Geodesic Structure of the Accelerated Stephani Universe

For the spherically symmetric Stephani cosmological model with an accelerated expansion, we investigate the main scenarios of the test particle and photon motion. We show that a comoving observer sees an appropriate picture. In the case of purely radial motion, the radial velocity decreases slightly with time due to the universe expansion. Both particles and photons spiral out of the center when the radial coordinate is constant. In the case of the motion with arbitrary initial velocity, the observable radial distance to the test particle can increase under negative observable radial velocity.

Shadow of a Schwarzschild black hole surrounded by a Bach–Weyl ring

We have studied the shadows of a Schwarzschild black hole surrounded by a Bach–Weyl ring through the backward ray-tracing method. The presence of Bach–Weyl ring leads to that the photon dynamical system is non-integrable and then chaos would appear in the photon motion, which affects sharply the black hole shadow. The size and shape the black hole shadow depend on the black hole parameter, the Bach–Weyl ring mass and the Weyl radius between black hole and ring. Some self-similar fractal structures also appear in the black hole shadow, which originates from the chaotic lensing. We also study the change of the image of Bach–Weyl ring with the ring mass and the Weyl radius. Finally, we analyze the invariant manifolds of Lyapunov orbits near the fixed points and discuss further the formation of the shadow of a Schwarzschild black hole with Bach–Weyl ring.

3 Dimensional Motion of Photon and Its Energy

Since the electron is the photon-generator and the electron is rotating around itself and around the nucleus, the emitted photon from the electron should have the effect of these rotating motions. So, the photon has a three-dimensional motion, including a transition movement and a rotary motion. And it traverses in a helical trajectory. By using this definition, we have proved wave-particle duality at the same time and introduce a new equation for the photon motion and its energy.

Profiled spectral lines of Keplerian rings orbiting in the regular Bardeen black hole spacetimes

Considering the regular Bardeen black hole spacetimes, we test the observational effects of the general relativistic solutions coupled to non-linear electrodynamics (NED) by studying the photon motion in the effective geometry governed by the spacetime geometry and the NED Lagrangian. We focus our attention to the observationally important case of profiled spectral lines generated by rings radiating in a fixed frequency and orbiting the black hole along circular geodesics of the Bardeen spacetime. Such profiled spectral lines are observed in active galactic nuclei and in microquasars, giving sufficient data for the test of regular black holes. We expect that such radiating rings could arise around the Galaxy central supermassive black hole SgrA*, and the related profiled spectral lines could give important additional information to those obtained by direct observations due to the Event Horizon (GRAVITY) Telescope. We demonstrate that the profiled spectral lines of the radiating rings predict strong signatures of the NED effects on the photon motion – namely the frequency shift to the red edge of the spectrum, and narrowing of the profile, by more than one order in comparison with the case of the profiles generated purely by the spacetime geometry, for all values of the magnetic charge and the inclination angle of the observer. The specific flux is substantially suppressed and for extended Keplerian disks even the shape of the profiled line is significantly modified due to the NED effect.

MOTION OF A VECTOR PARTICLE IN A CURVED SPACETIME IV: ASYMPTOTICAL SHAPE OF CAUSTIC

The studies of influence of spin on a photon motion in a Schwarzschild spacetime is continued. In the previous paper2the first-order correction to the geodesic motion is reduced to a non-uniform linear ordinary differential equation and the equation obtained has been solved by the standard method of integration of the Green function. If each photon draws a world line specified by this solution, then light rays from infinitely distant source form a caustic which does not appear without the spin-gravity interaction. The goal of this work is to obtain explicit form of caustic.