- #1

- 192

- 6

[tex]d\bar x^\alpha = \frac{{\partial \bar x^\alpha }}{{\partial x^\beta }}dx^\beta[/tex] and [tex]d^4 \bar x = \frac{{d^4 x}}{J}[/tex]. So since:[tex]\bar g^{\alpha \beta } = g^{\mu \tau } \frac{{\partial \bar x^\alpha }}{{\partial x^\mu }}\frac{{\partial \bar x^\beta }}{{\partial x^\tau }}[/tex] I figured [tex]d^{10} \bar g = \frac{{d^{10} g}}{{J^2 }}[/tex]. I would also like the requirements that [tex]g_{00} < 0[/tex], [tex]\det [g_{\alpha \beta } ] < 0[/tex], and [tex]\det [\gamma _{ij} ] > 0[/tex] where [tex]\det [g_{\alpha \beta } ] = g_{00} \det [\gamma _{ij} ][/tex]. Any suggestions or guesses?