84 research outputs found
On-shell symmetries
We define on-shell symmetries and characterize them for Lagrangian systems.
The terms appearing in the variation of the Poincare'-Cartan form, which vanish
because of field equations, are found to be strongly constrained if the space
of solutions has to be preserved. The behaviour with respect to solution
dragging is also investigated in order to discuss relations with the theory of
internal symmetries of a PDE.Comment: 13 page
Further Extended Theories of Gravitation: Part I
We shall here propose a class of relativistic theories of gravitation, based
on a foundational paper of Ehlers Pirani and Schild (EPS).All "extended
theories of gravitation" (also known as f(R) theories) in Palatini formalism
are shown to belong to this class. In a forthcoming paper we shall show that
this class of theories contains other more general examples. EPS framework
helps in the interpretation and solution of these models that however have
exotic behaviours even compared to f(R) theories.Comment: 10 pages. Some refs adde
A constructive approach to bundles of geometric objects on a differentiable manifold
A constructive approach to bundles of geometric objects of finite rank on a differentiable manifold is proposed, whereby the standard techniques of fiber bundle theory are extensively used. Both the point of view of transition functions (here directly constructed from the jets of local diffeomorphisms of the basis manifold) and that of principal fiber bundles are developed in detail. These, together with the absence of any reference to the current functorial approach, provide a natural clue from the point of view of physical applications. Several examples are discussed. In the last section the functorial approach is also presented in a constructive way, and the Lie derivative of a field of geometric objects is defined. \ua9 1983 American Institute of Physics
Universality of Einstein Equations for the Ricci Squared Lagrangians
It has been recently shown that, in the first order (Palatini) formalism,
there is universality of Einstein equations and Komar energy-momentum complex,
in the sense that for a generic nonlinear Lagrangian depending only on the
scalar curvature of a metric and a torsionless connection one always gets
Einstein equations and Komar's expression for the energy-momentum complex. In
this paper a similar analysis (also in the framework of the first order
formalism) is performed for all nonlinear Lagrangians depending on the
(symmetrized) Ricci square invariant. The main result is that the universality
of Einstein equations and Komar energy-momentum complex also extends to this
case (modulo a conformal transformation of the metric).Comment: 21 pages, Late
About Boundary Terms in Higher Order Theories
It is shown that when in a higher order variational principle one fixes
fields at the boundary leaving the field derivatives unconstrained, then the
variational principle (in particular the solution space) is not invariant with
respect to the addition of boundary terms to the action, as it happens instead
when the correct procedure is applied. Examples are considered to show how
leaving derivatives of fields unconstrained affects the physical interpretation
of the model. This is justified in particularl by the need of clarifying the
issue for the purpose of applications to relativistic gravitational theories,
where a bit of confusion still exists. On the contrary, as it is well known for
variational principles of order k, if one fixes variables together with their
derivatives (up to order k-1) on the boundary then boundary terms leave
solution space invariant.Comment: 7 page
Entropy of Self-Gravitating Systems from Holst's Lagrangian
We shall prove here that conservation laws from Holst's Lagrangian, often
used in LQG, do not agree with the corresponding conservation laws in standard
GR. Nevertheless, these differences vanish on-shell, i.e. along solutions, so
that they eventually define the same classical conserved quantities.
Accordingly, they define in particular the same entropy of solutions, and the
standard law S=A/4 is reproduced for systems described by Holst's Lagragian.
This provides the classical support to the computation usually done in LQG for
the entropy of black holes which is in turn used to fix the Barbero-Immirzi
parameter.Comment: 4 pages, no figures; just acknowledgments change
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