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.
We determine the analytic expression of the Rayleigh potential associated to the general relativistic Poynting-Robertson effect. This constitutes the first example of a physical dissipative system treated analytically in General Relativity. The employed approach and further implications are discussed.
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.
We prove the stability of the critical hypersurfaces associated with the three-dimensional general relativistic Poynting-Robertson effect. The equatorial ring configures to be as a stable attractor and the whole critical hypersurface as a basin of attraction for this dynamical system. We introduce a new, simpler (in terms of calculations), and more physical approach within the Lyapunov theory. We propose three different Lyapunov functions, each one carrying important information and very useful for understanding such phenomenon under different aspects.
We propose the Lagrangian formulation for describing the motion of a test particle in a general relativistic, stationary, and axially symmetric spacetime. The test particle is also affected by a radiation field, modeled as a coherent flux of photons traveling along the null geodesics of the background spacetime, including the general relativistic Poynting-Robertson effect. The innovative part of this work is to prove the existence of the potential linked to the dissipative action caused by the Poynting-Robertson effect in General Relativity through the help of an integrating factor, depending …
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 m…
Ever since the first discovery of Poynting and Robertson, the radiation source has been treated as merely a point. Even in a very few studies where the size of the source has been taken into account, the treatment of the problem remained largely non-relativistic. In the present work, we address the issue of the finite size effects on the Poynting-Robertson effect in a fully relativistic manner for the first time. As a result, the emergence and the characteristic of the critical point/suspension orbit can be studied in a systematic and detailed manner.
We determine for the first time in the literature the analytic form of the Rayleigh potential of the general relativistic Poynting-Robertson effect. The employed procedure is based on the use of an integrating factor and a new integration strategy where the test particle's dissipated energy represents the fundamental variable. The obtained results and their implications are discussed. Finally, concluding remarks and future projects are drawn.
The general relativistic version is developed for Robertson's discussion of the Poynting-Robertson effect that he based on special relativity and Newtonian gravity for point radiation sources like stars. The general relativistic model uses a test radiation field of photons in outward radial motion with zero angular momentum in the equatorial plane of the exterior Schwarzschild or Kerr spacetime.
In my doctoral thesis, I have focussed my attention on radiation processes in high-energy astrophysics connected with the accretion flow physics around compact objects. Generally, a radiation field beside to exert an outward radiation pressure, there is also the presence of a radiation drag force, which both can drastically change or even halt the motion of the surrounding matter. 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. The thesis is organised in…
We develop a model-independent procedure to single out static and spherically symmetric wormhole solutions based on the general relativistic Poynting-Robertson effect and the extension of the ray-tracing formalism in generic static and spherically symmetric wormhole metrics. Simulating the flux emitted by the Poynting-Robertson critical hypersurface (i.e., a stable structure where gravitational and radiation forces attain equilibrium) or also from another X-ray source in these general geometrical environments toward a distant observer, we are able to reconstruct, only locally to the emission r…
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 …
As a sequel to our recent works challenging toward the systematic inclusion of the effect of radiation on the trajectory of a test particle orbiting around a luminous spinning relativistic star eventually aiming at its application to the accretion flow. We explore in the present work the fine structure of the trajectory of test particle just entering the ``suspension orbit" under the purpose of a detailed investigation of test particle's trajectory in the vicinity of the ``suspension orbit". We end up with a rather puzzling behavior that, contrary to our expectation, the specific angular momen…
We consider a further extension of our previous works in the treatment of the three-dimensional general relativistic Poynting-Robertson effect, which describes the motion of a test particle around a compact object as affected by the radiation field originating from a rigidly rotating and spherical emitting source, which produces a radiation pressure, opposite to the gravitational pull, and a radiation drag force, which removes energy and angular momentum from the test particle. The gravitational source is modeled as a non-spherical and slowly rotating compact object endowed with a mass quadrup…
In this paper we investigate the three-dimensional (3D) motion of a test particle in a stationary, axially symmetric spacetime around a central compact object, under the influence of a radiation field. To this aim we extend the two-dimensional (2D) version of the Poynting-Robertson effect in General Relativity (GR) that was developed in previous studies. The radiation flux is modeled by photons which travel along null geodesics in the 3D space of a Kerr background and are purely radial with respect to the zero angular momentum observer (ZAMO) frames. The 3D general relativistic equations of mo…
We investigate the three-dimensional motion of a test particle in the gravitational field generated by a non-spherical compact object endowed with a mass quadrupole moment, described by the Erez-Rosen metric, and a radiation field, including the general relativistic Poynting-Robertson effect, coming from a rigidly rotating spherical emitting source located outside of the compact object. We derive the equations of motion for test particles influenced by such radiation field, recovering the two-dimensional description, and the weak-field approximation. This dynamical system admits the existence …
We study the motion of a test particle in a stationary, axially and reflection symmetric spacetime of a central compact object, as affected by interaction with a test radiation field of the same symmetries. Considering the radiation flux with fixed but arbitrary (non-zero) angular momentum, we extend previous results limited to an equatorial motion within a zero-angular-momentum photon flux in the Kerr and Schwarzschild backgrounds. While a unique equilibrium circular orbit exists if the photon flux has zero angular momentum, multiple such orbits appear if the photon angular momentum is suffic…
A spinning particle in the Schwarzschild spacetime deviates from geodesic behavior because of its spin. A spinless particle also deviates from geodesic behavior when a test radiation field is superimposed on the Schwarzschild background: in fact the interaction with the radiation field, i.e., the absorption and re-emission of radiation, leads to a friction-like drag force responsible for the well known effect which exists already in Newtonian gravity, the Poynting-Robertson effect. Here the Poynting-Robertson effect is extended to the case of spinning particles by modifying the Mathisson-Papap…
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 hol…
We investigate the three-dimensional, general relativistic Poynting-Robertson effect in the case of rigidly rotating spherical source which emits radiation radially in the local comoving frame. Such radiation field is meant to approximate the field produced by the surface of a rotating neutron star, or by the central radiating hot corona of accreting black holes; it extends the purely radial radiation field that we considered in a previous study. Its angular momentum is expressed in terms of the rotation frequency and radius of the emitting source. For the background we adopt a Kerr spacetime …
We discuss the effect of the Poynting flow on the magnetically dominated thin accretion disk, which is simplified to a two-dimensional disk on the equatorial plane. It is shown in the relativistic formulation that the Poynting flux by the rotating magnetic field with Keplerian angular velocity can balance the energy and angular momentum conservation of a steady accretion flow.
