Abstract
Objectives: A systematic study on the general relativistic Poynting-Robertson effect has been developed so far by introducing different complementary approaches, which can be mainly divided in two kinds: (1) improving the theoretical assessments and model in its simple aspects, and (2) extracting mathematical and physical information from such system with the aim to extend methods or results to other similar physical systems of analogue structure. Methods/Analysis: We use these theoretical approaches: relativity of observer splitting formalism; Lagrangian formalism and Rayleigh potential with a new integration method; Lyapunov theory os stability. Findings: We determined the three-dimensional formulation of the general relativistic Poynting-Robertson effect model. We determine the analytical form of the Rayleigh potential and discuss its implications. We prove that the critical hypersurfaces (regions where there is a balance between gravitational and radiation forces) are stable configurations. Novelty/Improvement: Our new contributions are: to have introduced the three-dimensional description; to have determined the general relativistic Rayleigh potential for the first time in the General Relativity literature; to have provided an alternative, general and more elegant proof of the stability of the critical hypersurfaces.
Highlights
The last four years have been witness of revolutionary discoveries in astrophysics, which have seen as protagonists these two significant events: (1) the first detection of gravitational waves from the binary black hole (BH) GW151226 [1, 2] and from the binary neutron star (NS) GW170817 [3] thanks to the LIGO and VIRGO collaborations; (2) the first imaging of the matter motion around the supermassive BH in the center of M87 Galaxy [4,5,6,7,8,9] thanks to the strong efforts spent on building the Event Horizon Telescope (EHT) and the synergetic cooperation between EHT and Black Hole Cam project
The closure condition translates in solving a partial differential equation for the integrating factor μ, which in the general relativistic PR case can be solved by separation of variables [31]; 2) Writing the dissipative force in terms of the dissipated energy E and passing the derivative operatore from the velocity field to the dissipated energy E by applying the chain rule, we can have through some simple algebraic calculations an analytical form of the Rayleigh potential in terms of the dissipated energy E
In this work we have presented three different and complementary approaches to study the general relativistic PR effect
Summary
The last four years have been witness of revolutionary discoveries in astrophysics, which have seen as protagonists these two significant events: (1) the first detection of gravitational waves from the binary black hole (BH) GW151226 [1, 2] and from the binary neutron star (NS) GW170817 [3] thanks to the LIGO and VIRGO collaborations; (2) the first imaging of the matter motion around the supermassive BH in the center of M87 Galaxy [4,5,6,7,8,9] thanks to the strong efforts spent on building the Event Horizon Telescope (EHT) and the synergetic cooperation between EHT and Black Hole Cam project. The forces acting on the test particle are: the gravitational field, directed toward the compact object and opposite to the radiation pressure, pointing outward, and the PR effect This phenomenon is triggered each time the radiation field invests the test particle, raising up its temperature, which for the Stefan-Boltzmann law starts re-emitting radiation. The test particle is considered as an ideal black body in thermal equilibrium, meaning that all the absorbed energy is isotropically re-emitted
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