The description of motion in relativity requires more than one concept of speed. Coordinate speed is the coordinate distance measured by the observer divided by the coordinate time

Coordinate time

In the theory of relativity, it is convenient to express results in terms of a spacetime coordinate system relative to an implied observer. In many coordinate systems, an event is specified by one time coordinate and three spatial coordinates...

 of the observer. Proper speed

Proper velocity

In relativity, proper-velocity, also known as celerity, is an alternative to velocity for measuring motion. Whereas velocity relative to an observer is distance per unit time where both distance and time are measured by the observer, proper velocity relative to an observer divides observer-measured...

 is the local proper distance divided by the local proper time

Proper time

In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...

. For example, at the event horizon

Event horizon

In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case...

 of a black hole the coordinate speed of light is zero, while the proper speed is c. The coordinate speed of light (both instantaneous and average) is slowed in the presence of gravitational field

Gravitational field

The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

s. The local instantaneous proper speed of light is always c. However, the average proper speed of light will differ from c in the presence of a gravitational gradient.


In an inertial frame an observer cannot detect their motion via light signals as the speed of light in a vacuum is constant. This means an observer can detect when their motion is accelerated by studying light signals.

See also

• Shapiro time delay
• Frame-dragging
  Frame-dragging
  Einstein's general theory of relativity predicts that non-static, stationary mass-energy distributions affect spacetime in a peculiar way giving rise to a phenomenon usually known as frame-dragging...
  
  
• Lense–Thirring precession
• Sagnac effect
  Sagnac effect
  The Sagnac effect , named after French physicist Georges Sagnac, is a phenomenon encountered in interferometry that is elicited by rotation. The Sagnac effect manifests itself in a setup called ring interferometry. A beam of light is split and the two beams are made to follow a trajectory in...
  
  
• Gravitational time dilation
  Gravitational time dilation
  Gravitational time dilation is the effect of time passing at different rates in regions of different gravitational potential; the lower the gravitational potential, the more slowly time passes...
  
  
• Gravitational redshift
  Gravitational redshift
  In astrophysics, gravitational redshift or Einstein shift describes light or other forms of electromagnetic radiation of certain wavelengths that originate from a source that is in a region of a stronger gravitational field that appear to be of longer wavelength, or redshifted, when seen or...