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General relativity: gravity is curved spacetime
1915· Theory
ProvenTested many times; part of working physics.
Einstein's 1915 theory of gravity: mass and energy curve spacetime, and objects move along the straightest paths through that curved spacetime.
See it on the Science map →How it works
Newton said gravity is a force pulling across space. Einstein said there is no pull: the Sun dents spacetime, and Earth simply follows the straightest path available, which happens to loop around the Sun. Matter tells spacetime how to curve; spacetime tells matter how to move. The theory predicts bent light, slower clocks near mass, black holes, gravitational waves, and an expanding universe.
Why it matters
It is our theory of gravity, the universe's large-scale structure and its history. Black holes, the Big Bang model and GPS accuracy all depend on it.
Think of it like
Like a heavy ball on a trampoline: smaller balls roll toward it, not pulled by a rope, but following the slope it creates.
How we know
Mercury's orbit (1915), the 1919 eclipse, gravitational redshift (1959), the binary pulsar (1974), LIGO's gravitational waves (2015) and black hole images (2019) all match.
Still a mystery
It breaks down inside black holes and at the Big Bang, and clashes with quantum physics. Dark matter and dark energy may hint it is incomplete.
Connections (20)
▸Newton's law of gravity was replaced by General relativity: gravity is curved spacetimeProven
The relationship
Newton treated gravity as an instant force pulling across empty space. General relativity replaced that picture with curved spacetime, where changes travel at light speed. For weak gravity and slow speeds, Einstein's equations give back Newton's results almost exactly, so Newton remains a highly accurate approximation used for most engineering and spaceflight.
How the link was found
Einstein built general relativity from 1907 to 1915, deliberately requiring that it reproduce Newton's law in everyday conditions.
Why it's proven
General relativity matches Newton where Newton works, and beats it where Newton fails: Mercury's orbit, light bending, gravitational waves and clock rates.
Open questions and mysteries
Galaxy rotation speeds disagree with both theories unless unseen dark matter exists; a few physicists instead propose modifying gravity again.
▸Albert Einstein created General relativity: gravity is curved spacetimeProven
The relationship
Einstein spent eight years extending relativity to gravity. Starting from the equivalence principle, he learned new geometry from his friend Marcel Grossmann and made several false starts. In November 1915 he presented the final field equations, describing how mass and energy curve spacetime and how that curvature guides motion.
How the link was found
Einstein, 1907-1915, finishing in Berlin; presented the field equations to the Prussian Academy on 25 November 1915.
Why it's proven
It explained Mercury's orbit at once, and has passed every test since, from eclipses to black-hole images.
Open questions and mysteries
Hilbert derived the same equations almost simultaneously; priority was debated but historians generally credit Einstein with the theory.
▸Special relativity was extended to gravity in General relativity: gravity is curved spacetimeProven
The relationship
Special relativity covers flat spacetime without gravity. Einstein generalized it by letting spacetime curve. In any small, freely falling region, general relativity reduces to special relativity, so the earlier theory becomes a local special case.
How the link was found
Einstein, 1907-1915, recognizing that Newton's instant gravity clashed with the light-speed limit.
Why it's proven
Tests of both theories succeed, and general relativity reproduces special relativity wherever gravity is negligible.
Open questions and mysteries
Settled. The deeper puzzle is merging general relativity with quantum physics.
▸Equivalence principle: gravity = acceleration was the key insight for General relativity: gravity is curved spacetimeProven
The relationship
If gravity feels the same as acceleration, then gravity can be described by the shape of spacetime rather than as a force. Free fall becomes the natural, straight motion. Einstein turned this idea into a theory where mass curves spacetime and objects follow its curves.
How the link was found
Einstein's 1907 insight, developed into general relativity by 1915.
Why it's proven
The principle holds to about one part in a thousand trillion, and general relativity built on it passes every test.
Open questions and mysteries
Whether it holds for quantum systems at all scales is still being tested.
▸Curved (non-Euclidean) geometry provided the math for General relativity: gravity is curved spacetimeProven
The relationship
Einstein concluded that gravity is not a force but the curving of spacetime by mass and energy. Objects follow the straightest possible paths through that curved geometry. Describing curvature that varies from place to place, in four dimensions, required Riemann's geometry and the tensor calculus built on it.
