The property of charge invariance follows from the vanishing divergence of the charge-current four-vector \( j^\mu=(c\rho,{\vec j}) \) , with \( \partial_\mu j^\mu=0. \)

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 of the observer. Proper speed is the local proper distance divided by the local proper time. For example, at the event horizon of a black hole the coordinate speed of light is zero, while the proper speed is c.[1] The coordinate speed of light (both instantaneous and average) is slowed in the presence of gravitational fields. The local instantaneous proper speed of light is always c.
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
Lense–Thirring precession
Sagnac effect
Gravitational time dilation
Gravitational redshift


Locality hypothesis and the speed of light, G.Longhi, 2006
Propagation of light in non-inertial reference frames

Relativity and the Nature of Spacetime, Vesselin Petkov, Springer, 2009, ISBN 978-3-642-01952-4, Chapter: 7


Black hole complementarity
de Sitter space

1 Exact solutions
2 Black hole uniqueness
3 See also

Physics Encyclopedia

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