Black Holes: From A to Z

1. What is a black hole?

A black hole is a region of spacetime where gravity is so strong that nothing, not even light, can escape once it crosses a boundary called the event horizon. It is not a hole in the sense of an empty opening, and it is not a cosmic vacuum cleaner. It is a concentration of mass, so dense that the escape speed at its edge equals the speed of light, about 299,792 km/s.

Black holes are a direct prediction of Einstein's general theory of relativity (1915), which describes gravity as the curvature of spacetime produced by mass and energy. When enough mass is packed into a small enough volume, spacetime curves so strongly that every future path inside the horizon leads inward, toward the centre.

Escape velocity: the intuition

To leave a planet you need to move faster than its escape velocity: about 11.2 km/s for Earth, 617 km/s at the Sun's surface. Compress the same mass into a smaller sphere and the escape velocity at its surface rises. A black hole is what you get when that speed reaches 299,792 km/s. Newtonian physics happens to give the same horizon radius, but only relativity explains what happens to time, light and space there.

Why we cannot see them directly

Light from inside the horizon can never reach us, so the hole itself emits nothing (apart from extremely faint Hawking radiation). We detect black holes by what they do to their surroundings: heating gas, bending light, pulling on stars and shaking spacetime.

Average density falls as mass rises: a billion-solar-mass black hole has an average density lower than water. The extreme density is at the singularity, not spread through the horizon's volume.

2. Anatomy of a black hole

Singularity

At the centre, classical general relativity predicts a point (or, for rotating holes, a ring) of infinite density where known physics breaks down. Most physicists believe a theory of quantum gravity will replace this prediction with something finite.

Event horizon

The one-way surface of no return. It is not a material surface. An astronaut crossing a large black hole's horizon would notice nothing special locally, yet could never send a signal back out.

Photon sphere

At 1.5 r_s (non-rotating case), light can orbit the hole on unstable circular paths. This produces the bright ring seen in images from the Event Horizon Telescope.

ISCO

The innermost stable circular orbit, at 3 r_s for a non-rotating hole. Matter inside it plunges rapidly inward. Spin pulls this radius closer for prograde orbits.

Accretion disk and jets

Gas spiralling in forms a disk that heats to millions of degrees through friction and magnetic turbulence, shining brightly in X-rays. Magnetic fields can launch narrow jets of plasma at nearly light speed, a process described by Blandford and Znajek (1977).

Ergosphere

A rotating (Kerr) black hole drags spacetime around with it. Inside the ergosphere nothing can stand still relative to distant stars, and energy can in principle be extracted (the Penrose process).

3. History: how humans discovered black holes

The story runs over more than two centuries, from a speculative thought experiment to a photograph.

Newtonian "dark stars" (1783–1796)

English clergyman John Michell reasoned in 1783 that a star massive enough would have an escape velocity exceeding the speed of light, making it invisible. In 1796 the French mathematician Pierre-Simon Laplace independently made a similar argument. Light was then thought of as particles, so the idea was fairly natural, and it was later forgotten when wave theory of light took over.

Relativity and the first solution (1915–1916)

Einstein published general relativity in November 1915. Within weeks, Karl Schwarzschild, serving on the Russian front, found the exact solution for the spacetime around a spherical mass. It contained a radius at which the equations seemed to misbehave. Einstein himself doubted such objects could physically exist.

Stellar death and collapse (1930–1939)

In 1930 Subrahmanyan Chandrasekhar calculated that a white dwarf heavier than about 1.4 solar masses cannot support itself against gravity. Arthur Eddington resisted the conclusion, but it proved correct (Chandrasekhar shared the 1983 Nobel Prize). In 1939 J. Robert Oppenheimer and Hartland Snyder showed that a sufficiently massive star would collapse indefinitely, producing what we now call a black hole.

The golden age (1958–1975)

David Finkelstein (1958) clarified that the horizon is a one-way membrane rather than a true singularity. Roy Kerr found the solution for rotating black holes in 1963. In the same year Maarten Schmidt identified quasars as extremely distant, immensely luminous objects, soon explained as supermassive black holes feeding on gas. Roger Penrose proved in 1965 that singularities are an inevitable result of collapse. The name "black hole" was popularised by John Archibald Wheeler in 1967. In 1964 X-ray detectors on rockets found Cygnus X-1, and by 1971 it became the first strong stellar black hole candidate in a binary system. In 1971 Hawking proved the area theorem, and in 1972 Jacob Bekenstein proposed that black holes have entropy.

Quantum twist (1974)

Stephen Hawking showed that quantum effects near the horizon make black holes emit a faint thermal glow, so they slowly lose mass. This tied together gravity, thermodynamics and quantum theory, and created the information paradox.

