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

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

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

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

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

What gravitational time dilation means — clocks run slower in stronger gravitational fields

"Gravitational time dilation: stronger gravity slows clocks relative to weaker gravity."

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

Riemannian geometry underpins general relativity, describing curved spacetime

How do the results from LIGO and Virgo collaborations provide evidence for gravitational waves, thereby supporting the predictions of general relativity?

LIGO and Virgo detectors' measurements of gravitational wave signals confirm Einstein's general relativity predictions