Geodesic Deviation: Deriving Formula with Schtuz's Book

Terilien
Messages
140
Reaction score
0
Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
 
Physics news on Phys.org
You can try, for instance, http://www.mth.uct.ac.za/omei/gr/chap6/node11.html

This seems like a rather direct and straightforwards approach to me, even more direct than MTW's. Of course it is a bit mathematically impure, in that it assumes a convenient coordinate system, but I think assuming an inertial coordinate system for one of the observers makes the physics more apparent.
 
Last edited by a moderator:
Terilien said:
Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
The derivation I placed on my web page at

http://www.geocities.com/physics_world/gr/geodesic_deviation.htm

started out being a translation from Ohanian's book to my web page. However it seemed to end up being Ohanian's book and part of what I had to say since Ohanian made somethings hard to understand there. Enjoy. Any problems then e-mail me so we can set straight if there is something wrong.

Pete
 
In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this: $$ \partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}. $$ The integrability conditions for the existence of a global solution ##F_{lj}## is: $$ R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0 $$ Then from the equation: $$\nabla_b e_a= \Gamma^c_{ab} e_c$$ Using cartesian basis ## e_I...
Abstract The gravitational-wave signal GW250114 was observed by the two LIGO detectors with a network matched-filter signal-to-noise ratio of 80. The signal was emitted by the coalescence of two black holes with near-equal masses ## m_1=33.6_{-0.8}^{+1.2} M_{⊙} ## and ## m_2=32.2_{-1. 3}^{+0.8} M_{⊙}##, and small spins ##\chi_{1,2}\leq 0.26 ## (90% credibility) and negligible eccentricity ##e⁢\leq 0.03.## Postmerger data excluding the peak region are consistent with the dominant quadrupolar...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. The Relativator was sold by (as printed) Atomic Laboratories, Inc. 3086 Claremont Ave, Berkeley 5, California , which seems to be a division of Cenco Instruments (Central Scientific Company)... Source: https://www.physicsforums.com/insights/relativator-circular-slide-rule-simulated-with-desmos/ by @robphy
Back
Top