Observational era (1990s–present)

Astronomers tracked stars orbiting an invisible, compact object at the Milky Way's centre, Sagittarius A*. Teams led by Reinhard Genzel and Andrea Ghez measured the orbits for decades. On 14 September 2015 LIGO detected gravitational waves from two merging black holes (GW150914), announced in February 2016. In April 2019 the Event Horizon Telescope released the first image of a black hole's shadow, in galaxy M87. In May 2022 it released the image of Sagittarius A*.

Nobel Prizes marked this progress: Physics 2017 (Weiss, Barish, Thorne, for LIGO) and Physics 2020 (Penrose for the theory; Genzel and Ghez for the galactic-centre object).

Why it took so long

Three obstacles delayed acceptance. The mathematics was confusing: the Schwarzschild solution looks singular at the horizon, and only in 1958 (Finkelstein) was this shown to be a coordinate artefact. Authority also mattered: Einstein argued in 1939 that such objects could not form, and Eddington dismissed Chandrasekhar's limit. And technology: black holes are dark, so astronomy needed X-ray satellites, radio interferometry and laser detectors to see their effects.

Cygnus X-1 and a famous bet

Cygnus X-1 is a bright X-ray source about 7,200 light-years away, orbiting a blue supergiant. The star's orbit implied an unseen companion too heavy to be a neutron star (current estimate about 21 M☉). In 1974 Stephen Hawking bet Kip Thorne that it was not a black hole, as a kind of insurance, and conceded in 1990.

Quasars and galactic engines

When 3C 273 was found to be billions of light-years away yet outshining whole galaxies, astronomers needed a compact power source. Donald Lynden-Bell proposed in 1969 that gas falling onto massive black holes could release a large fraction of its rest-mass energy (up to tens of percent, versus 0.7% for hydrogen fusion). Today almost every large galaxy is thought to host a supermassive black hole; quasars are phases of heavy feeding.

Mapping the centre of the Milky Way

Using infrared telescopes (Keck in Hawaii, ESO's telescopes in Chile), the Ghez and Genzel teams tracked individual stars near Sgr A* through the 1990s and 2000s. The star S2 orbits every ~16 years, passing within ~120 times the Earth–Sun distance at about 3% of light speed. Its orbit requires roughly 4 million solar masses inside a region smaller than our Solar System. Observations of S2's closest approaches in 2018 and later confirmed gravitational redshift and relativistic orbital precession.

The thermodynamic era

In the early 1970s Bardeen, Carter and Hawking derived four laws of black hole mechanics that mirror thermodynamics (see Section 8). Bekenstein's claim that horizon area is entropy was at first resisted by Hawking, until his 1974 calculation vindicated it.

4. How black holes form

Stars shine by fusing light elements. Massive stars proceed from hydrogen to helium, carbon, oxygen, and onwards until their cores are iron, which cannot release energy through fusion. With no outward pressure, the core collapses in under a second. If what remains exceeds roughly 2 to 3 solar masses (the Tolman–Oppenheimer–Volkoff limit, whose exact value is uncertain), neutron degeneracy pressure fails and a black hole forms. Some massive stars may collapse directly without a bright supernova.

Other routes exist: mergers of neutron stars or black holes, collapse of dense gas clouds in the early universe, and the growth of seeds through accretion and mergers over billions of years. The origin of supermassive black holes is still an active research topic, especially since the James Webb Space Telescope has found surprisingly massive ones very early in cosmic history.

Stage by stage: the death of a massive star

Heavier fuels burn hotter and far faster. Once the iron core exceeds roughly the Chandrasekhar mass, electrons are squeezed into protons, forming neutrons and releasing neutrinos that drain pressure. The core falls inward at a substantial fraction of light speed. If the bounce and neutrino heating succeed, the outer layers explode as a supernova and a neutron star remains. If not, the remnant becomes a black hole. Some stars may collapse with no bright explosion at all ("failed supernova"); the star N6946-BH1, which faded from view, is a candidate.

The pair-instability gap

Very massive helium cores (roughly 65 to 130 M☉) are expected to explode completely, leaving no black hole, so models predict a gap in remnant masses between about 50 and 130 M☉. Gravitational-wave detections within this range, such as the ~85 M☉ component of GW190521, challenge the models and suggest repeated mergers or other pathways.

Seeds of supermassive black holes

Quasars appear when the universe was under a billion years old, with masses near a billion suns. Steady growth is limited by the Eddington limit, where radiation pressure from infalling gas balances gravity (about 1.3×10³¹ W per solar mass). Two main scenarios exist:

• Light seeds: remnants of the first stars (~10 to 100 M☉) that grow rapidly, perhaps with super-Eddington episodes.
• Heavy seeds: direct collapse of giant gas clouds forming 10,000 to 100,000 M☉ black holes without a star stage.

JWST and Chandra found UHZ1, a black hole of tens of millions of solar masses seen about 470 million years after the Big Bang, which favours heavy seeds. JWST has found many other unexpectedly early active nuclei.

