Wednesday, October 06, 2004
SOME WORKOUTS IN TENSOR ANALYSIS
While reviewing on Tensor Analysis, the chief mathematical language of the General Theory of Relativity, as way of preparing myself in case our paper would be accepted for oral presentation in the upcoming physics conferencethis 28th of October, I came across an inspiration to write a short mathematical exposition on some of the important mathematical entities in Tensor Analysis that are vital to the General Relativity. This short mathematical exposition that I am planning to write and post on our temporary GR website will include mathematical workouts on covariant differentiations, derivations on basic tensor identities that include Bianchi identity, short remarks on diffeomorphism and derivations on Lie derivaives of one-forms and (0, 2) tensors, leading to the diffeomorphism invariance of metric tensors. Much of those that I've started reviewing are based mostly on references that I obtained from the internet, written by the most reliable experts like Sean Carroll, Peter Dunsbye, the Nobel laureate G. 't Hooft, and several lec notes from MIT and Harvard wesites. If this is gone through and completed I also plan to submit this to the arXiv: gr-qc, that if I'll be able know how to do Latex of pdf but for the meanwhile, I'll be posting this on our GR website so that anyone who may happen to scan it may e-mail us his/her suggestions and corrections.