General Relativity (GR31–GR41)

11 operators covering Einstein’s general relativity — from the equivalence principle to the Friedmann equation and gravitational waves.

GR31 — Equivalence Principle

a_grav = a_inertial

Gravitational and inertial mass are identical. The conceptual foundation of general relativity.

GR32 — Einstein Tensor

G_μν = R_μν − ½ R g_μν

Encodes spacetime curvature from the Ricci tensor and scalar curvature.

GR33 — Einstein Field Equations

G_μν + Λg_μν = 8πG/c&sup4; T_μν

The master equation of general relativity — geometry of spacetime equals energy-momentum content. Used in Globe app for coordinate mapping.

GR34 — Geodesic Equation

d²x^μ/dτ² + Γ^μ_{αβ} (dx^α/dτ)(dx^β/dτ) = 0

Free-fall trajectories in curved spacetime. Objects follow geodesics unless acted on by non-gravitational forces.

GR35 — Gravitational Time Dilation

Δt = Δt&sub0; √(1 − 2GM/rc² − v²/c²)

Combined gravitational and velocity time dilation. Used in ZSP’s K_temporal kernel for time-locked key generation.

GR36 — Length Contraction

L = L&sub0; √(1 − 2GM/rc²)

Lengths contract in strong gravitational fields (gravitational length contraction).

GR37 — Schwarzschild Radius

r_s = 2GM/c²

Event horizon radius of a non-rotating black hole. Below this radius, escape velocity exceeds the speed of light.

GR38 — Gravitational Waves

□h_μν + κ ∂_t h_μν = −16πG/c&sup4; T_μν

Linearised Einstein equations for gravitational wave propagation. Metric perturbations ripple through spacetime.

GR39 — Cosmological Constant

Λ = 3H&sub0;² Ω_Λ / c²

Dark energy density parameterised by the Hubble constant and density parameter.

GR40 — Friedmann Equation

(à/a)² = 8πG/3 ρ − kc²/a² + Λc²/3

Governs the expansion of the universe. Scale factor evolution from energy density, curvature, and cosmological constant.

GR41 — Cosmological Redshift

z = (λ_obs − λ_emit) / λ_emit

Wavelength stretching due to cosmic expansion. Relates observed and emitted wavelengths to the scale factor.

API Usage

Call any operator via the Compute API:

curl -X POST https://zeq.dev/api/zeq/compute \
  -H "Content-Type: application/json" \
  -H "Authorization: Bearer zk_live_..." \
  -d '{"query": "Schwarzschild radius of a 10 solar mass black hole", "operators": ["GR37, KO42"]}'

The 7-step wizard protocol selects the right operators automatically when you omit the operators field. KO42 is always included.