Event Horizon

Full definition

The event horizon is one of the strangest ideas in modern physics. It is not a material surface, not a membrane, not anything you could touch if you passed through it. It is a causal boundary: the limit beyond which no event can ever reach you from outside. The name is literal — beyond this horizon, events are forever inaccessible to a distant observer.

Physically, it is the surface where escape velocity exactly equals the speed of light. Inside it, you would have to go faster than c to escape — forbidden by special relativity. Anything crossing the horizon is thus permanently severed from the outside Universe, including light itself. Hence 'black hole'.

The horizon's size depends on a single quantity: the black hole's mass. It is the Schwarzschild radius R_s = 2GM/c², found by Karl Schwarzschild in 1916 (published from the Russian front, months before his death). For a 10 M☉ stellar black hole, R_s ≈ 30 km. For the supermassive M87* (6.5 × 10⁹ M☉), R_s ≈ 1.9 × 10¹⁰ km — about 120 times the Earth-Sun distance, larger than our entire Solar System.

Subtle but crucial: the horizon has no 'thickness'. It is a geometric surface of fixed radius (for a static, non-rotating black hole). An observer crossing it feels nothing locally — no impact, no barrier. Only after the fact, trying to turn back, do they discover the irreversibility. Seen from outside, their fall appears to slow indefinitely as they near the horizon: extreme gravitational time dilation.

Formula and orders of magnitude

The horizon of a Schwarzschild black hole (non-rotating, uncharged) has the eponymous radius:

R_s = 2GM / c²

with G = 6.674 × 10⁻¹¹ m³/(kg·s²) and c = 3 × 10⁸ m/s. Numerically: R_s [km] ≈ 2.95 × M [in M☉].

Some concrete values:

• Earth (6 × 10²⁴ kg) → R_s ≈ 8.87 mm (grape-sized). • Sun (hypothetical) → R_s ≈ 2.95 km. • Typical stellar black hole (10 M☉) → R_s ≈ 30 km. • Intermediate black hole (10,000 M☉) → R_s ≈ 30,000 km (1/7 Earth's radius). • Sagittarius A* (4.3 × 10⁶ M☉) → R_s ≈ 1.27 × 10⁷ km (~17 R☉). • M87* (6.5 × 10⁹ M☉) → R_s ≈ 1.9 × 10¹⁰ km (~120 AU).

For rotating black holes (Kerr metric), the causal boundary splits into: (a) the outer horizon, where R = R_s for a non-rotating case, shrunk in Kerr, (b) the inner horizon, (c) the ergosphere — zone where spacetime is dragged. Most astrophysical black holes rotate ('spin' a ≈ 0.5-0.998), but R_s remains a good approximation within a factor of 2.

A horizon's area can never decrease (second law of black hole mechanics, Hawking 1971). It is a form of cosmic entropy.

Types of causal boundaries

'Event horizon' covers several concepts in general relativity.

Schwarzschild horizon. Non-rotating, uncharged black hole — the simplest case. Spherical boundary of radius R_s = 2GM/c². The one most often pictured.

Kerr horizon. Rotating black hole. No longer spherical but flattened at the poles, accompanied by an outer ergosphere where frame dragging is so strong that no object can remain stationary. Real stellar collapse produces mostly Kerr black holes.

Reissner-Nordström horizon. Electrically charged black hole. Theoretical case — astrophysical black holes don't retain significant net charge (rapidly neutralized by accretion).

Apparent horizon vs event horizon. Relativistic subtlety: the apparent horizon is the surface where light rays stop escaping at a given instant. The event horizon is defined globally by the set of trajectories that will never reach infinity. In a static spacetime they coincide. During collapse or black hole mergers, they differ.

Cosmological horizon. Large-scale analog: the maximum distance from which a signal can reach us given the accelerating expansion of the Universe. Not a black hole, but the mathematical notion is close.

Rindler horizon. For a uniformly accelerating observer in flat spacetime — a notion that inspired the discovery of Hawking radiation via the analogous Unruh effect.

How do we observe a horizon?

You never see the horizon itself (invisible by definition), but you can image its shadow — the dark silhouette projected onto the luminous matter orbiting around it.

Direct imaging with EHT. On April 10, 2019, the Event Horizon Telescope collaboration published the first direct image of a black hole horizon: M87*, at the center of galaxy M87 (Virgo Cluster, 55 million ly away). The image shows a luminous ring of hot plasma (~10⁹ K) around a dark spot of ~42 microarcseconds, corresponding to ~2.6 × R_s — the predicted 'shadow'. On May 12, 2022, the same collaboration imaged Sagittarius A*'s horizon at the center of the Milky Way. EHT combines 8 radio telescopes across the globe in Very Long Baseline Interferometry (VLBI) at 230 GHz.

Dynamical detection. Orbits of S-stars near the galactic center (Genzel, Ghez — 2020 Nobel Prize) confirmed that 4 × 10⁶ M☉ fit within a region smaller than Mercury's orbit around the Sun. This is consistent with an event horizon and incompatible with any configuration of visible matter.

Gravitational waves. The waveform produced during a black hole merger (LIGO-Virgo-KAGRA, ~100 detections since 2015) crucially depends on the presence of a horizon. The 'ringdown' phase corresponds to the vibrations of the newly formed horizon. No deviation from the Kerr model has been detected.

Absence of surface emission. If the Galactic Center held a material surface (even exotic) instead of a horizon, accreting matter should radiate upon impact. The absence of such emission is strong evidence for a genuine horizon at Sgr A*.

What about amateur astronomy? The horizon is unreachable even for the largest optical telescopes. But you can point at the regions where they hide: M87 (Virgo Cluster, magnitude 8.6) and the galactic center (Sagittarius), via our sky map tool.

Not to be confused with

The horizon is often conflated with other relativistic concepts.

Singularity. The singularity is the central point of a black hole, where general relativity predicts infinite density. The horizon is NOT the singularity: it sits at R_s from the center, far outside. The singularity is hidden behind the horizon (Penrose's cosmic censorship conjecture).

Black hole. The black hole is the entire object (horizon + interior). The horizon is only its visible outer boundary. A black hole has no 'physical size' in the classical sense — one can only point to where its horizon begins.

Black hole shadow. The image EHT released shows the shadow, not the horizon itself. The shadow is larger than the horizon (by a factor of ~2.6) because light bends in the strong gravitational field — an extreme gravitational lens.

Photon sphere. Surface at r = 1.5 × R_s where light can orbit circularly around the black hole. It produces the bright ring visible in the EHT image. It sits OUTSIDE the horizon, not at it.

Ergosphere (Kerr). Zone around the horizon where spacetime is dragged by the black hole's rotation, preventing any object from staying still (even at the speed of light). It exists FOR rotating black holes and wraps around the horizon without being identical to it.

Cosmological horizon. Boundary beyond which light no longer has time to reach us given cosmic expansion. Not a black hole — the opposite effect (accelerated expansion instead of gravitational attraction).