# Warp Drive Space-times in the Weak Field Limit

## Mentor 1

Dr. Mary Krizan

## Location

Union Wisconsin Room

## Start Date

24-4-2015 2:30 PM

## End Date

24-4-2015 3:45 PM

## Description

Einstein’s seminal 1916 manuscript “The Foundation of the General Theory of Relativity” constitutes one of the two pillars of modern physics, envisioning a curved space-time manifold which prescribes free fall trajectories, and an equivalence between gravitation and acceleration. As typically conducted by General Relativity physicists, Practitioners of the theory first specify a stress-energy tensor, a rigorous mathematical description of a local matter-energy distribution and its dynamics; the stress-energy tensor serves as the basis for the Einstein Field Equations which, when solved, precisely describe the resulting space-time curvature. In 1994, Miguel Alcubierre reversed this methodology and first described a space-time curvature independent of the stress-energy tensor. He related a space-time geometry which, though it violated several energy conditions endemic to General Relativity physics, appeared to exhibit superluminal (i.e. faster than light) characteristics. We first survey existing literature concerning the physics of warp drive space-times, including a brief historical retrospective and a summary of drawbacks. We then propose a modification to the Alcubierre space-time in order to circumvent these energy condition violations, approximating the geometry in the weak field limit as Fourier and Fourier-Bessel Series compositions of gravitational wave solutions. The weak field warp drive space-time is then analyzed for its physical properties, with a discussion of implications for General Relativity research and the actual engineering of warp drive space-times.

Warp Drive Space-times in the Weak Field Limit

Union Wisconsin Room

Einstein’s seminal 1916 manuscript “The Foundation of the General Theory of Relativity” constitutes one of the two pillars of modern physics, envisioning a curved space-time manifold which prescribes free fall trajectories, and an equivalence between gravitation and acceleration. As typically conducted by General Relativity physicists, Practitioners of the theory first specify a stress-energy tensor, a rigorous mathematical description of a local matter-energy distribution and its dynamics; the stress-energy tensor serves as the basis for the Einstein Field Equations which, when solved, precisely describe the resulting space-time curvature. In 1994, Miguel Alcubierre reversed this methodology and first described a space-time curvature independent of the stress-energy tensor. He related a space-time geometry which, though it violated several energy conditions endemic to General Relativity physics, appeared to exhibit superluminal (i.e. faster than light) characteristics. We first survey existing literature concerning the physics of warp drive space-times, including a brief historical retrospective and a summary of drawbacks. We then propose a modification to the Alcubierre space-time in order to circumvent these energy condition violations, approximating the geometry in the weak field limit as Fourier and Fourier-Bessel Series compositions of gravitational wave solutions. The weak field warp drive space-time is then analyzed for its physical properties, with a discussion of implications for General Relativity research and the actual engineering of warp drive space-times.