3D Black Hole Simulator: Geodesic Ray Tracing, Lensing and the Photon Ring

What Geodesic Ray Tracing Is

Geodesic ray tracing is a method used to simulate the paths that light takes through curved spacetime, as described by Einstein's theory of general relativity. In the context of black holes, it allows us to visualize how light behaves in the strong gravitational fields near these objects.

By integrating null geodesics (paths followed by photons) using numerical methods like Runge-Kutta 4th order integration on Binet form, we can accurately model the behavior of light rays as they curve around a black hole's event horizon and interact with its surroundings.

Why It Matters

Understanding geodesic ray tracing is crucial for interpreting astronomical observations. The effects of gravitational lensing, such as the formation of an Einstein ring or the appearance of a photon ring, provide valuable insights into the nature and distribution of mass in the universe.

Moreover, this technique helps astronomers test general relativity by comparing theoretical predictions with observational data, making it a cornerstone in modern astrophysics.

Real-World Examples

The 3D black hole simulator demonstrates how geodesic ray tracing can be used to model the appearance of black holes as seen from various distances and angles. For instance, the simulation shows the shadow cast by a black hole, which is a result of light being bent around it.

Another example is the photon ring, a bright annular structure that forms just outside the event horizon due to multiple scattering of light rays. This phenomenon has been observed in images of supermassive black holes at the centers of galaxies.

How It Works

The simulator uses a numerical integration method, specifically Runge-Kutta 4th order (RK4), to solve the geodesic equations in curved spacetime. This approach is applied on a Binet form of the Schwarzschild metric, which describes the geometry around a non-rotating black hole.

Each pixel in the simulation represents a light ray that follows these geodesics, creating a realistic visual representation of how light behaves near a black hole.

Frequently asked questions

Try it live

Everything above runs in your browser — open 3D Black Hole Simulator: Geodesic Ray Tracing, Lensing and the Photon Ring and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.