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Concept
Geometrized unit system
Summary
A geometrized unit system, geometric unit system or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity.
The geometrized unit system is not a completely defined system. Some systems are geometrized unit systems in the sense that they set these, in addition to other constants, to unity, for example Stoney units and Planck units.
This system is useful in physics, especially in the special and general theories of relativity. All physical quantities are identified with geometric quantities such as areas, lengths, dimensionless numbers, path curvatures, or sectional curvatures.
Many equations in relativistic physics appear simpler when expressed in geometric units, because all occurrences of G and of c drop out. For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes r = 2m. For this reason, many books and papers on relativistic physics use geometric units. An alternative system of geometrized units is often used in particle physics and cosmology, in which 8πG = 1 instead. This introduces an additional factor of 8π into Newton's law of universal gravitation but simplifies the Einstein field equations, the Einstein–Hilbert action, the Friedmann equations and the Newtonian Poisson equation by removing the corresponding factor.
Practical measurements and computations are usually done in SI units, but conversions are generally quite straightforward.
In geometric units, every time interval is interpreted as the distance travelled by light during that given time interval. That is, one second is interpreted as one light-second, so time has the geometric units of length. This is dimensionally consistent with the notion that, according to the kinematical laws of special relativity, time and distance are on an equal footing.
Energy and momentum are interpreted as components of the four-momentum vector, and mass is the magnitude of this vector, so in geometric units these must all have the dimension of length.
Official source
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