Warp drive solutions in spherical coordinates with anisotropic matter configurations

TL;DR

This paper investigates how isotropic and anisotropic fluids affect spherically symmetric warp metrics, exploring energy conditions, the impact of a cosmological constant, and the behavior of solutions in both stationary and dynamic regimes.

Contribution

It provides new numerical solutions for warp drive metrics with anisotropic matter, analyzing energy conditions and the effects of a cosmological constant in spherical coordinates.

Findings

Regions where energy conditions are partially satisfied

Solutions exhibit diverse behaviors under different conditions

Total mass remains positive throughout evolution

Abstract

In this work we study the influence of isotropic and anisotropic fluids on the spherically symmetric warp metric. We evaluate the energy conditions and the influence of including a cosmological constant type term. We find that, considering this term, there is a trade-off between the weak and strong energy conditions. The obtained solutions are numerical and we solve the system for both the stationary and the full regime. The influence of imposing the zero expansion condition has been explored. We find a wide diversity of behaviours for the solutions. In general there are regions of spacetime where the energy conditions can be at least partially satisfied. Finally, we calculate the value of the total mass using the density found in the numerical simulations, finding examples where it remains positive during the entire evolution of the system.