An interactive symbolic-GR workbench built on SymPy. Start from a metric ansatz and apply physical assumptions one step at a time — static, spherically symmetric, and so on — watching how each assumption reshapes the metric tensor and the differential equations it implies. It derives the Christoffel, Riemann, Ricci, and Einstein tensors exactly, extracts the Einstein field equations, and lets you test a candidate against known solutions (Schwarzschild, for instance, collapses the vacuum equations to 0 = 0). Solve those equations and you have a complete metric — which feeds straight into GR below.

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Give it a metric and it returns the spacetime trajectories. Geodesics are treated as Hamiltonian flows and integrated with a structure-preserving symplectic scheme (following two papers) across an extended phase space of 4-position and 4-momentum — high-order error control and stable accuracy over long timescales, even for non-separable Hamiltonians. Define any metric symbolically, let it solve the energy component of the initial momentum from conservation laws, and push many test particles through at once. The natural partner to sym_gr: solve for a metric there, integrate its geodesics here. Below: geodesic orbits around a Kerr black hole (M=1, a=0.5), 4th order.