Deflection in higher dimensional spacetime and asymptotically non-flat spacetimes

Abstract

Using a perturbative technique, in this work we study the deflection of null and timelike signals in the extended Einstein-Maxwell spacetime, the Born-Infeld gravity and the charged Ellis-Bronnikov (CEB) spacetime in the weak field limit. The deflection angles are found to take a (quasi-)series form of the impact parameter, and automatically takes into account the finite distance effect of the source and observer. The method is also applied to find the deflections in CEB spacetime with arbitrary dimension. It's shown that to the leading non-trivial order, the deflection in some $n$-dimensional spacetimes is of the order $\mathcal{O}(M/b{)}^{n-3}$. We then extended the method to spacetimes that are asymptotically non-flat and studied the deflection in a nonlinear electrodynamical scalar theory. The deflection angle in such asymptotically non-flat spacetimes at the trivial order is found to be not $\pi$ anymore. In all these cases, the perturbative deflection angles are shown to agree with numerical results extremely well. The effects of some nontrivial spacetime parameters as well as the signal velocity on the deflection angles are analyzed.

30 pages, 7 figures; title modified; to match published version in Class.Quant.Grav

References in corpus (11)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• Applications of the Gauss-Bonnet theorem to gravitational lensing
• Multiple Images of a Highly Magnified Supernova Formed by an Early-Type Cluster Galaxy Lens
• Finite-distance corrections to the gravitational bending angle of light in the strong deflection limit
• Einstein-Yang-Mills black hole solution in higher dimensions by the Wu-Yang Ansatz
• Kerr-Newman-Jacobi geometry and the deflection of charged massive particles
• Perturbative deflection angle, gravitational lensing in the strong field limit and the black hole shadow
• Scalar Hairy Black Holes in the presence of Nonlinear Electrodynamics
• Deflection and Gravitational lensing of null and timelike signals in the Kiselev black hole spacetime in the weak field limit

Cited by in corpus (1)

• Microlensing and event rate of static spherically symmetric wormhole