StellarLens - Overview

StellarLens is an interactive, real-time web application that visualizes the mesmerizing phenomenon of gravitational lensing around a black hole. Leveraging advanced 3D graphics, custom shaders, and modern web technologies.

Sample: Light rays bending around a black hole, with lensing graph overlay.

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🔬 Scientific Background

Schwarzschild Metric and Gravitational Lensing

The Schwarzschild metric describes the spacetime geometry around a non-rotating, spherically symmetric mass such as a black hole. In Schwarzschild coordinates, the line element is:

$$ ds^2 = -\left(1-\frac{2GM}{rc^2}\right)c^2dt^2 + \left(1-\frac{2GM}{rc^2}\right)^{-1}dr^2 + r^2(d\theta^2 + \sin^2\theta d\phi^2) $$

where $G$ is the gravitational constant, $M$ is the mass of the black hole, $c$ is the speed of light, and $r$ is the radial coordinate. Light rays (null geodesics) passing near the black hole are deflected due to spacetime curvature.

Einstein Deflection Angle

For a light ray passing at impact parameter $b$ (distance of closest approach), the total deflection angle $\alpha$ in the weak-field limit is:

$$ \alpha \approx \frac{4GM}{c^2 b} $$

This is the classic Einstein formula for gravitational lensing. For strong lensing (close to the event horizon), higher-order terms or numerical integration of the geodesic equations are required.

Algorithmic Implementation

Component	Description
Ray Tracing	Traces light rays backward from the camera through each pixel, computing deflection based on the Schwarzschild metric
GLSL Shader	Computes apparent position of background sources using lensing deflection, utilizing black hole mass and event horizon parameters
Numerical Integration	For accurate near-horizon visualization, integrates the null geodesic equations: $$\left(\frac{du}{d\phi}\right)^2 + u^2 = \frac{1}{b^2}$$ where $u = 1/r$ and $\phi$ is the azimuthal angle

Summary

The project combines the Schwarzschild metric, Einstein's deflection formula, and real-time GPU-based ray tracing to visualize gravitational lensing. The approach balances analytic solutions for efficiency and numerical integration for accuracy near the event horizon, all implemented in performant GLSL shaders for interactive exploration.

🚀 Key Features

Feature	Description
Real-Time 3D Visualization	Uses Three.js for high-performance, GPU-accelerated rendering
Physically-Inspired Lensing	Custom GLSL fragment shaders simulate light deflection based on Einstein radius
Interactive GUI Controls	lil-gui for real-time parameter adjustment
Ray Path Visualization	Visual representation of light ray bending around black holes
Post-Processing Effects	Cinematic bloom and glow using UnrealBloomPass and EffectComposer
Dynamic Info Panel	Real-time display of simulation parameters and debugging info
Lensing Graph Overlay	Interactive plots of deflection angles vs. impact parameters
Responsive Architecture	Clean ES modules and responsive UI for all devices

🛠️ Technologies & Concepts

Core Technologies

• Three.js: 3D rendering, camera controls, scene management
• GLSL Shaders: Custom shaders for gravitational lensing simulation
• JavaScript ES Modules: Modern, modular codebase architecture
• HTML5 & CSS3: Responsive layouts and UI components

Scientific Concepts

• Gravitational lensing
• Einstein radius calculation
• Event horizon physics
• Ray tracing in curved spacetime
• Light deflection in strong gravity fields

📦 Getting Started

# Clone the repository
git clone https://github.com/Rhishavhere/StellarLens.git

# Navigate to project directory
cd StellarLens

# Install dependencies
npm install

# Start development server
npx serve

Once running, use the GUI controls to explore different lensing scenarios and visualize ray paths around the black hole.

📚 Usage

• Adjust lensing strength, event horizon, and bloom via the GUI.
• Observe real-time changes in the visualization and info panel.
• View the lensing graph overlay for scientific analysis.