Back and Forth

Numerically,

${\gamma} = \sqrt{\frac{{ d }_{ s }-{d}_{n}}{{d}_{e}-{d}_{n}}. \frac{{ d }_{ e}-{d}_{n}}{{d}_{B}-{d}_{n}}-1}$

where ${d}_{s}$ is the space density on the surface of the sphere created.

The term,

 $\frac{{ d }_{ s }-{d}_{n}}{{d}_{e}-{d}_{n}}$

gives the relative compression ratio with respect to space density on Earth and,

$\frac{{ d }_{ e}-{d}_{n}}{{d}_{B}-{d}_{n}}$

is the reciprocal of the compression ratio above which travelling back in time is possible.

To travel forward in time, set the compression ratio on the surface of the sphere to $\frac{{ d }_{B }-{d}_{n}}{{d}_{e }-{d}_{n}}$ and wait as time move forward.  Time stand still in the sphere, but beyond the sphere time passes normally.  At lower compression ratio,

${\gamma} = \sqrt{1-\frac{{ d }_{ s }-{d}_{n}}{{d}_{e}-{d}_{n}}. \frac{{ d }_{ e}-{d}_{n}}{{d}_{B}-{d}_{n}}}$

Time in the sphere is slowed but not at zero speed.