B General Relativity & Grav. Time Dilation Qn

[IXWELL]

hello I'm korean high school student and sorry for my poor English.
I saw $t_0=t_f\sqrt{1 -\frac{ 2GM}{rc^2}}$ in wikipedia.
does $\sqrt{1 -\frac{ 2GM}{rc^2}}$ of this equation have name like lorentz factor $\frac{1}{\sqrt{1 -\frac{v^2}{c^2}}}$of $t=\frac{t_0}{\sqrt{1 -\frac{v^2}{c^2}}}$ ?
or is it just called time dilation equation?
I just want to know if there is a word specifically referring to factor $\sqrt{1 -\frac{ 2GM}{rc^2}}$.

 

[jedishrfu]

You can read more about that factor here in the wikipedia article on Gravitational Time Dilation where they use the Lorentz factor and the escape velocity to get the $\sqrt{1 -\frac{ 2GM}{rc^2}}$ factor.

https://en.wikipedia.org/wiki/Gravitational_time_dilation

Here is the LATEX for the factor of interest:

# # \sqrt{1 -\frac{ 2GM}{rc^2}} # #

NOTE: Remove the spaces between "# #" to activate the web page mathjax latex rendering code.

Please take some time to learn LATEX for entering equations here. The cut/paste of images just doesn't work out well. There is a link to LATEX formatting in my signature section at the bottom of this post.

 

[Ibix]

You might call it the gravitational time dilation factor or the gravitational red shift factor. It doesn’t really have a name because it wasn't an independent discovery like the Lorentz factor, it's just a part of Schwarzschild's solution of Einstein's equations. It's also not particularly general because gravitational time dilation is only really applicable in some circumstances - it cannot be defined for things like a pair of orbiting black holes, for example