Re: Tidal Force Tensor

[EMAIL PROTECTED] (WaiteDavid137) wrote:
> It would be a bad term if they did.

It's entirely appropriate and the understanding behind it is fairly
standard, centering on the equation of geodesic deviation:
   d^2/ds^2 (J^i(q(s))) + 2/3 R^i_{jkl} q^j'(s) q^l'(s) J^k(q(s)) = 0,
that describes the deformation
                      J^i(q(s)) = d/da q(a,s)|a=0
that takes place along a bundle of geodesics (q(a,s): a in [-D,D];
q(0,s) = q(s)) due to the gravitational field.

This is covariant and does not disappear in any frame, and is
given in invariant form by:
                  (Del_q')^2 J + R(J,q') q' = 0
in terms of the curvature operator
                R(u,v) = [Del_u, Del_v] - Del_{[u,v]}.

An account of this will probably be found in any standard
reference on Riemannian geometry, and is developed in Landsman [1],
section II.3.

Reference:
[1] Landsman, N.P., 1998: Mathematical Topics Between Classical
    and Quantum Mechanics, Springer-Verlag.