Geometrized unit system

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In physics, especially in the general theory of relativity, geometrized units or geometric units constitute a physical unit system in which all physical quantities are expressed in the unit of length: meter. In this system, the speed of light and the gravitational constant are set to unity: c = 1 and G = 1. The Boltzmann constant is sometimes also included (k = 1).

Equations often appear especially simple when expressed in the geometric unit system, because many of the constants tend to drop out. For example, the Schwarzschild radius of a black hole with mass m is simply r = 2 m.

In geometrical units, a time interval is expressed as the distance travelled by light in that interval: a second is equivalent to a light second. Mass can be expressed in meters using the conversion factor G/c2. For example, the Sun's mass of 2.0×1030 kg in SI units is equivalent to 1.5 km—half the Schwarzschild radius of a black hole with that mass.

Other examples of conversion factors are given in the table below. The smallness of many factors reflects the fact that relativistic effects are only noticeable when large masses or high speeds are considered.

Conversion between geometrized and SI units
quantity factor numeric value
time c 3.00 × 108 m/s
mass G/c2 7.43 × 10−28 m/kg
force G/c4 8.26 × 10−45 m/N
temperature Gk/c4 1.14 × 10−67 m/K

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