 dimensions which have been or could be used in applications to General Relativity are noted.

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arXiv1994

Ashtekar's New Variables and Positive Energy

We discuss earlier unsuccessful attempts to formulate a positive gravitational energy proof in terms of the New Variables of Ashtekar. We also point out the difficulties of a Witten spinor type proof. We then use the special orthonormal frame gauge conditions to obtain a locally positive expression for the New Variables Hamiltonian and thereby a ``localization'' of gravitational energy as well as a positive energy proof.

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arXiv1994

Another positivity proof and gravitational energy localizations

Two locally positive expressions for the gravitational Hamiltonian, one using 4-spinors the other special orthonormal frames, are reviewed. A new quadratic 3-spinor-curvature identity is used to obtain another positive expression for the Hamiltonian and thereby a localization of gravitational energy and positive energy proof. These new results provide a link between the other two methods. Localization and prospects for quasi-localization are discussed.

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