Dissipative systems are usually present in all physical fields (e.g., Kinetic theory of gas, Quantum Mechanics, Astrophysics, Cosmology, String Theory), since they are able to furnish a more realistic description of the phenomenon under study. However, the attained modeling-accurateness is also responsible, most of the time, in loss of existence, smoothness, and symmetries of the solutions, presence of topologically complex structures featuring chaotic behaviour, and difficulties in the numerical integration process. In the literature, several methods have been proposed, going from mathematical to numerical analysis.
The “relative drawbacks” of some approaches relies on the fact that they are very targeted for the problem to solve or very technical, involving advanced mathematical concepts.
In my talk I present a new analytic method developed in collaboration with Dr. Emmanuele Battista, which configures to be simple in its mathematical formulation and implementation, and of broad application. The genesis of this method takes place when we were aiming at determining the Rayleigh dissipative potential of the general relativistic Poynting-Robertson effect.
This is a dissipative system in General Relativity involved in X-ray electromagnetic radiation processes occurring in high-energy astrophysics around compact objects, like black holes and neutron stars, and it is responsible to efficiently remove energy and angular momentum from the bodies affected by the radiation. I will give more details about this effect from a theoretical and astrophysical point of view.
Finally, I show how the above-mentioned method applies to this effect and which are the consequences. In the conclusions I analyse the implications of the method and show its future perspectives.
This talk is essentially based on the following three papers:
[1] De Falco, V.; Battista, E.; Falanga M. ”Lagrangian formulation of the Poynting-Robertson effect”, PRD, 2018, 97, 8 (10.1103/PhysRevD.97.084048)
[2] De Falco, V.; Battista, E.; ”Analytical Rayleigh potential for the general relativistic Poynting- Robertson effect”, Europhysics Letters, 2019, 127, 30006 (10.1209/0295-5075/127/30006)
[3] De Falco, V.; Battista E., ”Poynting-Roberston effect as a dissipative system in general relativity”, PRD, 2020, 101, 064040 (10.1103/PhysRevD.101.064040)
