Karl Schwarzschild, a German astrophysicist serving on the Russian front in World War I, solved Einstein's general-relativity field equations for the simplest case — the spacetime around a non-rotating point mass — and sent the solution to Einstein in January 1916. He died of pemphigus, a rare autoimmune skin disease, four months later, age 42. The Schwarzschild solution contained a feature that took four decades to take seriously: at a critical radius r_s = 2GM/c², the metric became singular and light could not escape. The phenomenon was treated as a mathematical curiosity until X-ray astronomy in the 1960s found binaries that could only be explained by compact, dark, gravitationally collapsed objects. Black holes are real. The 2019 Event Horizon Telescope image of M87's central black hole — a luminous ring around a darkness the size of our solar system — was the first direct visual confirmation.
A black hole is a region of spacetime where gravity is so strong that nothing — not even light — can escape. The boundary is the event horizon: matter and information can fall in, but nothing can come out. For a non-rotating black hole of mass M, the horizon is at the Schwarzschild radius r_s = 2GM/c² — 3 km for one solar mass, 9 mm for the Earth's. Inside the horizon, all timelike paths lead to a central singularity of formally infinite curvature, where general relativity itself breaks down. The no-hair theorem (Israel, Carter, Hawking, 1960s–70s) states that a stationary black hole is completely characterized by just three numbers — mass, electric charge, and angular momentum. The Kerr solution (1963) generalizes Schwarzschild's to rotating black holes; Kerr-Newman to charged-rotating ones. Stellar-mass black holes form from the gravitational collapse of massive star cores when fusion can no longer support them; supermassive black holes (millions to billions of solar masses) reside at the centers of nearly all galaxies, including the Milky Way's Sgr A* (~4 × 10⁶ solar masses, confirmed by 2020 Nobel laureates Genzel and Ghez). Hawking radiation (1974): black holes are not perfectly black — quantum effects at the horizon cause them to emit thermal radiation at T = ℏc³/(8πk_BGM), inversely proportional to mass. The information paradox — Hawking radiation appears thermal and apparently carries no information, but unitary quantum mechanics requires information to be conserved — is a central open problem in quantum gravity. Gravitational waves from binary black-hole mergers, first detected by LIGO in 2015, are now routinely observed and provide direct experimental access to strong-field general relativity.
Gravitational-wave astronomy (LIGO/Virgo/KAGRA, with future LISA) has detected over a hundred black-hole mergers and constrained black-hole populations across the universe. The Event Horizon Telescope has imaged both M87's black hole (2019) and Sgr A* (2022), with a Sgr A* movie expected before 2030. Black-hole thermodynamics has emerged as a precision frontier of theoretical physics: the Bekenstein-Hawking entropy (S = A/4 in Planck units) constrains every quantum-gravity proposal. Holography (the AdS/CFT correspondence) emerged from black-hole physics and is now a major theoretical framework, used in condensed-matter and gauge-theory work. The firewall paradox, the fuzzball proposal, and the ER=EPR conjecture are open foundational problems. Black holes are simultaneously the simplest and the most extreme objects in physics.