Investigating the Stable Dynamics of Ghost-Ridden Systems with the Space-Time Finite Element Method

This work investigates the dynamics of a stable ghost-ridden system. Ghost systems contain at least one negative degree of freedom and have generally been deemed unstable. However, recent studies show that under certain conditions, these systems can evolve stably. The system of interest in this work consists of two scalar fields, one of which is associated with a negative kinetic energy term; this is where the ghost originates. To investigate the dynamics of this system, the Space-Time Finite Element Method (FEM) is implemented to solve its equations of motion. The advantage of using this method is that time and space are treated simultaneously, eliminating time integration errors. The system is to be solved in d+1 dimensional cases, where d is the number of spatial dimensions plus one temporal. Previous work using implicit integration has shown that the 1+1 and 2+1 cases are dynamically stable, but the 3+1 case is incomplete. Work has been done with the Space-Time FEM and the 1+1 and 2+1 cases. Future work will include completion of the 3+1 case. Furthermore, a gravitationally interacting source term will be added, and the system will be treated with a more generally curved space rather than flat Minkowski space.