Shaun David Brocus Fell

Proca theories are a simple massive extension of the typical electromagnetic field. Such a simple modification of the underlying theory can have tremendous phenomenological implications, particularly in the case of early-universe high-energy physics, structure formation, and various dark matter models. On the theoretical side, they arise naturally in certain string theories and axionic interactions. Phenomenologically, Proca fields can be produced in the early universe from quantum fluctuations. This leads the Proca field to be an excellent candidate for the dark matter particle. Naturally, generalizations of the Proca field can lead to even richer astrophysical implications, providing possible solutions to many challenges across a wide range of astrophysical phenomena.

While numerical simulations offer unparalleled precision and robustness in studying complex physical systems, their execution is often hindered by complexity, costliness, and time consumption due to the intricate equations involved. This challenge is already encountered in General Relativity, where non-flat spacetimes exacerbate the computational burden. This complexity is further intensified when dealing with additional degrees of freedom. To address this challenge head-on, we introduce GRBoondi, a groundbreaking fixed-background numerical relativity code designed to provide a unified interface for numerically solving Generalized Proca theories. GRBoondi grants users the ability to make arbitrary modifications to the Proca equations of motion on any background, providing a robust and versatile tool for exploring diverse classes of Generalized Proca theories. This letter serves as part of the submission of GRBoondi to the Journal of Open Source Software. For access to the code, please visit https://github.com/ShaunFell/GRBoondi.git.

Warp drives in Einstein's general theory of relativity provide a unique mechanism for manned interstellar travel. It is well-known that the classical superluminal soliton spacetimes require negative energy densities, likely sourced by quantum processes of the uncertainty principle. It has even been claimed by few that negative energy densities are a requirement of superluminal motion. However, recent studies suggest this may not be the case. A general decomposition of the defining variables and the corresponding decomposition of the Eulerian energy are studied. A geometrical interpretation of the Eulerian energy is found, shedding new light on superluminal solitons generated by realistic energy distributions. With this new interpretation, it becomes a relatively simple matter to generate solitonic configurations, within a certain subclass, that respect the positive energy constraint. Using this newfound interpretation, a superluminal solitonic spacetime is presented that possesses positive semi-definite energy. A modest numerical analysis is carried out on a set of example configurations, finding total energy requirements four orders of magnitude smaller than the solar mass. Extraordinarily, the example configurations are generated by purely positive energy densities, a tremendous improvement on the classical configurations. The geometrical interpretation of the Eulerian energy thus opens new doors to generating realistic warp fields for laboratory study and potential future manned interstellar travel.

Warp drives in Einstein’s general theory of relativity provide a unique mechanism for manned interstellar travel. It is well-known that the classical superluminal soliton spacetimes require negative energy densities, likely sourced by quantum processes of the uncertainty principle. It has even been claimed by few that negative energy densities are a requirement of superluminal motion. However, recent studies suggest this may not be the case. A general decomposition of the defining variables and the corresponding decomposition of the Eulerian energy are studied. A geometrical interpretation of the Eulerian energy is found, shedding new light on superluminal solitons generated by realistic energy distributions. With this new interpretation, it becomes a relatively simple matter to generate solitonic configurations, within a certain subclass, that respect the positive energy constraint. Using this newfound interpretation, a superluminal solitonic spacetime is presented that possesses positive semi-definite energy. A modest numerical analysis is carried out on a set of example configurations, finding total energy requirements four orders of magnitude smaller than the solar mass. Extraordinarily, the example configurations are generated by purely positive energy densities, a tremendous improvement on the classical configurations. The geometrical interpretation of the Eulerian energy thus opens new doors to generating realistic warp fields for laboratory study and potential future manned interstellar travel.