Black Hole
A black hole is a region of spacetime where gravity is so extreme that nothing — not even light or other electromagnetic radiation — can escape once past the event horizon, the point of no return. Black holes form when massive stars collapse at the end of their lives (stellar black holes), or may grow supermassive through accretion and mergers in galactic centres. The boundary of a black hole is described by the Schwarzschild radius (for non-rotating black holes), and their properties are encapsulated by the "no-hair theorem": a black hole is fully described by only three parameters — mass, charge, and spin.
Key Formula
r_s = 2GM / c²
LaTeX: r_s = \frac{2GM}{c^2}
| Symbol | Meaning | Unit |
|---|---|---|
| r_s | Schwarzschild radius (event horizon radius) | meter (m) |
| G | Gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²) | N·m²/kg² |
| M | Mass of the black hole | kilogram (kg) |
| c | Speed of light (3 × 10⁸ m/s) | m/s |
Worked Example
Problem
Calculate the Schwarzschild radius of the Sun (mass M☉ = 1.989 × 10³⁰ kg). If the Sun were compressed to this size, it would become a black hole.
Solution
Step 1: Write down the Schwarzschild radius formula: r_s = 2GM / c². Step 2: Substitute values: r_s = 2 × (6.674 × 10⁻¹¹) × (1.989 × 10³⁰) / (3 × 10⁸)². Step 3: Numerator = 2 × 6.674 × 10⁻¹¹ × 1.989 × 10³⁰ = 2.655 × 10²⁰. Step 4: Denominator = (3 × 10⁸)² = 9 × 10¹⁶. Step 5: r_s = 2.655 × 10²⁰ / 9 × 10¹⁶ = 2,950 m ≈ 2.95 km.
Answer
The Sun's Schwarzschild radius ≈ 2.95 km — compress the entire Sun into a sphere of 3 km radius to form a black hole
Types and Properties of Black Holes
| Type | Mass Range | Formation | Example | Schwarzschild Radius |
|---|---|---|---|---|
| Stellar | 3–100 M☉ | Core collapse of massive star | Cygnus X-1 | 9–300 km |
| Intermediate | 100–10⁵ M☉ | Dense star cluster mergers | HLX-1 | 0.3–300 AU |
| Supermassive | 10⁶–10¹⁰ M☉ | Galactic centre growth | Sgr A* (4×10⁶ M☉) | 0.08–200 AU |
| Primordial (hypothetical) | 10⁻⁸ kg – M☉ | Early universe density fluctuations | Not yet confirmed | Sub-atomic – km |
| M87* (imaged 2019) | 6.5 × 10⁹ M☉ | Supermassive | First BH image (EHT) | ~130 AU |
| Sagittarius A* | 4 × 10⁶ M☉ | Milky Way galactic centre | Nearest SMBH | ~0.08 AU |
Interactive Tools
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Related Terms
General Relativity
General relativity is Albert Einstein's geometric theory of gravitation, published in 1915, which describes gravity not as a force but as the curvature of spacetime caused by mass and energy. Massive objects warp the fabric of spacetime, and other objects follow curved paths (geodesics) through this warped spacetime, which we perceive as gravitational attraction. The theory has been confirmed by numerous observations including gravitational lensing, gravitational redshift, the precession of Mercury's orbit, and the detection of gravitational waves.
Gravitational Waves
Gravitational waves are ripples in the fabric of spacetime generated by accelerating massive objects, predicted by Einstein's general theory of relativity in 1916 and directly detected for the first time by the LIGO collaboration on September 14, 2015 (event GW150914). These distortions propagate at the speed of light as transverse waves, alternately stretching and squeezing spacetime in perpendicular directions. The detection of gravitational waves opened an entirely new observational window on the universe, allowing astronomers to study events such as merging black holes and neutron stars that are otherwise invisible to electromagnetic telescopes.
Spacetime
Spacetime is the four-dimensional continuum that combines the three dimensions of space (x, y, z) with the one dimension of time (t) into a single mathematical framework, first described by Hermann Minkowski in 1908 based on Einstein's special relativity. In this framework, events are described by four coordinates, and the separation between events is measured by the spacetime interval, which remains invariant under Lorentz transformations. In general relativity, spacetime is not flat but can be curved by mass and energy, and this curvature is what we experience as gravity.
The term "black hole" was coined by physicist John Archibald Wheeler in a 1967 lecture at the NASA Goddard Institute, replacing earlier terms "frozen star" and "collapsed star." The concept dates to John Michell (1783) and Laplace (1796), who considered "dark stars" from which light could not escape using Newtonian mechanics.