Dominant energy condition for a kinetic scalar field
= Dominant energy condition for a kinetic scalar field
For a <scalar field> with $X=-q^2/2$, Lagrangian $F(X)$ and <stress-energy tensor> $T_{ab}=F\prime q_aq_b+Fg_{ab}$, the inequalities $A=F\prime\ge0$ and $Y=XF\prime-F\ge0$ imply the <dominant energy condition> for any gradient type. In a local <Lorentz frame>, $\rho=A(q_0^2+\sum_iq_i^2)/2+Y\ge0$ and $\rho^2-\sum_iT_{0i}^2=A^2X^2+A(q_0^2+\sum_iq_i^2)Y+Y^2\ge0$.