Black Holes
A black hole is a region of spacetime where gravity is so strong that nothing — not even light — can escape. They are not holes in space. They are objects: the most gravitationally extreme objects in the observable universe, and the places where general relativity breaks down.
1. How Black Holes Form
In a normal star, radiation pressure from nuclear fusion pushes outward, balancing the inward pull of gravity. Stars exist in this uneasy equilibrium for millions to billions of years.
When fuel runs out, the outward pressure vanishes. For stars roughly 8–20 solar masses, the iron core collapses in under a second. The collapse halts at nuclear density as the neutron star "bounces," launching a shockwave that destroys the outer star: a core-collapse supernova. What remains is a neutron star or, if the remnant core exceeds ~3 M☉ (the Tolman–Oppenheimer–Volkoff limit), a black hole.
Supermassive black holes (millions to billions of M☉) form from early-universe gas clouds and grow by accretion and galaxy mergers over cosmic time. Their formation is still an active research area.
2. The Schwarzschild Radius
Karl Schwarzschild found the first exact solution to Einstein's field equations in 1916 — just weeks after Einstein published general relativity. For any mass M, there is a critical radius below which light cannot escape:
G = 6.674 × 10⁻¹¹ N·m²/kg²
c = 3 × 10⁸ m/s
Some examples:
The Sun is nowhere near becoming a black hole — it's 10 orders of magnitude too large for its mass, and it will die as a white dwarf.
3. Anatomy of a Black Hole
- Singularity: The mathematical centre where density is infinite and general relativity breaks down. Not a "point" in space — a moment in time you inevitably fall toward once inside the horizon.
- Event horizon: The spherical surface at radius r_s. Not a physical surface — you'd feel nothing special crossing it. But it's a one-way membrane: no signal or matter can return.
- Photon sphere: At 1.5 r_s, photons can orbit in circles — but the orbit is unstable. This is what creates the glowing ring in EHT images.
- Innermost stable circular orbit (ISCO): At 3 r_s for a non-rotating black hole (6 r_s in conventional units). Accretion disks end here — inside, matter spirals inward rapidly.
- Accretion disk: Spiralling infalling matter forms a superheated disk that radiates X-rays. The brightest X-ray sources in the sky are accreting black holes.
4. Orbits and the Photon Sphere
General relativity predicts that even light curves in a gravitational field. Near a black hole, the deflection is extreme. At exactly r = 1.5 r_s, a photon can circle the black hole indefinitely — but the orbit is unstable. A tiny perturbation sends it either spiralling in or flying out.
ISCO (stable orbits start here): r_ISCO = 3 · r_s
Shadow diameter observed: ≈ 5.2 · r_s
The gravitational time dilation near a black hole is enormous. An observer far away sees a clock hovering just outside the event horizon tick infinitely slowly. From the infalling observer's perspective, they cross the horizon in finite proper time — they just can't tell anyone what they found inside.
5. Hawking Radiation
Stephen Hawking showed in 1974 that black holes are not entirely black. Quantum field theory in curved spacetime predicts that black holes emit thermal radiation with a temperature:
For a solar-mass black hole: T_H ≈ 6 × 10⁻⁸ K — essentially zero.
Smaller BH → higher T → faster evaporation.
As the black hole radiates, it loses mass. The evaporation time scales as M³. A solar-mass black hole would take ~10⁶⁷ years to evaporate — far longer than the age of the universe. Only primordial mini-black holes (if they exist) could finish evaporating now.
6. The EHT Image
In April 2019, the Event Horizon Telescope collaboration released the first image of a black hole: the supermassive black hole M87*, at the centre of the galaxy Messier 87, 55 million light-years away, with a mass of 6.5 × 10⁹ M☉.
The EHT is not a single telescope — it's a planet-scale interferometer: 8 radio telescopes on 4 continents observing at 1.3 mm wavelength, combined via very long baseline interferometry (VLBI). The angular resolution is 20 microarcseconds — enough to read a newspaper in Los Angeles from New York.
The image shows a bright ring (~42 μas diameter, matching 5.2 r_s) and a darker central shadow. The brighter southern arc is where infalling matter's Doppler boost brightens the approaching side. In 2022, EHT imaged Sgr A* — the black hole at the Milky Way centre, 4 million M☉ and 27,000 light-years away.
7. Types of Black Holes
- Stellar black holes (3–100 M☉): remnants of massive stars. ~10⁹ estimated in the Milky Way.
- Intermediate mass (10²–10⁵ M☉): found in dense star clusters; relatively rare candidates observed.
- Supermassive (10⁶–10¹⁰ M☉): found at centres of almost all large galaxies. Sgr A* (4×10⁶ M☉) at Milky Way centre; Ton 618 at 6.6×10¹⁰ M☉ — the largest known.
- Primordial: Hypothetical black holes formed from density fluctuations in the early universe. If small enough, they would be evaporating today and could explain some dark matter.
- Rotating (Kerr) black holes: Real astrophysical black holes all spin. A Kerr metric replaces the simple Schwarzschild solution; the ergosphere outside the horizon allows energy extraction (Penrose process).