5. Types of black holes

By properties

Theory says a black hole is described entirely by three numbers: mass, spin and electric charge (the "no-hair theorem"). That gives four classical families: Schwarzschild (no spin, no charge), Kerr (spinning), Reissner–Nordström (charged) and Kerr–Newman (both). Real black holes are expected to be spinning and essentially neutral.

Intermediate-mass black holes: the missing link

Between about 100 and 100,000 solar masses, evidence is scarce. Candidates include HLX-1 (a bright X-ray source in galaxy ESO 243-49, possibly ~20,000 M☉) and a 2024 study of stellar motions in the globular cluster Omega Centauri, which inferred a central black hole of at least ~8,000 M☉. Gravitational waves from GW190521 (remnant ~142 M☉) also fall in this regime.

Primordial black holes

In the early 1970s Stephen Hawking and Bernard Carr proposed that density fluctuations in the first moments of the universe could create black holes of almost any mass. They are a dark matter candidate, but microlensing, cosmic microwave background and evaporation constraints rule out most mass ranges as the full explanation. Narrow windows remain.

Spin matters

Spin is expressed as a number from 0 to 1 (maximal). Fast spin shrinks the ISCO, so infalling matter radiates more efficiently: up to ~42% of rest-mass energy in the extreme case versus ~5.7% with no spin. Spin also affects jet power. It is measured from X-ray spectra (iron-line shapes) and gravitational-wave signals.

6. The strange physics

Time dilation

Time runs slower in strong gravity. To a distant observer, an object falling toward the horizon appears to slow down and fade, never quite crossing. The falling object itself experiences crossing in finite time.

Spaghettification

Tidal forces stretch an infalling body. For a stellar-mass hole the stretching becomes lethal well outside the horizon; for a supermassive one, a person could cross the horizon before tides become severe.

Gravitational lensing

Light bends around massive objects. Near a black hole this creates distorted, multiple images and the glowing ring seen by the EHT.

Frame dragging

Spinning masses twist surrounding spacetime. Close to a rapidly spinning black hole, nothing can avoid being swept along.

Tidal disruption events

When a star wanders too close, it is torn apart, and a portion of its gas forms a short-lived, extremely bright flare.

Thermodynamics

Black hole area never decreases in classical theory, which mirrors entropy. Bekenstein and Hawking showed the entropy is proportional to horizon area (S = k A / 4ℓ_P²), not volume, a result that hints at deep links between gravity and information.

A journey to a black hole

The maximum proper time from horizon to singularity is about πGM/c³: roughly 0.00015 seconds for a 10 M☉ hole, about a minute for Sgr A*, and around a day for M87*. Tidal forces determine whether the traveller is destroyed first, which happens outside the horizon for small holes.

Extracting energy: Penrose and Blandford–Znajek

Roger Penrose showed in 1969 that an object entering the ergosphere and splitting, with one piece falling in on a counter-rotating orbit, lets the other escape with more energy than the original, at the cost of the hole's spin. The electromagnetic version, Blandford–Znajek, uses magnetic fields threading the horizon to tap rotational energy and drive jets. The jet of M87 is consistent with it.

Merger: inspiral, merger, ringdown

Two black holes orbit, losing energy as gravitational waves, so they spiral together faster (inspiral). At merger the signal peaks: GW150914 briefly radiated about 3.6×10⁴⁹ W, more than the combined light output of all the stars in the observable universe. The remnant then rings like a bell (ringdown) and settles into a Kerr black hole. Ringdown frequencies test the no-hair theorem.

7. How we detect something invisible

LIGO has since detected hundreds of mergers. GW150914 involved holes of about 36 and 29 solar masses merging into one of about 62, with roughly three solar masses radiated away as gravitational wave energy. In 2025 an event named GW231123 revealed a merger producing a remnant of about 225 solar masses, among the heaviest observed through gravitational waves. Pulsar timing arrays (NANOGrav and partners, 2023) found evidence of a background hum likely from supermassive black hole pairs.

The EHT image is a ring of glowing gas around a dark centre. The dark area is the "shadow," about 2.5 times larger than the horizon, due to light bending. It matches the predictions of general relativity.

Inside LIGO and Virgo

LIGO has two L-shaped detectors, in Hanford (Washington) and Livingston (Louisiana), each with 4 km arms. Lasers bounce between mirrors; a passing gravitational wave changes the arm lengths by about 10^-18 m, roughly a thousandth of a proton's width. Two sites help locate sources and reject local noise. Virgo (Italy) and KAGRA (Japan) join the network, which has catalogued hundreds of merger candidates. Planned observatories include Cosmic Explorer, the Einstein Telescope and the space-based LISA, expected in the 2030s, which will detect supermassive black hole mergers.

