of the Solar System from a proto-stellar cloud (then known as cosmogony). A variational form of the virial theorem was developed in 1945 by Ledoux. A tensor form of the virial theorem was developed by Parker, Chandrasekhar and Fermi. The following generalization of the virial theorem has been established by Pollard in 1964 for the case of the inverse square law: A boundary term otherwise must be added. Inclusion of electromagnetic fields The virial theorem can be extended to include electric and magnetic fields. The result is where is the moment of inertia, is the momentum density of the electromagnetic field, is the kinetic energy of the "fluid", is the random "thermal" energy of the particles, and are the electric and magnetic energy content of the volume considered. Finally, is the fluid-pressure tensor expressed in the local moving coordinate system and is the electromagnetic stress tensor, A plasmoid is a finite configuration of magnetic fields and plasma. With the virial theorem it is easy to see that any such configuration will expand if not contained by external forces. In a finite configuration without pressure-bearing walls or magnetic coils, the surface integral will vanish. Since all the other terms on the right hand side are positive, the acceleration of the moment of inertia will also be positive. It is also easy to estimate the expansion time . If a total mass is confined within a radius , then the moment of inertia is roughly , and the left hand side of the virial theorem is . The terms on the right hand side add up to about , where is the larger of the plasma pressure or the magnetic pressure. Equating these two terms and solving for , we find where is the speed of the ion acoustic wave (or the Alfvén wave, if the magnetic pressure is higher than the plasma pressure). Thus the lifetime of a plasmoid is expected to be on the order of the acoustic (or Alfvén) transit time. Relativistic uniform system In case when in the physical system the pressure field, the electromagnetic and gravitational fields are taken into account, as well as the field of particles’ acceleration, the virial theorem is written in the relativistic form as follows: where the value exceeds the kinetic energy of the particles by a factor equal to the Lorentz factor of the particles at the center of the system.