New trends in the general relativistic Poynting-Robertson effect modeling

The general relativistic Poynting-Robertson (PR) effect is a very important dissipative phenomenon occurring in high-energy astrophysics. Recently, it has been proposed a new model, which upgrades the two-dimensional (2D) description in the three-dimensional (3D) case in Kerr spacetime. The radiation field is considered as constituted by photons emitted from a rigidly rotating spherical source around the compact object. Such dynamical system admits the existence of a critical hypersurface, region where the gravitational and radiation forces balance and the matter reaches it at the end of its motion. Selected test particle orbits are displayed. We show how to prove the stability of these critical hypersurfaces within the Lyapunov theory. Then, we present how to study such effect under the Lagrangian formalism, explaining how to analytically derive the Rayleigh potential for the radiation force. In conclusion, further developments and future projects are discussed.Comment: 15 pages; 4 figures; contributions in the book "Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity - Domoschool 2019" edited by Sergio Luigi Cacciatori Alexander Kamenshchik,2022, Birk\"auser. arXiv admin note: substantial text overlap with arXiv:2006.01462, arXiv:1911.0364

Coupling Poynting-Robertson effect in mass accretion flow physics

The physics of accretion onto compact objects has been experiencing for several decades by now a golden age in terms of theoretical knowledges and observational discoveries. Compact objects release the gravitational energy of the accreted matter in the form of persistent emission or thermonuclear type-I X-ray burst. This radiation field carries out energy and momentum that is transferred back to the interacting plasma inside the accretion disk. The radiation field entails a radiation pressure and a radiation drag force, which both can drastically change or even halt the whole mass transfer (especially when their intensity reaches the Eddington limit). The radiation drag force, known as Poynting-Robertson effect, acts as a dissipative force against the matter's orbital motion, removing very efficiently angular momentum and energy from it. To describe suitably the radiation processes around static compact objects, the Schwarzschild metric is usually employed. To this aim, I have developed a mathematical method for deriving a set of high-accurate approximate polynomial formulae to easily integrate photon geodesics in a Schwarzschild spacetime. Starting from the general relativistic treatment of the Poynting-Robertson effect led by Bini et al., I gave two fundamental contributions in such research field. In a first work, I proved through the introduction of an integrating factor that such effect admits a Lagrangian formulation, very peculiar propriety for a dissipative system in General Relativity. In the other work, I have extended the two dimensional general relativistic PR model in three dimensions. Once the theoretical apparatus has been developed, it is important to learn the state of art about the observational high-energy astrophysics. For such reasons, I focussed my energy on the data analysis of three accreting millisecond X-ray pulsars: IGR~J00291+5934, IGR~J18245-2452, and SAX~J1748.9-2021. This thesis offers innovative ideas in the field of radiation processes involving the Poynting-Robertson effect in high-energy astrophysics, opening thus up future interesting perspectives both in theoretical and observational physics. As conclusion, we propose possible further developments and applications

Epicyclic frequencies in the equatorial plane around stationary and axially symmetric wormhole geometries

Epicyclic frequencies are usually observed in X-ray binaries and constitute a powerful astrophysical mean to probe the strong gravitational field around a compact object. We consider them in the equatorial plane around a general stationary and axially symmetric wormhole. We first search for the wormholes' existence, distinguishing them from a Kerr black hole. Once there will be available observational data on wormholes, we present a strategy to reconstruct the related metrics. Finally, we discuss the implications of our approach and outline possible future perspectives.Comment: 10 pages, 2 figures, 2 Tables; accepted for publication in Phys. Rev.

Approximate analytical calculations of photon geodesics in the Schwarzschild metric

We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been introduced empirically. We then derive for the first time an approximate analytical equation for the solid angle. We discuss the accuracy and range of applicability of the new equations and present a few simple applications of them to known astrophysical problems.Comment: 8 pages, 10 Figures; Received: 08 June 2016 / Accepted: 04 August 2016and accepted from A&

New approaches to the general relativistic Poynting-Robertson effect

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.Comment: 12 pages, 5 figures, accepted on the 1st of June 2020 on Emerging Science Journa

General relativistic Poynting-Robertson effect to diagnose wormholes existence: static and spherically symmetric case

We derive the equations of motion of a test particle in the equatorial plane around a static and spherically symmetric wormhole influenced by a radiation field including the general relativistic Poynting-Robertson effect. From the analysis of this dynamical system, we develop a diagnostic to distinguish a black hole from a wormhole, which can be timely supported by several and different observational data. This procedure is based on the possibility of having some wormhole metrics, which smoothly connect to the Schwarzschild metric in a small transition surface layer very close to the black hole event horizon. To detect such a metric-change, we analyse the emission proprieties from the critical hypersurface (stable region where radiation and gravitational fields balance) together with those from an accretion disk in the Schwarzschild spacetime toward a distant observer. Indeed, if the observational data are well fitted within such model, it immediately implies the existence of a black hole; while in case of strong departures from such description it means that a wormhole could be present. Finally, we discuss our results and draw the conclusions.Comment: 17 pages, 11 figures, 1 Table. Paper accepted on April 30, 2020 on Physical Review

Timescales of the chaos onset in the general relativistic Poynting-Robertson effect

It has been proved that the general relativistic Poynting-Robertson effect in the equatorial plane of Kerr metric shows a chaotic behavior for a suitable range of parameters. As a further step, we calculate the timescale for the onset of chaos through the Lyapunov exponents, estimating how this trend impacts on the observational dynamics. We conclude our analyses with a discussion on the possibility to observe this phenomenon in neutron star and black hole astrophysical sources.Comment: 11 pages; 4 figures; 3 tables; accepted for publication on PR

Detection of chaos in the general relativistic Poynting-Robertson effect: Kerr equatorial plane

The general relativistic Poynting-Robertson effect is a dissipative and non-linear dynamical system obtained by perturbing through radiation processes the geodesic motion of test particles orbiting around a spinning compact object, described by the Kerr metric. Using the Melnikov method we find that, in a suitable range of parameters, chaotic behavior is present in the motion of a test particle driven by the Poynting-Robertson effect in the Kerr equatorial plane.Comment: 10 pages, 8 figures; published on Phys. Rev.