The expression for the divergence in spherical polar coordinates is the same from this Harvard site and VAPS, so that is a useful check. so Eqs. (1) to (8) of the note have been checked as correct. This means that Eqs. (9) to (15) of the note are correct. The protocol also seems to be correct.
To: EMyrone@aol.com
Sent: 28/08/2016 20:44:22 GMT Daylight Time
Subj: Re: 356(4): Spacetime Velocity Field Induced by a Static Electric FieldThe divergence and gradient terms in spherical coordinates are different, see
http://isites.harvard.edu/fs/docs/icb.topic970148.files/Spherical_coord.pdfThe (v*grad) v term then reads for two arbitrary vector functions a and b:
(a*grad) b =
The diff. eqs. with full angular dependenced are o11-o13 in the protocol. For pure r dependence, the results are o15-o17.
This gives constant solutions for v[theta] and v[phi]. These will only be different from zero if a constant background potential is considered, for example an overlay of constant aether flow.
The solution for component v[r] is o20/o21. For %c=0, this is of type 1/sqrt(r), not of 1/r as expected. This needs to be clarified.Horst
Am 27.08.2016 um 12:55 schrieb EMyrone:
In spherical polar coordinates this is found by solving Eqs. (13) to (15) simultaneously. In general, the velocity field has a very interesting structure in three dimensions. The simultaneous numerical solution of Eqs. (13) to (15) also gives the spacetime velocity field set up by a static gravitational field g (the acceleration due to gravity). This entirely original type of velocity field exists in a spacetime defined as a fluid. The spacetime can also be called an “aether”, or “vacuum”. Any boundary conditions can be used. A magnetic and gravitomagnetic field also set up aether velocity fields.
