The Spacetime Finite Element Method to Investigate Ghost-Ridden Systems

A ghost-ridden system is defined as having at least one negative degree of freedom. The system investigated here is simple, consisting of two scalar fields. One of the fields is associated with a negative kinetic energy term which provides the system with a ghost. Systems such as these have generally been deemed physically unstable; therefore, when a negative degree of freedom arises, the work being done does not continue. However, it was recently discovered that not all ghost-ridden systems are physically unstable which is the grounds for this work. Past work with implicit integration has shown that the 1+1 and 2+1 cases are physically stable; however, completion of the 3+1 case was not feasible with this method. Thus, the spacetime finite element method (FEM) is utilized to computationally solve the equations of motion that arise from the ghost system. This is done with the use of South Dakota State University’s cluster, Roaring Thunder. This particular FEM treats space and time simultaneously, eliminating time integration errors. So far work has been done on the 1+1 and 2+1 cases. Future work focuses on completing the 3+1 case as well as adding an extra gravitationally interacting source term and treating the system with a more general curved space than flat Minkowski space.