black_hole

Project Overview

Introduction

The Black Hole Simulation project aims to visualize the visual distortion caused by extreme gravity, a phenomenon known as gravitational lensing. By solving the geodesic equations for light rays passing near a black hole, we can generate physically accurate images of what a black hole might look like to an observer.

Goals

1. Ray-tracing: Implement ray tracing to simulate gravitational lensing mechanics.
2. Accretion Disk: Simulate a glowing disk of matter orbiting the black hole.
3. Spacetime Curvature: Provide a visual representation of how mass curves spacetime using a distorted grid.
4. Real-time Performance: Optimize calculations to run at interactive frame rates (60FPS+).

Technical Approach

The simulation is built using C++ and OpenGL. It employs a hybrid approach:

• CPU: Handles the main simulation loop, window management, and basic physics for non-relativistic interactions.
• GPU (Compute Shaders): performs the heavy lifting of ray marching through curved spacetime. We use Runge-Kutta 4 (RK4) integration to solve the geodesic equations for each pixel in parallel.

Simulating Sagittarius A*

The default configuration simulates Sagittarius A*, the supermassive black hole at the center of the Milky Way galaxy.

• Mass: $\approx 8.54 \times 10^{36}$ kg (approx 4 million solar masses).
• Schwarzschild Radius ($r_s$): The event horizon radius, calculated as $r_s = \frac{2GM}{c^2}$.

Visualizations

2D Lensing (CPU)

A simpler 2D implementation (2D_lensing.cpp) demonstrates the path of individual light rays as they are deflected by the black hole’s gravity.

3D Simulation (GPU)

The full 3D simulation (black_hole.cpp + geodesic.comp) renders a complete scene with:

• A background starfield (or full-screen quad).
• An accretion disk with relativistic Doppler beaming effects (approximated).
• Gravitational redshift/blueshift (visualized via color intensity).