Steven Robert Brandt | Searcharxiv

arXiv2026

Exploring Particle Geodesics in a Warp Drive Spacetime

Although the Alcubierre Warp Drive is theoretically capable of providing faster-than-light travel, it may be difficult to use for this purpose. But is it useful for slower-than-light travel? We begin by observing the that the warp bubble will act to protect the ship from dust particles and other space debris (a potentially serious hazard even at 10% the speed of light). We then explore several modifications of the Alcubierre Warp Drive, e.g. a "deflector shield", with the perspective of keeping a ship safe from collisions with particles, projectiles, rogue planets, and other dangers of space travel.

gr-qc↗

arXiv2026

Accelerating Numerical Relativity Simulations with New Multistep Fourth-Order Runge-Kutta Methods

Many HPC applications that solve differential equations rely on the Runge-Kutta family of methods for time integration. Among these methods, the fourth-order accurate RK4 scheme is especially popular. This time integration scheme requires applications to evaluate four intermediate stages to take one time step. Depending on the complexity of the problem being solved, the evaluation of these intermediate stages can be computationally expensive. In this paper we develop explicit fourth-order accurate Multistep Runge-Kutta (MSRK) methods. The advantage of such methods is that they re-use data from previous time steps, thus requiring fewer intermediate stage evaluations and potentially speeding up applications. We outline a procedure to obtain and tune the method's coefficients by adjusting their stability regions in an attempt to maximize the size that a time step can take. We validate and evaluate our new methods in the context of Numerical Relativity applications using the EinsteinToolkit. We believe, however, that these methods and results should generalize to other applications using explicit Runge-Kutta methods.

gr-qc↗