Simulating a Black Hole

A real-time black hole simulation built from scratch in C++ and OpenGL, featuring gravitational lensing, relativistic ray tracing, and geodesic integration based on the Schwarzschild metric.

The simulation models Sagittarius A*, the supermassive black hole at the center of the Milky Way (mass ≈ 8.54 × 10³⁶ kg), and renders the visual effects of extreme spacetime curvature.

Features

• 3D GPU Black Hole — Real-time compute shader ray marching with RK4 geodesic integration, adaptive step size, accretion disk with Doppler beaming and gravitational redshift, procedural starfield background, N-body gravity, and dynamic resolution scaling
• 2D Gravitational Lensing — Interactive 2D visualization of light ray deflection around a Schwarzschild black hole using RK4 integration in polar coordinates, with click-to-spawn rays and fading trails
• CPU Ray Tracers — Two CPU-based reference implementations: a Whitted-style ray tracer and an OpenMP-parallelized geodesic ray tracer
• Spacetime Grid — Visual representation of spacetime curvature around massive objects

Project Structure

File	Description
black_hole.cpp	Main 3D GPU simulation — compute shader dispatching, camera controls, N-body physics, accretion disk, UBO management
geodesic.comp	OpenGL 4.3 compute shader — GPU null geodesic integration (RK4), adaptive stepping, Doppler/redshift coloring, starfield
grid.vert / grid.frag	Vertex and fragment shaders for the spacetime curvature grid
2D_lensing.cpp	2D gravitational lensing visualization with modern OpenGL (VAO/VBO), interactive ray spawning
CPU-geodesic.cpp	CPU-based 3D geodesic ray tracer with OpenMP parallelization
ray_tracing.cpp	CPU Whitted-style ray tracer (spheres, reflections, shadows)
CMakeLists.txt	Build configuration with CMake and vcpkg integration
vcpkg.json	Dependency manifest (GLFW, GLM, GLEW)

Prerequisites

• C++17 compiler (MSVC, GCC, or Clang)
• CMake 3.21 or higher
• vcpkg package manager
• OpenGL 4.3 compatible GPU (for the 3D compute shader simulation)
• Visual Studio (recommended on Windows) or any compatible build system

Dependencies

Managed automatically via vcpkg:

• GLFW — Windowing and input
• GLEW — OpenGL extension loading
• GLM — Mathematics library

Building

1. Clone the repository

git clone https://github.com/andrebuilds/simulating-black-hole.git
cd simulating-black-hole

2. Configure with CMake

cmake -B build -S . -DCMAKE_TOOLCHAIN_FILE=<path-to-vcpkg>/scripts/buildsystems/vcpkg.cmake

Replace <path-to-vcpkg> with your vcpkg installation path (e.g., C:/vcpkg).

vcpkg will automatically download and install all dependencies on the first run.

3. Build

Build a specific target:

# 3D GPU Black Hole (recommended)
cmake --build build --target BlackHole3D --config Release

# 2D Gravitational Lensing
cmake --build build --target BlackHole2D --config Release

Or build everything:

cmake --build build --config Release

4. Run

# 3D Simulation
./build/Release/BlackHole3D.exe

# 2D Lensing
./build/Release/BlackHole2D.exe

Note: Shader files (.vert, .frag, .comp) are automatically copied to the output directory during the build.

Controls

BlackHole3D (3D GPU Simulation)

Key	Action
W / A / S / D	Move camera forward / left / backward / right
Mouse	Look around (free camera)
G	Toggle N-body gravity on/off
ESC	Close the window

BlackHole2D (2D Lensing)

Input	Action
Left Click	Spawn a new light ray at the cursor position

Physics

The simulation solves null geodesics (light paths) in Schwarzschild spacetime. The Schwarzschild metric describes the geometry of spacetime around a non-rotating, uncharged black hole:

$$ds^2 = -\left(1 - \frac{r_s}{r}\right)c^2 dt^2 + \left(1 - \frac{r_s}{r}\right)^{-1} dr^2 + r^2 d\Omega^2$$

where $r_s = \frac{2GM}{c^2}$ is the Schwarzschild radius.

Light rays are traced by integrating the geodesic equations using the 4th-order Runge-Kutta (RK4) method. The GPU compute shader uses adaptive step sizes — smaller steps near the event horizon for accuracy, larger steps far away for performance.

Visual Effects

• Gravitational Lensing — Light bends around the black hole, distorting the background starfield
• Accretion Disk — Hot inner regions appear blue-white, cooler outer regions appear red-orange
• Doppler Beaming — The approaching side of the disk appears brighter (relativistic D³ boosting)
• Gravitational Redshift — Light escaping the gravitational well is redshifted
• Einstein Ring — Light from directly behind the black hole forms a ring around it

Technical Details

• Geodesic integration uses RK4 on both CPU and GPU
• The compute shader processes each pixel independently, making it massively parallel
• Dynamic resolution: lower resolution while the camera is moving, full resolution when stationary
• N-body gravity uses Newton's third law optimization (compute each pair once)
• Double precision (double) is used for physics calculations to avoid floating-point artifacts near the event horizon

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Developed by andrebuilds