How the link was found
Einstein's friend Marcel Grossmann pointed him to Riemannian geometry in 1912; Einstein completed general relativity in November 1915.
Why it's proven
Mercury's orbit (1915), starlight bending (1919 eclipse), GPS timing, and gravitational waves detected in 2015 all match the curved-geometry predictions.
Open questions and mysteries
At the centre of black holes and at the Big Bang, curvature becomes infinite and the geometry breaks down; a quantum theory of gravity is needed.
▸General relativity: gravity is curved spacetime explained Mercury's orbit puzzle solvedProven
The relationship
Curved spacetime near the Sun slightly changes Mercury's orbit, causing the closest-approach point to rotate a little extra each orbit. The calculated extra amount, 43 arcseconds per century, matched the long-known discrepancy with Newton's gravity.
How the link was found
Einstein calculated it in November 1915, just before finalizing his field equations.
Why it's proven
Modern radar ranging to Mercury confirms the shift to better than one percent.
Open questions and mysteries
Settled. Similar tests now probe stars orbiting the black hole at the galaxy's center.
▸General relativity: gravity is curved spacetime predicted 1919 eclipse: gravity bends lightProven
The relationship
Curved spacetime bends light passing near the Sun. General relativity predicted a shift of 1.75 arcseconds for starlight grazing the Sun, double the Newtonian estimate. A total eclipse allowed the shift to be measured.
How the link was found
Einstein predicted the full value in 1915; Eddington and Dyson organized the May 1919 expeditions.
Why it's proven
The 1919 results favored Einstein; later radio measurements confirmed the value to better than one percent.
Open questions and mysteries
Debate continues over how carefully the 1919 data were handled.
▸General relativity: gravity is curved spacetime predicts Gravitational lensingProven
The relationship
Any mass curves the spacetime around it, and light follows that curve. A galaxy or cluster sitting between us and a more distant source acts like a giant, imperfect lens, bending the background light into arcs, rings or several copies, and often magnifying it. How strongly the image is bent tells us how much mass the lens holds.
How the link was found
Einstein worked out lensing by single stars in 1936 but thought it unobservable. Fritz Zwicky argued in 1937 that whole galaxies would make visible lenses.
Why it's proven
Walsh, Carswell and Weymann found the first lensed quasar in 1979. Thousands of lensed systems are now known, and the bending matches general relativity.
Open questions and mysteries
Lensing surveys of how clumpy matter is come out slightly lower than predictions from the early universe; whether that is a measurement issue or new physics is open.
▸General relativity: gravity is curved spacetime predicted Gravitational waves (LIGO, 2015)Proven
The relationship
In general relativity, spacetime is not rigid; it can ripple. When heavy objects accelerate, especially two black holes or neutron stars spiraling together, they send out waves that travel at light speed and alternately stretch and squeeze distances. The waves carry energy away, so the orbiting pair slowly spirals inward until it merges.
How the link was found
Einstein predicted the waves in 1916. In 1936 he briefly argued they did not exist, then corrected himself. LIGO's direct detection came on 14 September 2015.
Why it's proven
The Hulse-Taylor binary pulsar's orbit, tracked from 1974, shrinks exactly as wave energy loss predicts. LIGO's signals match computer simulations of merging black holes.
Open questions and mysteries
Waves from the very early universe, and the low-frequency background hinted at by pulsar-timing arrays in 2023, are not yet fully understood.
▸General relativity: gravity is curved spacetime adds "gravity slows time" to Time dilation: moving clocks run slowProven
The relationship
Special relativity says moving clocks run slow. General relativity adds that clocks deeper in a gravitational field also run slow compared with clocks higher up. Light climbing out of a gravity well loses energy and shifts toward red. The two effects can add or partly cancel, as they do for satellites.
How the link was found
Einstein predicted gravitational time dilation in 1907 from the equivalence principle, eight years before the full theory.
Why it's proven
Pound and Rebka measured it up a 22.5-meter tower at Harvard in 1959. Gravity Probe A's rocket-borne clock (1976) and optical clocks 33 cm apart (2010) confirmed it.
Open questions and mysteries
Near a black hole's edge, time effectively freezes for outside observers; what this means for information falling in is unresolved.
