The Virial Theorem In Cosmological Context

LT Jeffrey Swaim, USN

The virial theorem relates the average kinetic energy of a bounded system of particles to the potential energy function of particle interaction. For gravitational systems, the classical virial theorem is derived as a simple proportional relationship and applied to ob- servational data from the Coma galaxy cluster. A covariant virial theorem is also derived within the 3+1 formalism of general relativity, and compared to both non-relativistic virial tensor theorems and the expected result in the first post-Newtonian approximation.