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Pitts, J. Brian; Schieve, William C.

doi:10.1023/a:1017578424131

Cited by 7 publications

(5 citation statements)

References 61 publications

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“…Because the evolution of M(τ) is determined by an O(3,1) scalar Hamiltonian K, with τ as an external parameter (Poincaré invariant by definition), there is no conflict with the diffeomorphism invariance of general relativity. This approach will guide us toward the formal structures of a 5D manifold M 5 with coordinates (x, τ) on which we may perform a 4+1 foliation by choosing τ as the unambiguously preferred time direction (See [18,19] for discussion of general 5D spacetime with preferred foliation.). We refer to M 5 as a pseudo-spacetime to emphasize that despite the formal manifold structure, in specifying the physics we treat τ as a parameter and not a coordinate.…”

Section: Stueckelberg-horwitz-piron (Shp) Theorymentioning

confidence: 99%

A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric

Land

2020

Symmetry

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We propose a field theory for the local metric in Stueckelberg–Horwitz–Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines xμτ (μ=0,1,2,3) is parameterized by an external time τ. Combining insights from SHP electrodynamics and the ADM formalism in general relativity, we generalize the notion of a 4D spacetime M to a formal manifold M5=M×R, representing an admixture of geometry (the diffeomorphism invariance of M) and dynamics (the system evolution of Mτ with the monotonic advance of τ∈R). Strategically breaking the formal 5D symmetry of a metric gαβ(x,τ) (α,β=0,1,2,3,5) posed on M5, we obtain ten unconstrained Einstein equations for the τ-evolution of the 4D metric γμν(x,τ) and five constraints that are to be satisfied by the initial conditions. The resulting theory differs from five-dimensional (5D) gravitation, much as SHP U(1) gauge theory differs from 5D electrodynamics.

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Section: Stueckelberg-horwitz-piron (Shp) Theorymentioning

confidence: 99%

A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric

Land

2020

Symmetry

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“…6 Thus, Eq. (28) admits only purely spatial coordinate changes, consistently with the preferred-frame 5 We use the fact that, from (4) and (25), (30) with (31) and (32) apply then-but these are space-covariant equations. 6 However, we note also that a mere change in the time unit, T = aT , does not affect the time coordinate x 0 ≡ cT (since c becomes c = c/a), hence leaves Eqs.…”

Section: Scalar Field Equation and Energy Conservationmentioning

confidence: 99%

“…[4]. It admits a "physically observable preferred foliation" [5], in short a detectable ether. Yet, apart from the WEP violation to be discussed below, it seems to agree with observations [3,4].…”

Section: Introductionmentioning

confidence: 99%

Space isotropy and weak equivalence principle in a scalar theory of gravity

Arminjon¹

2006

Braz. J. Phys.

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We consider a preferred-frame bimetric theory in which the scalar gravitational field both influences the metric and has direct dynamical effects. A modified version ("v2") is built, by assuming now a locally-isotropic dilation of physically measured distances, as compared with distances evaluated with the Euclidean space metric. The dynamical equations stay unchanged: they are based on a consistent formulation of Newton's second law in a curved space-time. To obtain a local conservation equation for energy with the new metric, the equation for the scalar field is modified: now its l.h.s. is the flat wave operator. Fluid dynamics is formulated and the asymptotic scheme of post-Newtonian approximation is adapted to v2. The latter also explains the gravitational effects on light rays, as did the former version (v1). The violation of the weak equivalence principle found for gravitationally-active bodies at the point-particle limit, which discarded v1, is proved to not exist in v2. Thus that violation was indeed due to the anisotropy of the space metric assumed in v1.

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“…[33,34] and references therein. In such special relativistic theories of gravity one needs that the causality defined by the curved metric tensor be compatible with that of the underlying flat background metric [34,32], and this compatibility can be properly defined by the causal mapping. Nevertheless, our approach will be of complete general nature and not related to any, flat or not, fixed background.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, a causal relation-also called a causal mapping-will be a global diffeomorphism that simply maps future-directed vectors onto future-directed vectors. This idea has been considered previously, especially in connection with a possible theory of gravity on a flat background (see, e.g., [33,34] and references therein). In such special relativistic theories of gravity one requires that the causality defined by the curved metric tensor be compatible with that of the underlying flat background metric [34,32], and this compatibility can be properly defined by the causal mapping.…”

Section: Introductionmentioning

confidence: 99%

Causal relationship: a new tool for the causal characterization of Lorentzian manifolds

Gómez-Lobo

Senovilla

2003

Class. Quantum Grav.

126

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We define and study a new kind of relation between two diffeomorphic Lorentzian manifolds called causal relation, which is any diffeomorphism characterized by mapping every causal vector of the first manifold onto a causal vector of the second. We perform a thorough study of the mathematical properties of causal relations and prove in particular that two given Lorentzian manifolds (say V and W ) may be causally related only in one direction (say from V to W , but not from W to V ). This leads us to the concept of causally equivalent (or isocausal in short) Lorentzian manifolds as those mutually causally related and to a definition of causal structure over a differentiable manifold as the equivalence class formed by isocausal Lorentzian metrics upon it.Isocausality is a more general concept than the conformal relationship, because we prove the remarkable result that a conformal relation ϕ is characterized by the fact of being a causal relation of the particular kind in which both ϕ and ϕ −1 are causal relations. Isocausal Lorentzian manifolds are mutually causally compatible, they share some important causal properties, and there are one-to-one correspondences, which sometimes are non-trivial, between several classes of their respective future (and past) objects. A more important feature is that they satisfy the same standard causality constraints. We also introduce a partial order for the equivalence classes of isocausal Lorentzian manifolds providing a classification of all the causal structures that a given fixed manifold can have.By introducing the concept of causal extension we put forward a new definition of causal boundary for Lorentzian manifolds based on the concept of isocausality, and thereby we generalize the traditional Penrose's constructions of conformal infinity, diagrams and embeddings. In particular, the concept of causal diagram is given.Many explicit clarifying examples are presented throughout the paper.

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Untitled

Cited by 7 publications

References 61 publications

A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric

A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric

Space isotropy and weak equivalence principle in a scalar theory of gravity

Causal relationship: a new tool for the causal characterization of Lorentzian manifolds

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