▸General relativity: gravity is curved spacetime predicts Black holesProven
The relationship
Einstein's 1915 equations say mass curves spacetime. Put enough mass in a small enough region and the curvature becomes so steep that every path, even light's, bends back inward. The equations allow this outcome directly: Schwarzschild's 1916 solution, Oppenheimer and Snyder's 1939 collapsing star, and Roy Kerr's 1963 spinning version all describe black holes.
How the link was found
Karl Schwarzschild found the first solution in 1916; Oppenheimer and Snyder showed in 1939 that a collapsing star forms one; Penrose proved in 1965 that formation is generic.
Why it's proven
The math is exact. Observations confirm it: Cygnus X-1 (1970s), star orbits around the Milky Way's center, LIGO's 2015 merger signals, and Event Horizon Telescope images (2019, 2022).
Open questions and mysteries
Relativity also predicts a singularity at the center, which signals its own breakdown. What truly lies inside is unknown.
▸General relativity: gravity is curved spacetime allows The universe is expandingProven
The relationship
Einstein's equations say matter and energy curve spacetime. Applied to a universe evenly filled with matter, they forbid it from standing still: space must grow or shrink. Einstein disliked this and in 1917 added a 'cosmological constant' to hold it static. Others took the equations at face value and found expanding solutions. Expansion is a natural outcome of the theory.
How the link was found
Alexander Friedmann in 1922 and Georges Lemaître in 1927 independently found expanding solutions. Einstein accepted expansion around 1931 after Hubble's data.
Why it's proven
Hubble's 1929 measurements and modern surveys match the Friedmann-Lemaître equations, which remain the basis of all cosmological calculations.
Open questions and mysteries
Einstein's discarded cosmological constant returned in 1998 as dark energy. Why it has its tiny value is unexplained.
▸General relativity: gravity is curved spacetime permits on paper WormholesSpeculative
The relationship
Einstein's field equations accept many spacetime shapes as valid solutions, including tunnels joining two distant regions. The math does not say such shapes exist, only that they are allowed. Keeping a tunnel open long enough to pass through would require exotic matter with negative energy pushing outward; ordinary matter would make it pinch shut instantly.
How the link was found
Einstein and Nathan Rosen found the first such bridge in 1935. Michael Morris and Kip Thorne analyzed traversable wormholes in 1988.
Is it proven?
They are mathematically valid solutions, which is proven. Whether any exist in nature is not: there is no observation of a wormhole of any kind.
Open questions and mysteries
Whether enough negative energy can exist, and whether quantum gravity forbids wormholes outright, is unknown. Treat this link as speculation.
▸General relativity: gravity is curved spacetime clashes with quantum theory in Quantum gravity: the missing linkOpen question
The relationship
General relativity treats spacetime as a smooth, exact stage that bends. Quantum theory treats everything as fuzzy and uncertain. Gravity's source is energy, and in quantum theory energy fluctuates, so spacetime itself should fluctuate. When physicists apply the standard quantum recipe to gravity, the calculations produce infinities that cannot be removed. The two theories cannot both be right as written at very small scales.
How the link was found
The problem was recognized in the 1930s. 't Hooft and Veltman (1974) and Goroff and Sagnotti (1986) proved that the straightforward quantum version of gravity breaks down.
Is it proven?
The infinities are mathematical results, widely checked. In practice the clash only matters at extreme scales like black hole centers and the Big Bang, where no experiment can yet reach.
Open questions and mysteries
Which theory has to give way: quantum mechanics, relativity, or both? Is spacetime itself emergent from something deeper?
▸General relativity: gravity is curved spacetime describes gravity, the odd one out of The four forces of natureProven
The relationship
In general relativity, gravity is not a force pulling through space but the bending of space and time by mass. The other three forces are described as quantum fields trading particles. Gravity does not fit that pattern: no one has a working quantum version, and its hypothetical carrier particle, the graviton, has never been seen.
How the link was found
Einstein published general relativity in 1915. The mismatch with quantum theory was recognized by the 1930s and sharpened in the 1970s, when calculations showed quantum gravity gives uncontrollable infinities.
Why it's proven
General relativity is confirmed by Mercury's orbit, light bending (1919), GPS clocks, and gravitational waves (2015). No quantum effect of gravity has ever been measured.
Open questions and mysteries
Is gravity a force at all, or something more basic about space and time? Gravitons may be undetectable even in principle.