Motivated by the picture of a thin accretion disc around a black hole, radiating mainly in the direction perpendicular to its plane, we study the motion of test particles interacting with a test geodesic radiation flux originating in the equatorial plane of a Schwarzschild space-time and propagating initially in the perpendicular direction. We assume that the interaction with the test particles is modelled by an effective term corresponding to the Thomson-type interaction which governs the Poynting-Robertson effect. After approximating the individual photon trajectories adequately, we solve th…
Motion of test particles in the gravitational field associated with an electromagnetic plane wave is investigated. The interaction with the radiation field is modeled by a force term {\it à la} Poynting-Robertson entering the equations of motion given by the 4-momentum density of radiation observed in the particle's rest frame with a multiplicative constant factor expressing the strength of the interaction itself. Explicit analytical solutions are obtained. Scattering of fields by the electromagnetic wave, i.e., scalar (spin 0), massless spin $\frac12$ and electromagnetic (spin 1) fields, is s…
We investigate the dynamics of test particles undergoing friction forces in a Friedmann-Robertson-Walker (FRW) spacetime. The interaction with the background fluid is modeled by introducing a Poynting-Robertson-like friction force in the equations of motion, leading to measurable (at least in principle) deviations of the particle trajectories from geodesic motion. The effect on the peculiar velocities of the particles is investigated for various equations of state of the background fluid and different standard cosmological models. The friction force is found to have major effects on particle m…
A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann--Robertson--Walker and Gödel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally flat spacetimes. Exact solutions for the motion of the particle and general exact expressions for the momenta and velocities are displayed for different cases. In particular, the solution for the motion in spherically symmetric metrics is presented in the equatorial plane. The exact solutions are found using constants of motion of the particle, namely its mass,…
Motion of massive test particles in the nonvacuum spherically symmetric radiating Vaidya spacetime is investigated, allowing for physical interaction of the particles with the radiation field in terms of which the source energy-momentum tensor is interpreted. This "Poynting-Robertson-like effect" is modeled by the usual effective term describing a Thomson-type radiation drag force. The equations of motion are studied for simple types of motion including free motion (without interaction), purely radial and purely azimuthal (circular) motion, and for the particular case of "static" equilibrium; …
A "temporal analogue" of the standard Poynting-Robertson effect is analyzed as induced by a dust of particles (instead of a gas of photons) surrounding a Schwarzschild black hole. Test particles inside this cloud undergo acceleration effects due to the presence of a friction force, so that the fate of their evolution can be completely different from the corresponding geodesic motion. Typical situations are discussed of hyperbolic motion of particles scattered by the black hole in the presence of a dust filling the whole spacetime region outside the horizon as well as particles which free fall …
The energy content of cylindrical gravitational wave spacetimes is analyzed by considering two local descriptions of energy associated with the gravitational field, namely those based on the C-energy and the Bel-Robinson super-energy tensor. A Poynting-Robertson-like effect on the motion of massive test particles, beyond the geodesic approximation, is discussed, allowing them to interact with the background field through an external force which accounts for the exchange of energy and momentum between particles and waves. In addition, the relative strains exerted on a bunch of particles displac…
Accretion disks surrounding compact objects, and other environmental factors, deviate satellites from geodetic motion. Unfortunately, setting up the equations of motion for such relativistic trajectories is not as simple as in Newtonian mechanics. The principle of general (or Lorentz) covariance and the mass-shell constraint make it difficult to parametrize physically adequate 4-forces. Here, we propose a solution to this old problem. We apply our framework to several conservative and dissipative forces. In particular, we propose covariant formulations for Hooke's law and the constant force, a…
The motion of a test particle in the gravitational field of a non-spherical source endowed with both mass and mass quadrupole moment is investigated when a test radiation field is also present. The background is described by the Erez-Rosen solution, which is a static spacetime belonging to the Weyl class of solutions to the vacuum Einstein's field equations, and reduces to the familiar Schwarzschild solution when the quadrupole parameter vanishes. The radiation flux has a fixed but arbitrary (non-zero) angular momentum. The interaction with the radiation field is assumed to be Thomson-like, i.…
