Gravimagnetic Submarine Warfare?

"The Question is: What is The Question?" John Archibald Wheeler

Metric Engineering Investigations 1.6
Special Relativity considerations: In a global inertial frame in
Cartesian coordinates the frame-invariant small differential space-time
interval ds obeys

ds^2 = (cdt)^2 - dx^2 - dy^2 - dz^2

Any Lorentz transformation to another inertial frame in uniform relative
motion to the first preserves this Cartesian form. That is under the
action of O(1,3) x^u -> x^u'

ds^2 = (cdt')^2 - dx'^2 - dy'^2 - dz'^2

A transformation to an accelerated noninertial frame in 1905 special
relativity sense will formally look lie a transformation to curvilinear
coordinates with the possibility of off-diagonal terms. Not so however
for the trivial 3D change to spherical polar coordinates where

ds^2 = (cdt)^2 - dr^2 - r^2(dtheta^2 + sin^2thetadphi^2)

Example 1 uniformly accelerating noninertial frame in the Galilean
limit gt/c << 1

t' ~ t

z' ~ z - (1/2)gt^2

dz = dz' + gtdt

dz^2 = dz'^2 + (gt/c)^2(cdt)^2 + 2(gt/c)dz(cdt)

So the important part of the metric in the z'-t plane is

(cdt)^2[1 - (gt/c)^2] - dz'^2 - 2(gt/c)dz(cdt)

The mixed space-time off-diagonal cross-term is a longitudinal
"gravimagnetism" effect. In this case translational acceleration of the
noninertial frame is a source of gravimagnetism.

Bz = 2gt/c points along the z-axis direction of translational acceleration.

Special relativity where gt/c -> 1 changes this to the hyperbolic motion
problem using hyperbolic functions.

Example 2 Galilean relativity Wx'/c << 1 etc. limit of rotating
noninertial frame about z-axis

x = x'cosWt - y'sinWt
y = x'sinWt + y'cosWt

dx = dx'cosWt - x'sinWtdt - dy'sinWt - y'cosWtdt

dy = dx'sinWt + x'cosWt + dy'cosWt - y'sinWtdt

ds^ = [1 - W^2(x'^2 + y'^2)/c^2](cdt)^2 + (2Wy'/c)dx'(cdt)
-(2Wx'/c)dy'(cdt) - dx'^2 - dy'^2 - dz'^2

Note the inhomogeneous transverse gravimagnetism here from the physical
rotation of the noninertial frame. That is

Bx'(y') = 2Wy'/c

By'(x') = 2Wx'/c

The gravimagnetic 3-vector B = goi points in the plane perpendicular to
the axis of rotation. See Ray Chiao's "Gravity Radio" A(em).B(gravity)
interaction Hamiltonian papers online for the application of
gravimagnetism in rotating superconductors for the high efficiency
transduction between gravity waves and electromagnetic waves with
application to submarine warfare C^3 and a host of other applications to
the cosmology of the Big Bang if it can be achieved. Note the
"Stern-Gerlach" inhomogeneous gravimagnetic "potential well" for
gyroscopes in this solution. What happens in a medium c/n when n >> 1.
Will that enhance the strength of gravimagnetism?

Gravimagnetic Submarine Warfare?