This simulation demonstrates gravitational lensing around a black hole using approximations inspired by general relativity. The black hole is modeled with an event horizon defined by the Schwarzschild radius Rs = 2M (in geometric units where G = c = 1). The photon sphere, located roughly at 3M, is the region where light can orbit the black hole.
The simulation applies a thin-lens approximation to model light deflection. For an incoming ray at an angular distance θ from the black hole’s center,
the deflected ray is computed using a formula akin to:
β = θ - (θE2 / θ),
where θE (the Einstein radius) is proportional to the mass of the black hole. This approximation is tuned for visual plausibility.
In addition, a spin parameter (a dimensionless quantity) is included to simulate frame dragging, resulting in a spiral distortion
of the lensed image. All parameters are expressed in geometric units:
– Mass (M) is in geometric mass units,
– Distance (r) is measured in the same units,
– Spin (a) is dimensionless.