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.
