Routing (electronic design automation)

Quantum mechanics

Engineering

Curvature

Schwarzschild radius

Charged black hole

Orbit (dynamics)

Redshift

Gravitation

Spacetime

Aerospace engineering

Mathematical physics

Galaxy

Astrophysics

Computer science

Classical mechanics

Geology

Photon sphere

Computer network

Gravitational lens

Oceanography

Routing protocol

Deflection (physics)

Physics

Mathematics

Astronomy

Link-state routing protocol

Schwarzschild metric

Geometry

Particle (ecology)

Conformal map

Gaussian curvature

Black hole (networking)

General relativity

Circular orbit

Physical review. D/Physical review. D.

The purpose of this paper is twofold. First, we introduce a geometric approach to study the circular orbit of a particle in static and spherically symmetric spacetime based on Jacobi metric. Second, we apply the circular orbit to study the weak gravitational deflection of null and timelike particles based on Gauss-Bonnet theorem. By this way, we obtain an expression of deflection angle and extend the study of deflection angle to asymptotically nonflat black hole spacetimes. Some black holes as lens are considered such as a static and spherically symmetric black hole in the conformal Weyl gravity and a Schwarzschild-like black hole in bumblebee gravity. Our results are consistent with the previous literature. In particular, we find that the connection between Gaussian curvature and the radius of a circular orbit greatly simplifies the calculation.

Circular orbit of a particle and weak gravitational lensing