Black Holes and Relativity

How Black Holes Form

Stellar-mass black holes form when massive stars exhaust their nuclear fuel and collapse under their own gravity. A star more than roughly 20 to 25 times the mass of the Sun (the exact threshold depends on the star composition and other factors) will, at the end of its life, undergo a catastrophic collapse that no known force can halt. The core compresses past the density of a neutron star, and the matter falls within its own Schwarzschild radius, forming an event horizon and becoming a black hole. The outer layers of the star may be blown away in a supernova explosion, or the entire star may collapse directly without an explosion (a process called direct collapse).

Supermassive black holes, with masses ranging from millions to billions of solar masses, reside at the centers of most large galaxies. The Milky Way harbors Sagittarius A*, a supermassive black hole with a mass of about 4 million solar masses. How supermassive black holes form is an active area of research. They may grow from stellar-mass seeds that accumulate matter over billions of years, or they may form through the direct collapse of massive gas clouds in the early universe, or through the merger of intermediate-mass black holes.

Intermediate-mass black holes, with masses between roughly 100 and 100,000 solar masses, have been harder to find, but gravitational wave observations have provided evidence for some. The GW190521 event detected by LIGO in 2019 involved the merger of two black holes with masses of about 85 and 66 solar masses, producing a remnant of about 142 solar masses, the first confirmed intermediate-mass black hole.

The Event Horizon

The defining feature of a black hole is its event horizon, a boundary in spacetime beyond which nothing can escape. The event horizon is not a physical surface or barrier. It is a mathematical boundary: the set of points from which outward-directed light rays can just barely fail to escape to infinity. Once you cross the event horizon, every possible path through spacetime, even paths at the speed of light, leads further inward.

For a non-rotating, uncharged black hole (described by the Schwarzschild solution), the event horizon is a sphere with radius r = 2GM/c², where G is the gravitational constant, M is the black hole mass, and c is the speed of light. For a black hole with the mass of the Sun, this radius is about 3 kilometers. For Sagittarius A* at 4 million solar masses, the event horizon radius is about 12 million kilometers, roughly 17 times the radius of the Sun.

An observer falling through the event horizon of a sufficiently large black hole would notice nothing unusual at the moment of crossing. The spacetime curvature at the event horizon of a supermassive black hole is actually quite gentle, far less than the curvature at the surface of a neutron star. It is only the global structure of spacetime that makes the horizon special: once inside, all worldlines lead to the singularity.

Singularities and the Limits of General Relativity

At the center of a black hole, according to general relativity, lies a singularity: a point (or ring, in the case of a rotating black hole) where the curvature of spacetime becomes infinite and the known laws of physics break down. The singularity is not a place in the ordinary sense. It is a boundary of spacetime where predictions can no longer be made.

Most physicists believe that the singularity is not a physical reality but a sign that general relativity is incomplete. At the extreme densities and curvatures near the singularity, quantum gravitational effects are expected to become important, preventing the formation of a true mathematical singularity. However, since we do not yet have a complete theory of quantum gravity, the actual nature of the black hole interior remains unknown.

Roger Penrose proved in 1965 that singularity formation is a generic feature of gravitational collapse in general relativity, not an artifact of the special symmetry of the Schwarzschild solution. This singularity theorem, combined with Stephen Hawking extensions to cosmological contexts, earned Penrose the 2020 Nobel Prize in Physics.

Observational Evidence

Black holes cannot be seen directly (by definition, they emit no light from within the event horizon), but they reveal themselves through their effects on nearby matter and spacetime. Gas falling toward a black hole forms an accretion disc that heats to millions of degrees and emits intense X-rays. Jets of relativistic particles are launched perpendicular to the disc in some systems. The orbital motions of stars near galactic centers reveal the mass of the central supermassive black hole.

In 2019, the Event Horizon Telescope (EHT) collaboration produced the first image of a black hole, capturing the shadow of the supermassive black hole in galaxy M87 (M87*). The image showed a bright ring of emission surrounding a dark central region, the shadow cast by the event horizon against the glowing background of the accretion flow. The size and shape of the shadow matched the predictions of general relativity for a black hole of 6.5 billion solar masses. In 2022, the EHT released an image of Sagittarius A*, confirming a similar shadow structure for our own galaxy central black hole.

Gravitational wave observations by LIGO and Virgo have provided yet another confirmation, detecting the signals from dozens of binary black hole mergers. These observations reveal the masses, spins, and distances of the merging black holes, and the waveforms match the predictions of numerical general relativity with remarkable precision.

Hawking Radiation and Black Hole Thermodynamics

In 1974, Stephen Hawking showed that black holes are not entirely black. Quantum mechanical effects near the event horizon cause black holes to emit thermal radiation, now called Hawking radiation, with a temperature inversely proportional to the black hole mass. For stellar-mass black holes, this temperature is negligibly small, far below the temperature of the cosmic microwave background. For a black hole with the mass of the Sun, the Hawking temperature is about 60 nanokelvin.

Hawking radiation implies that black holes slowly lose mass and energy over time, eventually evaporating completely. For stellar-mass and supermassive black holes, the evaporation time vastly exceeds the current age of the universe. However, the theoretical possibility of evaporation raises deep questions about information conservation. If a black hole evaporates completely, what happens to the information about everything that fell in? This black hole information paradox remains one of the most important open problems in theoretical physics.