Energy Tensor for Charged Incoherent Dust in its Own Electromagnetic Field

Somnath Datta

Professor of Physics (Retired), National Council of Educational Research and Training, New Delhi

The Energy Tensor T µν dust of a distribution of incoherent charged dust is a sum of two constituent Energy Tensors, viz., the Energy Tensor Dµν of the dust taken as a flow of fluid, and the Energy Tensor Mµν of the Electromagnetic field created by the charges in the dust. The first one is obtained by first writing down the Equation of Motion of a perfect fluid, known as Euler’s equation, and upgrading the same to the 4-vector level. The second one is obtained by writing down the Conservation of Energy and Momentum in an Electromagnetic field and combining them into a single equation for the conservation of 4-momentum. It has been shown that the 4-divergence of the first one is equal and opposite to the 4-divergence of the second one. This leads to ∇αT αµ dust = 0, which is the relation to be satisfied by all Energy Tensors that can qualify to be the source term in Einstein’s Field Equation for gravity in his General Theory of Relativity.