Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

Agresti, J.; Pietri, R. De; Lusanna, Luca; Martucci, Luca

doi:10.1023/b:gerg.0000018089.84710.d6

Cited by 40 publications

(48 citation statements)

References 41 publications

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“…It can be obtained starting from a natural parametrization of the 3-metric and then by making an adaptation only to the rotation constraints (and not also the the supermomentum ones like in Refs. [3,16]). …”

Section: The York Map From a Shanmugadhasan Canonical Trans-formamentioning

confidence: 99%

“…(6.3) along the lines of Ref. [16] could be attempted by requiring |Rā(τ, σ)| << 1 [so that Q a ≈ 1 + ā γā a Rā]…”

Section: Equations Of Motion For the Tidal Effects Rā And πā In Smentioning

confidence: 99%

“…[16] will lead to the appearance of a gauge-dependent pseudo-square-mass term. This result, joined with Ref.…”

Section: Three Independent Green Functionsmentioning

confidence: 99%

“…[2,3,16,17,18], in presence of matter with Hamiltonian mass-energy density M(τ, σ) and 3-momentum density M r (τ, σ) (M depends on the 4-metric but not on its gradients) the primary and secondary constraints are…”

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confidence: 99%

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The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

2007

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3ĝ ij ). The preservation in time of these 4 gauge fixings generates other 4 gauge fixing constraints determining the lapse and shift functions consistently with the shape of the simultaneity 3-surface and with the choice of 3-coordinates on it (here is the main difference with the conformal approach and most of the approaches to numerical gravity). While the super-Hamiltonian constraint determines the conformal factor φ 6 , the super-momentum constraint determines 3 momenta (replacing the York gravitomagnetic potential 3 W i ). The remaining 2+2 degrees of freedom (the genuine 4 This is due to the influence of Mach principle, see for instance Chapter 5 of Ref.[23]. However, let us remark that the non-locality of the Dirac observables of the non-compact case (all the instantaneous 3-space is needed for their determination) has a Machian flavor. 5 Traceless and transverse with respect to the conformal 3-metric. 6 The only role of the conformal decomposition 3 g ij = φ 4 3ĝ ij is to identify the conformal factor φ as the natural unknown in the super-Hamiltonian constraint, which becomes the Lichnerowicz equation. See Ref.[1] for a different justification of this result based on constraint theory and the two notions of strong and weak ADM energy.

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Section: The York Map From a Shanmugadhasan Canonical Trans-formamentioning

confidence: 99%

“…(6.3) along the lines of Ref. [16] could be attempted by requiring |Rā(τ, σ)| << 1 [so that Q a ≈ 1 + ā γā a Rā]…”

Section: Equations Of Motion For the Tidal Effects Rā And πā In Smentioning

confidence: 99%

“…[16] will lead to the appearance of a gauge-dependent pseudo-square-mass term. This result, joined with Ref.…”

Section: Three Independent Green Functionsmentioning

confidence: 99%

mentioning

confidence: 99%

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The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

2007

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“…See Ref. [38] for the extension of this method to a regime of weak field but with relativistic velocities in the framework of a background-independent Hamiltonian linearization of tetrad gravity.…”

Section: Physical Individuation Of Space-time Points By Means Of mentioning

confidence: 99%

The physical role of gravitational and gauge degrees of freedom in general relativity – II: Dirac versus Bergmann observables and the objectivity of space-time

Lusanna

Pauri

2006

Gen Relativ Gravit

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This is the second of a couple of papers in which we aim to show the peculiar capability of the Hamiltonian ADM formulation of metric gravity to grasp a series of conceptual and technical problems that appear to have not been directly discussed so far. In this paper we also propose new viewpoints about issues that, being deeply rooted into the foundational level of Einstein theory, seem particularly worth of clarification in connection with the alternative programs of string theory and loop quantum gravity. The achievements of the present work include:1) the analysis of the so-called Hole phenomenology in strict connection with the Hamiltonian treatment of the initial value problem. The work is carried through in metric gravity for the class of Christoudoulou-Klainermann space-times, in which the temporal evolution is ruled by the weak ADM energy. It is crucial to our analysis the re-interpretation of active diffeomorphisms as passive and metric-dependent dynamical symmetries of Einstein's equations, a re-interpretation which enables to disclose their (nearly unknown) connection to gauge transformations on-shell; this is expounded in the first paper (gr-qc/0403081).2) the utilization of the Bergmann-Komar intrinsic pseudo-coordinates, defined as suitable functionals of the Weyl curvature scalars, as tools for a peculiar gauge-fixing to the super-hamiltonian and super-momentum constraints;3) the consequent construction of a physical atlas of 4-coordinate systems for the 4-dimensional mathematical manifold, in terms of the highly non-local degrees of freedom of the gravitational field (its four independent Dirac observables). Such construction embodies the physical individuation of the points of space-time as point-events, both in absence and presence of matter, and associates a non-commutative structure to each gauge fixing or 4-dimensional coordinate system. 4) a clarification of the multiple definition given by Peter Bergmann of the concept of (Bergmann) observable in general relativity. This clarification leads to the proposal of a main conjecture asserting the existence of i) special Dirac's observables which are also Bergmann's observables, ii) gauge variables that are coordinate independent (namely they behave like the tetradic scalar fields of the Newman-Penrose formalism). A by-product of this achievements is the falsification of a recently advanced argument asserting the absence of (any kind of) change in the observable quantities of general relativity. 5) a proposal showing how the physical individuation of point-events could in principle be implemented as an experimental setup and protocol leading to a standard of space-time more or less like atomic clocks define standards of time.In the end, against the well-known Einstein's assertion according to which general covariance takes away from space and time the last remnant of physical objectivity, we conclude that pointevents maintain a peculiar sort of objectivity. Also, besides being operationally essential for building measuring apparatuses for...

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Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity

Lusanna

Pauri

2007

Relativity and the Dimensionality of the World

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The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the Hole Argument can be bypassed by means of a specific physical individuation of point-events of the space-time manifold M 4 in terms of the autonomous degrees of freedom of the vacuum gravitational field (Dirac observables), while the Leibniz equivalence is reduced to differences in the non-inertial appearances (connected to gauge variables) of the same phenomena. ii) the chrono-geometric structure of a solution of Einstein equations for given, gauge-fixed, initial data (a 3-geometry satisfying the relevant constraints on the Cauchy surface), can be interpreted as an unfolding in mathematical global time of a sequence of achronal 3-spaces characterized by dynamically determined conventions about distant simultaneity. This result stands out as an important conceptual difference with respect to the standard chrono-geometrical view of Special Relativity (SR) and allows, in a specific sense, for an endurantist interpretations of ordinary physical objects in GR.To appear in the book Relativity and the Dimensionality of the World, A. van der Merwe ed., Springer Series Fundamental Theories of Physics.

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Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

Cited by 40 publications

References 41 publications

The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

The physical role of gravitational and gauge degrees of freedom in general relativity – II: Dirac versus Bergmann observables and the objectivity of space-time

Dynamical Emergence of Instantaneous 3-Spaces in a Class of Models of General Relativity

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