Spacetime Curvature & Geodesics

3D Flamm's paraboloid embedding visualization of curved 4D spacetime around a massive central body. Demonstrates Schwarzschild metric curvature funneling, stable orbital geodesics, and gravitational light ray deflection angles (Δφ ≈ 4GM/c²b).

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Central Mass (M) 1.2

Mass determining Schwarzschild radius r_s = 2GM/c²

Mathematical Formulation

69 chars high

Analytical Equation

G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}, \quad ds^2 = -\left(1-\frac{r_s}{r}\right)c^2dt^2 + \left(1-\frac{r_s}{r}\right)^{-1}dr^2 + r^2d\Omega^2

Compact Formula

z(r) = 2 * Math.sqrt(rs * (r - rs)); defAngle = (4 * GM) / (c^2 * b);

Renderer Logic

// Schwarzschild Spacetime Embedding & Null Geodesics
const depthZ = (130 * scale) - 2 * Math.sqrt(Math.max(0, rs * (r - rs))) * 4.2;
const defAmount = (4 * rs) / (dist + rs * 0.5);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#general-relativity #einstein-field-equations #spacetime-curvature #geodesics #gravitational-lensing #physics-study

Author: Relativity Core Target: 60 FPS

Spacetime Curvature & Geodesics

Live Parameters

Mathematical Formulation

Mathematical Tags

Export & Embed: Spacetime Curvature & Geodesics

4K PNG Snapshot

WebM Video (5s Loop)

HTML Iframe Embed