The effects of strong magnetic fields and rotation on soliton stars at finite temperature

We study the effects of strong magnetic fields and uniform rotation on the properties of soliton stars in Lee-Wick model when a temperature dependence is introduced into this model. We first recall the properties of the Lee-Wick model and study the properties of soliton solutions, in particular, the stability condition, in terms of the parameters of the model and in terms of the number of fermions N inside the soliton (for very large N) in the presence of strong magnetic fields and uniform rotation. We also calculate the effects of gravity on the stability properties of the soliton stars in the simple approximation of coupling the Newtonian gravitational field to the energy density inside the soliton, treating this as constant throughout. Following Cottingham and Vinh Mau, we also make an analysis at finite temperature and show the possibility of a phase transition which leads to a model with parameters similar to those considered by Lee and his colleagues but in the presence of magnetic fields and rotation. More specifically, the effects of magnetic fields and rotation on the soliton mass and transition temperature are computed explicitly. We finally study the evolution on these magnetized and rotating soliton stars with the temperature from the early universe to the present time.