Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gravitational Energy for GR and Poincare Gauge Theories: a Covariant
  Hamiltonian Approach   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 Poincar\'e gauge theories
(GR is 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
Poincar\'e transformations. They are best described in a local Poincar\'e 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 Poincar\'e gauge theories.

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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph