# Causal faster than light travel from travel-localized second time coordinate

## TL;DR

This paper proposes a general relativistic model with a compactified second time coordinate that theoretically allows for causal, faster-than-light travel without creating closed time-like loops, under certain conditions.

## Contribution

It introduces a novel higher-dimensional model with a second time coordinate enabling superluminal travel while maintaining causality, unlike simpler models.

## Key findings

- Superluminal travel possible without causality violation for v_max ≤ √2
- Modification of the second time coordinate affects local geometry
- Causality constraints prevent closed time-like loops

## Abstract

I present a {\em general relativistic} model with a compactified second time coordinate that {\em a priori} allows for causal, yet faster than light travel in the background of a FLRW geometry, by local modification of a higher dimensional background geometry, specifically with respect to the radius of the compactified time coordinate. The modification can be induced via the fields of the model. I show that one cannot convert (as possible in special relativistic models, or simple general relativistic models) the super-luminality into closed time-like loops violating causality, due to a novel combination of factors, at least for $v_{\rm max}\leq \sqrt{2}$. The physics of the second time is constrained by postulates derived from reasonable physical assumptions. I comment on the possibility of experimental implications of the model.