Covariant and locally Lorentz-invariant varying speed of light theories

TL;DR

This paper develops covariant and Lorentz-invariant frameworks for theories where the speed of light varies, exploring their classical and quantum implications, including unique solutions and potential cosmological and black hole phenomena.

Contribution

It introduces invariant definitions for varying speed of light theories and analyzes their classical, quantum, and gravitational dynamics, including novel solutions like fast-tracks and their relation to wormholes.

Findings

Invariant definitions for varying c theories established.

Discovery of quantum particle creation due to changing c.

Identification of flat-space string solutions with high c regions.

Abstract

We propose definitions for covariance and local Lorentz invariance applicable when the speed of light $c$ is allowed to vary. They have the merit of retaining only those aspects of the usual definitions which are invariant under unit transformations, and which can therefore legitimately represent the outcome of an experiment. We then discuss some possibilities for invariant actions governing the dynamics of such theories. We consider first the classical action for matter fields and the effects of a changing $c$ upon quantization. We discover a peculiar form of quantum particle creation due to a varying $c$. We then study actions governing the dynamics of gravitation and the speed of light. We find the free, empty-space, no-gravity solution, to be interpreted as the counterpart of Minkowksi space-time, and highlight its similarities with Fock-Lorentz space-time. We also find flat-space string-type solutions, in which near the string core $c$ is much higher. We label them fast-tracks and compare them with gravitational wormholes. We finally discuss general features of cosmological and black hole solutions, and digress on the meaning of singularities in these theories.