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تسجيل مستخدم جديدThree-dimensional general relativistic Poynting-Robertson effect II: Radiation field from a rigidly rotating spherical source
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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 geometry. We derive the equations of motion for test particles influenced by such radiation field, recovering the classical and weak-field approximation for slow rotation. We concentrate on solutions consisting of particles orbiting along circular orbits off and parallel to the equatorial plane, which are stabilized by the balance between gravitational attraction, radiation force and PR drag. Such solutions are found to lie on a critical hypersurface, whose shape may morph from prolate to oblate depending on the Kerr spin parameter and the luminosity, rotation and radius of the radiating sphere. For selected parameter ranges, the critical hypersurface intersects the radiating sphere giving rise to a bulging equatorial region or, alternatively, two lobes above the poles. We calculate the trajectories of test particles in the close vicinity of the critical hypersurface for a selected set of initial parameters and analyze the spatial and angular velocity of test particles captured on the critical hypersurface.
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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) v
ersion 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 motion that we derive are consistent with the classical (i.e. non-GR) description of the Poynting-Robertson effect in 3D. The resulting dynamical system admits a critical hypersurface, on which radiation force balances gravity. Selected test particle orbits are calculated and displayed, and their properties described. It is found that test particles approaching the critical hypersurface at a finite latitude and with non-zero angular moment are subject to a latitudinal drift and asymptotically reach a circular orbit on the equator of the critical hypersurface, where they remain at rest with respect to the ZAMO. On the contrary, test particles that have lost all their angular momentum by the time they reach the critical hypersurface do not experience this latitudinal drift and stay at rest with respects to the ZAMO at fixed non-zero latitude.
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 o
riginating 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 quadrupole moment and an angular momentum and it is formally described by the Hartle-Thorne metric. We derive the test particles equations of motion in the three-dimensional and two-dimensional cases. We then investigate the properties of the critical hypersurfces (regions, where a balance between gravitational and radiation forces is established). Finally, we show how this model can be applied to treat radiation phenomena occurring in the vicinity of a neutron star.
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 gene
ral 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 of a critical hypersurface, region where gravitational and radiation forces balance. Selected test particle orbits for different set of input parameters are displayed. The possible configurations on the critical hypersurfaces can be either latitudinal drift towards the equatorial ring or suspended orbits. We discuss about the existence of multiple hypersurface solutions through a simple method to perform the calculations. We graphically prove also that the critical hypersurfaces are stable configurations within the Lyapunov theory.
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 K
err 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.
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.
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