Consider the time speed equation,
\({ v }_{ t }= \sqrt {{ c }^{ 2 }-\cfrac { 2{ G }_{ o } }{ (x+r_{ e }) } }\)
Can space be so dense that at \( x=0\) that time speed is zero. That time itself stopped. Theoretically, that can happen when
\( { c }^{ 2 }=\cfrac { 2{ G }_{ o } }{ (r_{ e }) } \)
that is when \({ r }_{ eo }\) is given by the expression
\({ r }_{ eo }=\cfrac { 2{ G }_{ o } }{ { c }^{ 2 } }\) (*)
But first we have to calculate \({ G }_{ o }\). Using earth as an example, where \(g\) = 9.80665 ms-2 on the surface of earth, and \({ r }_{ e }\) = 6371 km, from previously
\(g=-{ G }_{ o }.\cfrac { 1 }{ { (x+{ r }_{ e }) }^{ 2 } }\), \(x=0\)
We have,
\( |g|=\cfrac { { G }_{ o } }{ { r }_{ e }^{ 2 } } \)
\({ G }_{ o }=|g|.{ { r }_{ e }^{ 2 } }\)
\({ G }_{ o }\) = 9.80665*(6.371e6 )^2 = 3.980484e14
With \(c\) = 299792458 ms-2, from equation * when
\({ r }_{ eo }\) = 0.00886 m time speed \({ v }_{ t }\) is zero.
This means that if earth is to be squeezed to a size of 8.86 mm, time would stand still on its surface.
