Rotating gravitational lenses: a kinematic approach (original) (raw)
Related papers
2010
This paper uses the Schwarzschild metric to derive an effective refractive index and acceleration vector that account for relativistic deflection of light rays, in an otherwise classical kinematic framework. The new refractive index and the known path equation are integrated to give accurate results for travel time and deflection angle, respectively. A new formula for coordinate acceleration is derived which describes the path of a massless test particle in the vicinity of a spherically symmetric mass density distribution. A standard ray-shooting technique is used to compare the deflection angle and time delay predicted by this new formula with the previously calculated values, and with standard first order approximations. Finally, the ray shooting method is used in theoretical examples of strong and weak lensing, reproducing known observer-plane caustic patterns for multiple masses.
A note on a linearized approach to gravitational lensing
Monthly Notices of the Royal Astronomical Society, 2011
A recent paper by Walters, Forbes and Jarvis presented new kinematic formulae for ray tracing in gravitational lensing models. The approach can generate caustic maps, but is computationally expensive. Here, a linearized approximation to that formulation is presented. Although still complicated, the linearized equations admit a remarkable closed-form solution. As a result, linearized approximations to the caustic patterns may be generated extremely rapidly, and are found to be in good agreement with the results of full non-linear computation. The usual Einstein-angle approximation is derived as a small angle approximation to the solution presented here.
A Simple Calculation of Gravitational Lensing on the Rotating Stars
2018
We propose a simple calculation to obtain the gravitational lensing on rotating stars. The calculation has been made by using a Lagrangian of Kerr metric and getting for deflection angle. The calculation has been reduced to slow-rotating stars and equatorials case () for maximum deflection angle .
Gravitational lensing by rotating stars
1998
The equations giving the position of the images of a point source by a rotating point lens are derived by a new, elementary method. It is shown that only two of the three im- ages are visible. It is argued that the projection of the angular momentum of the lens star on the lens plane can be measured if the lens is a rapidly rotating early type star. This is achieved by performing a series of astrometric measurements of the position of the images.
The Schwarzschild problem: a model for the motion in the solar system
1997
The motion in a field featured by a force function A/r+B/r3 (the Schwarzschild problem) constitutes a realistic model for the dynamics in the relativistic solar gravitational field. A qualitative study is performed by using the powerful tool of McGehee's transformations. The local flow on collision and infinity manifolds is described, allowing the study of orbits with very large eccentricities. For the case of parabolic-type motion, the global flow can be described. This qualitative analysis is very useful to the understanding of the motion of certain small bodies of the solar system (comets, some asteroids) at very small and very large distances from the Sun.
American Journal of Physics, 1996
In many metrics of physical interest, the gravitational field can be represented as an optical medium with an effective index of refraction. We show that, in such a metric, the orbits of both massive and massless particles are governed by a variational principle which involves the index of refraction and which assumes the form of Fermat's principle or of Maupertuis's principle. From this variational principle we derive exact equations of motion of Newtonian form which govern both massless and massive particles. These equations of motion are applied to some problems of physical interest.
An accurate Newtonian description of particle motion around a Schwarzschild black hole
Monthly Notices of The Royal Astronomical Society, 2013
A generalized Newtonian potential is derived from the geodesic motion of test particles in Schwarzschild space–time. This potential reproduces several relativistic features with higher accuracy than commonly used pseudo-Newtonian approaches. The new potential reproduces the exact location of the marginally stable, marginally bound and photon circular orbits, as well as the exact radial dependence of the binding energy and the angular momentum of these orbits. Moreover, it reproduces the orbital and epicyclic angular frequencies to better than 6 percent. In addition, the spatial projections of general trajectories coincide with their relativistic counterparts, while the time evolution of parabolic-like trajectories and the pericentre advance of elliptical-like trajectories are both reproduced exactly. We apply this approach to a standard thin accretion disc and find that the efficiency of energy extraction agrees to within 3 percent with the exact relativistic value, while the energy flux per unit area as a function of radius is reproduced everywhere to better than 7 percent. As a further astrophysical application we implement the new approach within a smoothed particle hydrodynamics code and study the tidal disruption of a main-sequence star by a supermassive black hole. The results obtained are in very good agreement with previous relativistic simulations of tidal disruptions in Schwarzschild space–time. The equations of motion derived from this potential can be implemented easily within existing Newtonian hydrodynamics codes with hardly any additional computational effort.
The geodetic effect along polar orbits in the Kerr spacetime
Physics Letters A, 1986
A gyroscope following a closed polar orbit in the Kerr spacetime is considered. An exact expression is derived giving the shift of the gyroscope's orientation per revolution in terms of the mass and angular momentum parameters of the Kerr metric and the orbit's coordinate radius.