General relativity

General relativity is built on the equivalence principle, which states that gravitational and inertial mass are equivalent, and that locally, a gravitational field is indistinguishable from an accelerated frame of reference.¹ This led Einstein to propose that gravity is a manifestation of spacetime curvature: mass and energy tell spacetime how to curve, and the curved spacetime tells matter how to move.² The theory is described by the Einstein field equations, which relate the geometry of spacetime (the Einstein tensor) to the stress-energy tensor.³

The three classical tests of general relativity were proposed by Einstein in 1916: the precession of the perihelion of Mercury, the deflection of light by the Sun, and the gravitational redshift of light.⁴ The perihelion shift of Mercury had been observed as an anomaly of 43 arcseconds per century, which general relativity explained exactly.⁵ The deflection of starlight during a solar eclipse was first measured by Arthur Eddington in 1919, confirming the theory and making Einstein famous.⁶ The gravitational redshift was later confirmed by the Pound–Rebka experiment in 1959.⁷

Modern tests include the time delay of radar signals (Shapiro effect), the geodetic effect and frame-dragging measured by Gravity Probe B, and the direct detection of gravitational waves by LIGO in 2015.⁸ General relativity is also crucial for the Global Positioning System (GPS), which requires corrections for both special and general relativistic time dilation to maintain accuracy.⁹ The theory also predicts black holes, which have been imaged by the Event Horizon Telescope.¹⁰

Beyond the well-known tests, general relativity has many subtle and surprising aspects. For example, the theory predicts the existence of gravitational time dilation, which causes clocks to run slower in stronger gravitational fields, a phenomenon that must be accounted for in satellite navigation.⁹ Another lesser-known consequence is the Lense–Thirring effect, or frame-dragging, where a rotating mass drags spacetime around it, an effect measured by the Gravity Probe B satellite.⁸ General relativity also leads to the concept of gravitational lensing, which has become a powerful tool in astronomy for studying dark matter and distant galaxies.¹¹ Additionally, the theory allows for the possibility of wormholes and closed timelike curves, though these remain speculative.¹² The mathematics of general relativity also inspired the development of differential geometry and has applications in other fields such as cosmology and the study of the early universe.¹³

Equivalence principle

The principle that gravitational and inertial mass are equivalent, and that a gravitational field is locally indistinguishable from an accelerated frame.

Spacetime

The four-dimensional continuum of space and time, which is curved by mass and energy in general relativity.

Einstein field equations

The set of equations in general relativity that relate the curvature of spacetime to the distribution of matter and energy.

Gravitational waves

Ripples in spacetime caused by accelerating massive objects, predicted by general relativity and directly detected in 2015.

Black hole

A region of spacetime where gravity is so strong that nothing, not even light, can escape.