Black Hole Geodesic Lab: Unveiling the Dance of Light and Gravity

What Are Geodesics?

Geodesics are the shortest paths between two points on a curved surface or spacetime. In general relativity, they represent the trajectories that light or particles follow in the presence of gravity.

In this simulation, geodesics illustrate how light rays bend around a black hole due to its strong gravitational field.

The Innermost Stable Circular Orbit (ISCO)

The ISCO is the smallest radius at which a particle can orbit a black hole in a stable circular path. Beyond this point, orbits become unstable and decay.

For a non-rotating Schwarzschild black hole, the ISCO occurs at 6 times the Schwarzschild radius (3 sqrt(3) M), as shown by the simulation.

Light Bending and Lensing

When light passes near a massive object like a black hole, it bends due to gravitational lensing. This effect is predicted by general relativity and can be observed in distant starlight.

The simulation demonstrates this with a ray-traced sky showing the Einstein ring, which is the image of a distant star as seen from Earth when it is directly behind a black hole.

Effective Potential and Precession

The effective potential in general relativity describes the energy required for a particle to move along different orbits. It includes both gravitational and centrifugal terms.

Precession refers to the change in direction of an orbiting object's angular momentum vector, which is significant near black holes due to their strong gravity.

Frequently asked questions

Try it live

Everything above runs in your browser — open Black Hole Geodesic Lab - 2D Light Bending, Shadow and ISCO and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.