Software · Alpha

GR Studio

Exact general relativity, with the receipts.

A symbolic calculation engine for curved spacetime. It computes the geometry exactly, carries every proof obligation it took on, and hands you the LaTeX for the paper. The examples below are exported from the engine. The Studio itself runs on your own machine.

Kerr Lab

Horizon and orbit structure.

Equatorial plane of a Kerr black hole in Boyer-Lindquist coordinates, in geometric units with M set to one. Drag the spin.

10 M
a/M = 0.0000
Outer horizon
2.0000 M
Inner horizon
0.0000 M
Ergosurface
2.0000 M
Photon, prograde
3.0000 M
Photon, retrograde
3.0000 M
ISCO, prograde
6.0000 M
ISCO, retrograde
6.0000 M
r± = M ± √(M2 − a2)
What the slider shows. The equatorial ergosurface sits at 2M for every spin while the outer horizon contracts toward M, so the ergoregion widens as the hole spins up. Prograde orbits are dragged inward and retrograde orbits are pushed out, reaching 9M for the retrograde ISCO and 4M for the retrograde photon orbit in the extremal limit.

Geometry identity

Are these two spacetimes the same?

Write a metric in two coordinate systems and the question of whether they describe the same geometry gets hard fast. There is no table to look this up in. The engine decides it on constant-curvature strata and shows the witness that settles it.

CK-0 constant-curvature local equivalence preview. The engine handles exact analytic four-dimensional Lorentzian constant-curvature metrics through Karlhede order q=1, on named local strata. It is not a general Cartan-Karlhede implementation. Cases outside that scope return INDETERMINATE rather than guessing, because a wrong SAME is worse than an honest unknown.

Verification

Frozen receipt.

Every certified run records the obligations it discharged, and the verdict is derived from those records rather than from a hard-coded answer.

CK-0 adversarial suite
40 / 40 passed
Full toolkit suite
150 / 150 passed
Independent math red-team
19 / 19 passed
Independent API and security
73 / 73 passed
Determinism
strict JSON, cross-process
Source integrity
SHA-256 hashed

Certified runs carry exact residuals for metric regularity, Lorentz signature, excluded poles, curvature identities, covariant derivative rank, and the stabilizer generators with their action on the curvature.