D'Inverno page 226 (tidal force on freely falling particle )

[shahram.t]

Hi every body,
I am new to PF so I apologise if a similar thread already exists.
I am reading d'Inverno Introducing Einstein's Relativity. On page 226 describes tidal forces on freely falling particle in Schwarzschild metric, I tried to deduce step by step but I can't get final three equations !?
Starting from relativistic equations of deviation how can I get differential equations of spatial motion ?!

 

[George Jones]

Hi every body,
I am new to PF so I apologise if a similar thread already exists.
I am reading d'Inverno Introducing Einstein's Relativity. On page 226 describes tidal forces on freely falling particle in Schwarzschild metric, I tried to deduce step by step but I can't get final three equations !?
Starting from relativistic equations of deviation how can I get differential equations of spatial motion ?!

Welcome to Physics Forums!

It's not completely trivial. Notice that d'Inverno writes "see Misner, Thorne, and Wheeler, for further details."

The orthonormal frame that d'Inverno gives on page 225 is not the orthonormal frame of the freely falling observer, it is the orthonormal frame of a hovering observer. The idea is to transform the Schwarzschild components of the Riemann tensor to frame of the hovering observer, and then to boost to the frame of the freely falling observer. See pages 821-822 of MTW.

I wrote a little about the hovering and freely falling frames in

https://www.physicsforums.com/showthread.php?p=848684#post848684.

 

[shahram.t]

Thanks a lot for your help George !