
The shadow cast by a black hole provides information about its geometry and charge.The black hole shadow is the dark, roughly circular region seen in images of a black hole, caused by the event horizon and the strong gravitational bending of light. It is not the event horizon itself, but rather the 'shadow' cast by the black hole against the bright background of hot gas or radiation behind it. Photons that pass too close to the black hole are captured and never reach the observer, creating a dark void. The size and shape of this shadow depend on the black hole's mass, spin, and charge, as well as on the geometry of space-time around it. The shadow is a direct visual manifestation of strong gravity, and its observation provides a powerful test of general relativity and alternative theories of gravity.
The concept of the black hole shadow was first discussed by James Bardeen in 1973, and later by Jean-Pierre Luminet in 1979, who produced the first simulated image. The first actual image of a black hole shadow was captured by the Event Horizon Telescope in 2019, for the supermassive black hole M87*.
The shadow forms because of the photon sphere — a region around the black hole where gravity is so strong that light can orbit. Photons that cross this sphere are either captured by the black hole or deflected into it, so they never escape to the observer. The boundary of the shadow corresponds to the set of photon trajectories that just barely escape. For a non-rotating (Schwarzschild) black hole, the shadow is a perfect circle with a radius of about 2.6 times the gravitational radius. For a rotating (Kerr) black hole, the shadow is slightly flattened on one side and offset, due to frame-dragging effects. The shadow's size scales directly with the black hole's mass, so measuring it can provide a precise mass estimate.
The shadow is used to measure black hole masses and spins, to test general relativity, and to constrain alternative theories of gravity, such as those involving extra dimensions or quantum corrections.
The shadow of a black hole is about 2.6 times larger than the event horizon itself, so the dark region we see in images is not the 'surface' of the black hole, but a gravitational illusion.
| r_{\text{sh}} | variable | Shadow radius as seen by a distant observer — length metre |
| r_{\text{H}} | variable | Event horizon radius of the black hole — length metre |
| r | variable | radial coordinate — radial coordinate metre |
| a | variable | specific angular momentum (spin parameter) — angular momentum per unit mass metre |
| Δ | variable | horizon function — horizon function metre squared |
| Δ' | variable | derivative of horizon function with respect to r — derivative of horizon function metre |
| ξ | variable | critical impact parameter (azimuthal) — impact parameter metre |
| η | variable | critical impact parameter (polar) — impact parameter metre squared |
| d/dr | operator | computes the rate of change of Δ with respect to r — derivative operator |


