▸Calculus: the math of change underlies General relativity: gravity is curved spacetimeProven
The relationship
General relativity describes gravity as curvature that changes from point to point, which is exactly what calculus handles: rates of change. Einstein needed differential geometry, the calculus of curved surfaces extended to four dimensions, to write equations linking the curvature of spacetime to the mass and energy within it.
How the link was found
Riemann developed curved-space geometry in 1854; Ricci and Levi-Civita built tensor calculus by 1900. Marcel Grossmann pointed Einstein to these tools in 1912.
Why it's proven
The equations written in this mathematics make precise predictions that match observation, from Mercury's orbit to gravitational-wave signals.
Open questions and mysteries
At the center of a black hole and the start of the Big Bang, the equations give infinities, suggesting the mathematics or the theory reaches its limit.
▸GPS runs on relativity tests every day General relativity: gravity is curved spacetimeProven
The relationship
Every GPS fix depends on satellite clocks running at the rate general relativity predicts for their height in Earth's gravity. If the theory were wrong, the corrections built into the system would be wrong too, and positions would drift measurably. Its steady, everyday accuracy is a continuous test of the theory.
How the link was found
The corrections were designed before GPS satellites launched in 1978. A 1977 test satellite first ran its clock uncorrected and drifted by the predicted amount.
Why it's proven
The system holds meter-level accuracy worldwide. Galileo satellites accidentally put in odd orbits in 2014 were used to confirm gravitational time dilation to high precision in 2018.
Open questions and mysteries
None major for this link. GPS is not precise enough to reveal any small deviations from general relativity.
▸First pictures of a black hole (2019) matched the shadow size predicted by General relativity: gravity is curved spacetimeProven
The relationship
General relativity predicts how strongly a black hole bends light, and so how large its dark shadow should appear for a given mass and distance. The Event Horizon Telescope measured M87*'s ring at about 42 microarcseconds across, roughly a donut on the Moon seen from Earth. That size matched relativity's prediction, using the mass measured from star motions.
How the link was found
The Event Horizon Telescope collaboration in 2019 for M87*, and in 2022 for Sagittarius A*, whose mass was known independently from decades of tracking nearby stars.
Why it's proven
Both shadows agreed with relativity to within about 10 percent, ruling out several alternative theories of gravity. Two very different black holes, 1,500 times apart in mass, fit the same prediction.
Open questions and mysteries
Sharper images could test relativity more precisely, including the predicted thin photon ring; current resolution cannot yet.
▸General relativity: gravity is curved spacetime gives gravity negative energy in A zero-energy universeSpeculative
The relationship
In Einstein's theory, mass-energy curves spacetime, and the bookkeeping of that curvature acts like negative energy. For a closed universe, Einstein's equations impose a strict condition: matter energy and gravitational energy must sum to exactly zero at all times. For an open, infinite universe there is no agreed way to total it at all.
How the link was found
Richard Feynman remarked in his 1962–63 Caltech lectures on gravitation that rough estimates put the universe's total energy near zero. The exact closed-universe result follows from Paul Dirac's and Arnowitt, Deser and Misner's reformulations of relativity (1958–62).
Is it proven?
The closed-universe zero is a mathematical identity accepted by relativists. Critics say that makes it trivial rather than deep. Whether our universe is closed is unknown.
Open questions and mysteries
By Einstein's equivalence principle, gravity has no energy you can pin to a single place. Is 'negative gravitational energy' then real physics, or an accounting convention?
▸General relativity: gravity is curved spacetime yields The Friedmann equations: the rules of expansionProven
The relationship
General relativity links spacetime's curvature to the energy, momentum and pressure it contains. For a uniform universe, the curvature side reduces to the expansion rate and its acceleration, and the content side to density and pressure. One twist has no Newtonian counterpart: pressure itself gravitates. That is why negative pressure can make expansion accelerate.
How the link was found
Einstein's equations date from November 1915. In 1934 Edward Milne and William McCrea showed the first Friedmann equation also follows from Newton's gravity for an expanding ball; the pressure term needs Einstein.
Why it's proven
General relativity passes every precision test, from Mercury to gravitational waves. On cosmic scales, Euclid and DESI compare the expansion with how fast structures grow, a direct check.
Open questions and mysteries
Does general relativity hold unchanged over billions of light-years? Modified-gravity theories try to explain acceleration without dark energy; so far none beats the standard version.