Gravitational time dilation is the difference in elapsed proper time between clocks located in different gravitational potentials or following different paths through curved spacetime. In general relativity, gravity is not described simply as a conventional force acting instantaneously across space. Mass and energy influence the geometry of spacetime, and clocks measure proper time along their worldlines within that geometry.
When two clocks are maintained at different gravitational potentials and later compared under suitable conditions, the clock deeper in a gravitational field generally accumulates less proper time than the clock farther away. Near Earth, a clock at sea level therefore runs very slightly slower relative to a clock at higher altitude. The effect becomes increasingly significant near compact massive objects such as neutron stars and black holes. Gravitational time dilation is a physical prediction of general relativity and has been confirmed experimentally using precision clocks, including comparisons involving different altitudes and gravitational potentials.
In the weak gravitational field around a spherical nonrotating body, a useful approximation is that the rate of a stationary clock depends on the gravitational potential. In the Schwarzschild solution, a stationary clock outside a spherical mass has a proper time relation involving the factor square root of one minus two times the gravitational constant times mass divided by radius times c squared.
As the radial coordinate decreases toward the Schwarzschild radius, this factor becomes smaller for a stationary clock relative to a distant coordinate description. The formula is exact within the assumptions of the Schwarzschild spacetime, while simpler approximations are used for weak fields. Near Earth's surface, gravitational time dilation is tiny but measurable because modern atomic clocks can resolve extraordinarily small frequency differences. The effect illustrates how general relativity modifies the classical idea that time flows at the same rate everywhere in a gravitational field.
The historical development of gravitational time dilation follows from Einstein's equivalence principle and general theory of relativity. The equivalence principle states, in simplified form, that locally the effects of a uniform gravitational field can resemble those of acceleration. Einstein realised that clocks at different heights in a gravitational field should therefore not necessarily tick at the same rate. General relativity later provided the mathematical framework in which gravitational effects arise from spacetime curvature.
Predictions such as gravitational redshift and gravitational time dilation emerged naturally from this theory. Experimental tests subsequently examined frequency shifts associated with differences in gravitational potential. The Pound Rebka experiment in 1959 measured gravitational redshift over a vertical height in Earth's gravitational field using gamma ray spectroscopy, providing an important direct confirmation of the predicted gravitational frequency shift. Modern optical clocks have made such effects measurable over height differences of remarkably small scale.
Gravitational time dilation is closely related to gravitational redshift. If a photon travels upward through a gravitational field, its frequency is measured differently by observers at different gravitational potentials. An observer higher in the gravitational field receives the signal at a lower frequency than the frequency associated with its emission under the appropriate stationary conditions, producing gravitational redshift. The same phenomenon can be described through the different rates of clocks at the emission and reception locations.
If a clock deeper in a gravitational field sends a periodic signal upward, a distant observer can interpret the lower received frequency as evidence that the lower clock runs more slowly. These are not separate unrelated effects but different observational descriptions of the spacetime geometry. The exact interpretation requires careful specification of the observers, coordinate system and photon trajectory, particularly in strong gravitational fields.
Gravitational time dilation is essential to satellite navigation and modern timing systems. A satellite orbiting Earth is farther from Earth's centre than a clock on the surface and therefore experiences a weaker gravitational potential, which tends to make its clock run faster according to general relativity. At the same time, the satellite's orbital velocity causes special relativistic time dilation, which tends to make its clock run slower. These effects have different physical origins and partially oppose one another.
The combined relativistic correction is large enough that ignoring it would cause satellite navigation systems to accumulate significant positional errors over time. The operation of global navigation satellite systems therefore provides a practical example in which relativistic timekeeping is not merely an abstract theoretical issue but a necessary engineering consideration.
Gravitational time dilation becomes especially dramatic near compact objects. For a distant observer describing a stationary clock near a nonrotating black hole, the Schwarzschild coordinate description assigns an increasingly slow rate as the clock approaches the event horizon. Locally, however, the falling clock does not experience its own time as stopping.
An observer freely falling through a sufficiently smooth region of the horizon can cross it in finite proper time and, in an idealised classical black hole, would not encounter a locally detectable boundary at the horizon solely because it is the horizon. The distinction between local proper time and distant coordinate time is therefore crucial. Statements that time literally stops at a black hole horizon usually refer to a particular distant coordinate description and should not be interpreted as a universal local experience.
Gravitational time dilation does not mean that gravity is a substance that physically slows the internal mechanism of every clock in the ordinary mechanical sense. Any sufficiently accurate physical clock responds to the spacetime conditions of its worldline, whether the clock is based on atomic transitions, electromagnetic oscillations or another physical process. The effect is universal because proper time is part of the geometry of spacetime rather than a peculiarity of a particular clock mechanism. Nevertheless, practical clocks also have engineering effects such as temperature sensitivity, acceleration sensitivity, magnetic fields and environmental perturbations, so experiments must control these factors. Precision relativistic measurements therefore require careful calibration and comparison procedures to distinguish gravitational effects from ordinary instrumental errors.
Gravitational time dilation is one of the most important observational consequences of general relativity because it connects the abstract geometry of spacetime with measurable clock rates and frequencies. It influences satellite navigation, precision geodesy, astrophysics, tests of fundamental physics and the interpretation of signals near compact objects. It also changes how scientists think about gravitational potential: in relativistic physics, differences in gravitational potential correspond to differences in proper time for appropriately stationary observers.
At weak fields the effect closely reproduces familiar gravitational potential calculations, while in strong fields the full spacetime metric is required. The central principle is that there is no universal gravitationally independent clock rate shared by all locations. The elapsed time measured by a clock depends on the spacetime path it follows.
