Submissions from Molly E. Dennison

[1]  faKiv:2403.07562 [pdf]
First-order differential equations of classical systems with a scalar field and a Hamiltonian in the presence of a gravitational wave signal
Comments: 17 pages, two columns

We investigate the dynamics of classical systems with a scalar field and a Hamiltonian in the presence of a gravitational wave signal. The scalar field is nonlocal in the vicinity of the horizon, and the Hamiltonian is a generalized nonlinear messian of the Einstein-Hilbert structure. Any two such systems can be studied as the diagrammatic representation of a torsional equation of motion. We find that the scalar field in the presence of the gravitational wave signal can generate a first-order differential equation of motion that is first-order in the degree of freedom of the Hamiltonian. We show that the equation of motion is first-order in the Kelvin-Taylor-Rouet-Higgs direction, and our results provide proof of the generalization of the results in the case of a scalar field and a Hamiltonian in the presence of a gravitational wave signal. In particular, the equation of motion is first-order in the Kelvin-Taylor direction in the regular direction, and we show that this equation is first-order in the normal direction, and that it is first-order in the Kelvin-Taylor direction in the non-periodic direction.