Inside the Event Horizon Telescope

The EHT links radio dishes across the globe at a wavelength of 1.3 mm to act as an Earth-sized telescope. M87* is ~55 million light-years away and its ring is only ~42 microarcseconds across, like spotting a doughnut on the Moon. Atomic clocks synchronise each station, and the petabytes of data were shipped to processing centres. Sgr A* is harder because its gas swirls in minutes, so the image is an average. Later polarisation maps of both holes show strong magnetic fields spiralling around them.

Dormant black holes

Gaia astrometry has found Gaia BH1 (~9.6 M☉), BH2 and BH3 (~33 M☉, announced 2024): quiet black holes orbiting ordinary stars without an X-ray glow. Many such holes likely exist; the Milky Way may hold tens of millions.

8. Hawking radiation and the end of a black hole

Quantum field theory predicts that near the horizon, pairs of virtual particles can be separated so that one escapes while the other falls in. The result looks like thermal radiation with temperature T = ħc³ / (8πGMk_B). A solar-mass black hole has a temperature of only about 60 nanokelvin, far colder than the cosmic microwave background (2.7 K), so today it absorbs more than it emits.

Only when the universe cools much further would stellar black holes begin to evaporate, taking around 10⁶⁷ years for a solar-mass hole and up to 10¹⁰⁰ years for the biggest. Small primordial black holes would evaporate far faster, finishing with a burst of high-energy particles. No such burst has been confirmed. Hawking radiation itself has not been directly observed, although laboratory analogues in fluids and optics support the idea.

The four laws of black hole mechanics

The Bekenstein–Hawking formula gives a solar-mass black hole an entropy of ~10⁷⁷ k_B, about 20 orders of magnitude more than the Sun's own. Black holes are the most entropic objects for their size. Gravitational-wave data have also been used to test the area theorem, finding the final horizon area exceeds the sum of the initial areas.

Why does it radiate?

The popular picture of particle pairs is a simplification. In Hawking's calculation, the vacuum state defined by a freely falling observer looks thermal to an observer outside. A close cousin is the Unruh effect: an accelerating observer sees warm radiation in empty space. Analogue experiments with sound waves in flowing Bose–Einstein condensates (Jeff Steinhauer) show correlated pairs and a thermal spectrum consistent with this idea.

9. Open puzzles

Black holes are also cosmic laboratories. They influence galaxy growth, since energy from jets can heat gas and shut down star formation (feedback). Black hole mass correlates with the motion of stars in its host galaxy bulge, called the M–σ relation.

The information paradox in more depth

Suppose a book falls in. Hawking's calculation says the outgoing radiation depends only on mass, spin and charge, so the book's contents seem lost, which would violate unitarity, a core rule of quantum mechanics. Proposed resolutions: information escapes subtly in correlations within the radiation; it stays in a remnant; unitarity fails; or the horizon is not smooth (firewall). Don Page showed that if information is preserved, the entanglement entropy of the radiation should rise and then fall at the "Page time", about halfway through evaporation. In 2019, calculations using quantum extremal surfaces ("islands") reproduced this Page curve, a major step, though in simplified models.

Roads to quantum gravity

• String theory: Strominger and Vafa (1996) counted microstates of certain black holes and matched the Bekenstein–Hawking entropy.
• Loop quantum gravity: suggests the singularity is replaced by a bounce, possibly a transition to a white hole.
• Fuzzballs: propose the interior is replaced by a quantum structure with no horizon.
• ER=EPR: Maldacena and Susskind suggest entangled particles are linked by microscopic wormholes.

What comes next

Upcoming tests include the next-generation EHT for sharper images and movies of the horizon, LISA for supermassive mergers, the Vera C. Rubin Observatory for tidal disruption events, and growing gravitational-wave catalogues that will test whether remnants behave exactly as Kerr black holes should.

10. Common myths

• "Black holes suck everything in." Far from the hole, gravity is the same as any object of equal mass. If the Sun became a black hole of one solar mass, Earth would keep orbiting normally (though dark and cold).
• "They are holes." They are regions of extreme mass and curved spacetime.
• "Nothing inside can be known." Observers outside can only measure mass, spin and charge, but the interior is described well by general relativity until the singularity.
• "Wormholes are proven." Mathematical solutions exist, but no evidence of real wormholes or white holes has been found.
• "Black holes are black." The hole is dark, but its surroundings are among the brightest objects in the universe.

11. A–Z glossary

Conclusion

In under a century, black holes moved from mathematical curiosity to the best-documented extreme objects in nature. We have weighed them, listened to them collide, and photographed their shadows. Yet the singularity, the fate of information, and the origin of the biggest giants remain unsolved. Each is a doorway toward a deeper theory uniting gravity and quantum physics.

Figures are approximate and reflect published estimates as of 2025; values for specific objects are revised as measurements improve.