Gμν+Λgμν=8πTμν

Exact spacetimes

Analytic solutions of the field equations, computed live from the metric

Drag to orbit the camera, scroll or pinch to change distance. Every pixel is a null geodesic integrated backward in Mino time from a zero-angular-momentum observer.
Custom launch:
Timelike and null geodesics from Hamilton's equations H = ½gμνpμpν, integrated with adaptive RK4 directly from the metric. v = 1 launches a photon; ψ is measured from the outward radial direction toward the prograde tangent, in the local orthonormal frame of the observer orthogonal to t = const.