]>

Table 1

$g_{\mu \nu }$ Semiclassical Classical $-N^2(t)$ $-\frac{{\gamma }^2{\delta }^2\left[{\left(\frac{\gamma \delta m}{2t^2}\right)}^2+1\right]}{1-(1+{\gamma }^2{\delta }^2){\left[\frac{\sqrt{1+{\gamma }^2{\delta }^2}+1-{(2m/t)}^{\sqrt{1+{\gamma }^2{\delta }^2}}(\sqrt{1+{\gamma }^2{\delta }^2}-1)}{\sqrt{1+{\gamma }^2{\delta }^2}+1+{(2m/t)}^{\sqrt{1+{\gamma }^2{\delta }^2}}(\sqrt{1+{\gamma }^2{\delta }^2}-1)}\right]}^2}$ $-\frac{1}{(2m/t)-1}$ $X^2(t)$ $\frac{{(2\gamma \delta m)}^2\left(1-(1+{\gamma }^2{\delta }^2){\left[\frac{\sqrt{1+{\gamma }^2{\delta }^2}+1-{(2m/t)}^{\sqrt{1+{\gamma }^2{\delta }^2}}(\sqrt{1+{\gamma }^2{\delta }^2}-1)}{\sqrt{1+{\gamma }^2{\delta }^2}+1+{(2m/t)}^{\sqrt{1+{\gamma }^2{\delta }^2}}(\sqrt{1+{\gamma }^2{\delta }^2}-1)}\right]}^2\right)t^2}{{(1+{\gamma }^2{\delta }^2)}^2{\left(1-{\left[\frac{\sqrt{1+{\gamma }^2{\delta }^2}+1-{(2m/t)}^{\sqrt{1+{\gamma }^2{\delta }^2}}(\sqrt{1+{\gamma }^2{\delta }^2}-1)}{\sqrt{1+{\gamma }^2{\delta }^2}+1+{(2m/t)}^{\sqrt{1+{\gamma }^2{\delta }^2}}(\sqrt{1+{\gamma }^2{\delta }^2}-1)}\right]}^2\right)}^2\left[\right(\frac{\gamma \delta m}{2}{)}^2+t^4]}$ $\frac{2m}{t}-1$ $Y^2(t)$ $\frac{1}{t^2}\left[{\left(\frac{\gamma \delta m}{2}\right)}^2+t^4\right]$ $t^2$