Gravitoelectromagnetism (GEM) is a long word for the analogy between linear electromagnetism and nonlinear general relativity split into 1+3 or 3+1 form by an observer congruence which can be done in a number of ways. This directory contains an incomplete LaTeX manuscript of a book in [slow] progress on this topic:

Gravitoelectromagnetism: the User Manual
Understanding Spacetime Splittings and Their Relationships

by R.T. Jantzen, Paolo Carini, Donato Bini.

The preface and introduction are contained in a single PDF file. [PDF table of contents navigation links now work]
[The whole unfinished book is a 1.2 MEG PDF file. Doesn't seem to open in Google Chrome? Try IE or Firefox.]

A useful summary of formulas from differential geometry relevant to GR may be found in the appendix.

The main LaTeX file gem.tex with two macro files bobmacrola.tex and gemmac.tex typesets the 5 chapter book with a long bibliography on the topic and an appendix of the differential geometry used:

This copy is made available with the understanding that it be appropriately referenced if it proves useful.