Theorem_energy_momentum_tensor_expansion.tex

%
% Copyright © 2018 Peeter Joot.  All Rights Reserved.
% Licenced as described in the file LICENSE under the root directory of this GIT repository.
%
\maketheorem{Expansion of the energy momentum tensor.}{thm:poyntingF:1240}{
Given a scalar parameter \( \alpha \), and a vector parameter \( \Ba = \sum_k a_k \Be_k \), the \textit{energy momentum tensor} of
\cref{dfn:poyntingF:1200} is a grade \((0,1)\)-multivector, and may be expanded in terms of \( \calE, \BS \) and \( \BT(\Ba) \) as
%\label{eqn:poyntingF:1120}
\begin{equation*}
T(\alpha + \Ba)
=
\alpha \lr{
   \calE + \frac{\BS}{c}
}
-
\Ba \cdot \frac{\BS}{c}
+ \BT(\Ba),
\end{equation*}
where \( \BT(\Be_i) \cdot \Be_j = -\Theta^{ij} \), or \( \BT(\Ba) = \Ba \cdot \lrT \).
} % theorem