Geometrized unit system

Lore & Background

Geometrized units were defined in the book Gravitation by Misner, Thorne, and Wheeler such that the speed of light c, the gravitational constant G, and Boltzmann constant kB are all set to 1. Some authors refer to these units as geometrodynamic units. In geometrized units, every time interval is interpreted as the distance travelled by light during that given time interval—one second is interpreted as one light-second, so time has the geometrized units of length. Energy and momentum are interpreted as components of the four-momentum vector, and invariant mass is the magnitude of this vector, so in geometrized units these must all have the dimension of length.

Reader's Guide

The geometrized unit system is significant because it simplifies many equations in relativistic physics, making them more natural and easier to work with. For example, the Schwarzschild radius of a nonrotating uncharged black hole with mass m becomes rs = 2m. An alternative 'rationalized' system uses 4πG or 8πG instead, simplifying equations such as the Einstein field equations, the Einstein–Hilbert action, the Friedmann equations, and the Newtonian Poisson equation. Conversion factors between SI and geometrized units are derived from c and G; for instance, the Sun's mass of 2.0×10³⁰ kg is equivalent to 1.5 km. The small numerical size of these conversion factors reflects that relativistic effects are only noticeable when large masses or high speeds are considered. The system is not fully defined, as different variants (e.g., Stoney units, Planck units) set additional constants to unity.

Did You Know?

• In geometrized units, one second is interpreted as one light-second, giving time the dimension of length.
• The Sun's mass of 2.0×10³⁰ kg is equivalent to 1.5 km in geometrized units.
• An alternative 'rationalized' system uses 4πG or 8πG instead of G alone.
• The Schwarzschild radius of a nonrotating uncharged black hole simplifies to rs = 2m in geometrized units.