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## Full-Text Articles in Physics

A Solution In Weyl Gravity With Planar Symmetry, James Thomas Wheeler

#### A Solution In Weyl Gravity With Planar Symmetry, James Thomas Wheeler

*James Thomas Wheeler*

We solve the Bach equation for Weyl gravity for the case of a static metric with planar symmetry. The solution is not conformal to the solution to the corresponding Einstein equation.

The Spacetime Co-Torsion In Torsion-Free Biconformal Spaces, James Thomas Wheeler

#### The Spacetime Co-Torsion In Torsion-Free Biconformal Spaces, James Thomas Wheeler

*James Thomas Wheeler*

In preceding studies, [TR Gamma minus, TR Gamma plus] we showed that the solution for the connection of flat biconformal space also solves the curved space field equations for the torsion and co-torsion. We continued this investigation with an attempt to solve the full set of torsion and co-torsion field equations, with only the assumption of vanishing torsion and the known form of the metric. We successfully reduced the torsion equations to a single equation. Here, we reduce that equation to its essential degrees of freedom. We find that the spacetime co-torsion is entirely determined by the scale vector and ...

Variation Of The Weyl Action, James Thomas Wheeler

#### Variation Of The Weyl Action, James Thomas Wheeler

*James Thomas Wheeler*

We show how to vary the fourth order Weyl gravity action to derive the Bach equation.

Torsion Free Biconformal Spaces: Reducing The Torsion Field Equations, James Thomas Wheeler

#### Torsion Free Biconformal Spaces: Reducing The Torsion Field Equations, James Thomas Wheeler

*James Thomas Wheeler*

Our goal is to solve the full set of torsion and co-torsion field equations of Euclidean biconformal space, with only the assumption of vanishing torsion. Here we begin by resolving the involution constraints, symmetry conditions and torsion field equation into a single equation for further study.

Gauge Theories Of General Relativity, James Thomas Wheeler

#### Gauge Theories Of General Relativity, James Thomas Wheeler

*James Thomas Wheeler*

General relativity can be seen as a gauge theory of the Lorentz, Poincaré, Weyl, de Sitter, or conformal groups. In most of these, there is little or no difference from the standard formulation in Riemannian geometry, but the higher symmetries — de Sitter and conformal — introduce new features and explain old ones. The potential presence of a cosmological constant, the spacetime metric, cosmological dust, symplectic structure, Kähler structure and even the existence of a timelike direction can all be seen to arise from the underlying group structure.

Weyl Gravity As General Relativity, James Thomas Wheeler

#### Weyl Gravity As General Relativity, James Thomas Wheeler

*James Thomas Wheeler*

When the full connection of Weyl conformal gravity is varied instead of just the metric, the resulting vacuum field equations reduce to the vacuum Einstein equation, up to the choice of local units, if and only if the torsion vanishes. This result differs strongly from the usual fourth-order formulation of Weyl gravity.