field exponentially coupled to a Maxwell field, with the magnitude of the dilaton coupling constant smaller in magnitude than some positive real number determined below, $0 \leq |\lambda| < \lambda_c$. The stress-energy tensor of the matter fields is $$T_{\mu \nu} = \, ^{(4)}\nabla_\mu \phi \,
^{(4)}\nabla_\nu \phi - {1 \over 2} g_{\mu \nu} \,
^{(4)}\nabla_\alpha \phi \,
^{(4)}\nabla^\alpha \phi + [F_{\mu \alpha} {F_\nu}^ \alpha
-{1 \over 4} g_{\mu \nu} F_{\alpha \beta} F^{\alpha \beta} ] e^{\lambda \phi}.$$ The matter fields satisfy the following equations. $$\begin{aligned}
^{(4)}\nabla_\alpha \, ^{(4)}\nabla^\alpha \phi & = & {\lambda \over 4}
 F_{\alpha \beta} F^{\alpha \beta}  e^{\lambda \phi}, \nonumber \\
^{(4)}\nabla_\mu (F^{\mu \nu} e^{\lambda \phi}) & = & 0, \nonumber \\
^{(4)}\nabla_{[ \alpha} F_{\beta \gamma ]} & = & 0. \nonumber\end{aligned}$$ The 3+1 decomposition of the stress-energy tensor is best expressed in terms of the electric spatial vector density ${\cal E}^a = \sqrt{g} \, F^{0a} e^{\lambda \phi}$ and the magnetic antisymmetric spatial tensor $F_{ab}$. $$\begin{aligned}
\rho & = & {1 \over 2} \{ (\partial_t \phi)^2 + g^{ab} e_a(\phi) e_b(\phi)
+{1 \over g} g_{ab} {\cal E}^a {\cal E}^b e^{-\lambda \phi} +
{1 \over 2} g^{ab} g^{ch} F_{ac} F_{bh} e^{\lambda \phi} \}, \nonumber \\
j_a & = & - \partial_t 