What the Schwarzschild solution describes — spacetime geometry around a non-rotating spherical mass

What the Kerr solution adds — spacetime around a rotating black hole, including frame-dragging

Kerr solution describes rotating black holes' spacetime, featuring frame-dragging effects

What gravitational lensing confirms — mass curves spacetime and bends the path of light

Gravitational lensing confirms that mass warps spacetime, bending light's trajectory

Why Einstein needed Riemannian geometry — curved spacetime requires non-Euclidean mathematics

Riemannian geometry underpins general relativity, describing curved spacetime

What the Penrose-Hawking singularity theorems prove — singularities are inevitable in general relativity under certain conditions

Theorems assert black holes and singularities arise from gravitational collapse in spacetime

What the Einstein field equations relate — the curvature of spacetime (Gμν) to the energy-momentum tensor (Tμν)

Einstein's field equations: Gμν = 8πTμν, relating spacetime curvature to energy-momentum

How Eddington's 1919 eclipse observation confirmed general relativity — starlight bent by the Sun

Eddington's eclipse observation showed starlight bending due to the Sun's gravity, confirming general relativity