Einstein field equationsequation
Einstein's equations are instructions on how mass and energy curve spacetime, like a heavy ball on a stretched rubber sheet. Planets and light follow the curves of this 'fabric'.
How it works
It manifests wherever gravity is strong: black holes, bending of light rays (gravitational lensing), time dilation near massive bodies. Example: calculating Mercury's orbit, which could not be explained by Newton.
💡 If the Sun were to suddenly disappear, the Earth would 'feel' it not instantly, but only after 8 minutes — that's how long it takes for the gravitational disturbance to reach us at the speed of light.
G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
G_{μν} — Einstein tensor, describing the curvature of spacetime; Λ — cosmological constant (Λ ≈ 1.1×10⁻⁵² m⁻²); g_{μν} — metric tensor, defining the geometry of spacetime; G — Newton's gravitational constant (G ≈ 6.67430×10⁻¹¹ m³·kg⁻¹·s⁻²); c — speed of light in vacuum (c ≈ 2.99792458×10⁸ m/s); T_{μν} — energy-momentum tensor, describing the distribution of matter and energy.
G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu}
G_{μν} — Einstein tensor; R_{μν} — Ricci tensor (curvature from the Riemann tensor); R — scalar curvature (trace of the Ricci tensor); g_{μν} — metric tensor.