Routing protocol

Physics

Gravitation

Photon sphere

Computer network

Mathematical physics

Black hole (networking)

Gravitational lens

Link-state routing protocol

Galaxy

Gravitational lensing formalism

Schwarzschild radius

General relativity

Gauss–Bonnet theorem

Schwarzschild metric

Einstein

Weak gravitational lensing

Charged black hole

Computer science

Astrophysics

Routing (electronic design automation)

Redshift

Strong gravitational lensing

Classical mechanics

Journal of Cosmology and Astroparticle Physics

Recently, a non-trivial $4D$ Einstein-Gauss-Bonnet (EGB) theory of gravity, by rescaling the GB coupling parameter as $\alpha/(D-4)$, was formulated in \cite{Glavan:2019inb}, which bypasses Lovelock's theorem and avoids Ostrogradsky instability. The theory admits a static spherically symmetric black hole, unlike $5D$ EGB or general relativity counterpart, which can have both Cauchy and event horizons. We generalize previous work, on gravitational lensing by a Schwarzschild black hole, in the strong and weak deflection limits to the $4D$ EGB black holes to calculate the deflection coefficients $\bar{a}$ and $\bar{b}$, while former increases and later decrease with increasing $\alpha$. We also find that the deflection angle $\alpha_D$, angular position $\theta_{\infty}$ and $u_{m}$ decreases, but angular separation $s$ increases with $\alpha$. The effect of the GB coupling parameter $\alpha$ on positions and magnification of the source relativistic images is discussed in the context of SgrA* and M87* black holes. A brief description of the weak gravitational lensing using the Gauss-Bonnet theorem is presented.

Gravitational lensing by black holes in the 4<i>D</i> Einstein-Gauss-Bonnet gravity

Gravitational lensing by black holes in the 4D Einstein-Gauss-Bonnet gravity