# The Warp Drive: Superluminal Travel within General Relativity

## TL;DR

This paper explores new solutions to Einstein's equations for warp drive spacetimes using various matter-energy sources, suggesting superluminal travel might be feasible within general relativity without requiring negative energy.

## Contribution

It introduces novel solutions for warp drive metrics considering different matter sources, expanding the theoretical possibilities for superluminal travel within Einstein's framework.

## Key findings

- Solutions with dust, perfect fluid, and charged matter are found.
- Shock wave solutions relate to Burgers-type equations.
- Warp drives may connect to vacuum energy and topological effects.

## Abstract

In 1994, Miguel Alcubierre proposed that the well-known special relativistic limitation that particles cannot travel with velocities higher than light speed can be bypassed when such trips are considered globally within specific general relativistic frameworks, using a warped region of spacetime in the shape of a bubble that transports particles with mass traveling through spacetime with superluminal speed. Although initial results indicated this scenario as nonphysical, since it would seem to require negative mass-energy density, recent theoretical analyses suggest that such a nonphysical situation may not always be true. This thesis presents newfound solutions for the Einstein field equations, considering the Alcubierre warp drive spacetime metrics. The central premise is to study the fluid matter as the gravity source, rather than the more common vacuum or negative energy sources, to explore the potential for generating superluminal velocities, or \textit{warp speeds}, through a warped region in the spacetime. Such solutions have various matter-energy sources: dust particles, perfect fluid, quasi-perfect fluid with anisotropic pressures, charged dust, and a perfect fluid within a cosmological constant spacetime. A connection between some of these solutions featuring shock waves described by a Burgers-type equation with a term on the right-hand side of the equation purely dependent on time is also shown. This could mean warp drives are closely related to vacuum energy and possibly have topological effects such as shock waves.