Double layers in Weyl geometry and some physical implications

TL;DR

This thesis explores Double Layer Theories within Weyl Gravity, analyzing their mathematical foundations, variations, and physical implications, and contrasting them with General Relativity to deepen understanding of Weyl geometric structures.

Contribution

It provides a detailed formulation of Double Layers in Weyl Gravity, including action variation and physical interpretation of surface energy tensors, expanding on prior theoretical frameworks.

Findings

Surface energy tensor terms have meaningful physical implications.

Weyl gravity exhibits distinct features compared to General Relativity.

The variation process clarifies the role of quadratic Lagrangian parameters.

Abstract

In this thesis, we attempt to gain a more complete insight into Double Layer Theories in Weyl Gravity. In order to do this, we first establish the premise of Weyls Theory, including its provenance, development and flaws. This is all discussed in the first five chapters of the thesis. After having established Weyls Infinitesimal geometry and his gauged (scalar-tensor) gravity theory, we move onto the topic at hand, namely, Double Layers. We define the action to be used and describe the volume of integration (especially the Singular Hyper Surface) across which the action principle is setup. We define our gauss Normal Coordinate system and the scheme which we follow when we undertake our calculation. The following sections detail the variation process, in a succinct manner, taking turn by turn, each of the four parameters of our Quadratic Lagrangian. In the last chapter, we conclude the thesis by gleaning out the meaning behind our newfound surface energy tensor terms and what they might imply physically, as well as drawing a clearer picture of contrast between General Relativity and Weyl gravity.