For brevity we will now assume that this also the solution of the Kerr spacetime when a=0, and the egrosphere has minimal frame dragging so that it corresponds to a photon sphere of Schwarzchild black hole. From the last section we know if the Kerr spacetime is set with a=0 we may conclude that

0=R00-T00=(1/2)[T11+T22+T33]

However if R00-T00>0, for the proposed spacetime that would imply that it is given by a Kerr geometry. This is also reveals a problem with the Kerr spacetime the geodesics of photons no longer remain symmetric. However under ideal cases it is somewhat easy to calculate the stress-energy associated with angular momentum tensors by

a=GJ/Mc3

which would alter the noted energy density from the previous section of

The problem with this method is that it will only yield the total angular momentum of the system.

Now for the interesting part the inner horizon of the Kerr Spacetime would have an inner egrosphere, which would act to frame drag the space located between the outer and inner horizons, resulting from the fact that inner horizon has a higher angular momentum via conservation laws. This is a simple supposition to make when one understand the properties of the Kerr spacetime and that of angular momentum (to aid in further exploration refer to figure 2 below through this discussion).

However, what becomes interesting is when one considers the Kerr Spacetime moving in the the x coordinate, as depicted with dx in figure 2. The region between the outer horizon (A') and inner horizon (B'), which is labeled as E, in region E the inner frame dragging egrosphere (not depicted), would be forced to fold on itself in the direction of travel. Thus the frame dragging effect begins to compress in front of the inner horizon, and from A' is forced to expand in the opposite direction, this is the property associated with the warp drive spacetime. From the graph it is seen that if a particle travels in region B' it is allowed to escape back into region E through the warp drive space, and from quantum theory has to potential to interact with the outer egrosphere again (possibly generating a new kind of quantum pressure), but this is speculation. One potential problem as seen from figure 2 is that there appears to exist a double coordinate transformation when one the compares Kerr metric with the Schwarzchild Warp Drive. The first being r(vs2*1-f(rs))1/2-->r' and the second coordinate transformation corresponding to x(vh21-f(x))1/2-->x', before I go into that problem I would like to discuss how the Kerr spacetime effect to geodesics such that light traveling to or from a Kerr horizon is manipulated by a lapse function. As light enters the horizon the light becomes ever more blue shifted, while a light beam attempting to leave becomes ever more red shifted the magnitude of this lapse function is given by:

g_00={1-(2GM)'A'(r's)[vsr'*1-f'(r's)]2}
g_11={[v2*1-f(x)]2 dr'2/1-(2GM/r)'}
g_22=g_33=-1.

so one has a solution which corresponds to:

In comparison to the Kerr metric one can make a generic substitution of order

With this solution figure 2 becomes rather obvious. What is more interesting is that when the line element (v*1-f(x))2 is removed from the right hand one has, d*1-f/dx which is identical to the original Kerr solution. Thus the coordinate transformation takes on the role of a lapse function of the inner horizon, roughly corresponding to:

a=kgM(r/S)(D)1/2/2pD.

Therefore indicating the compression of the of the inner ergosphere in the direction of travel of the horizon as function of the inner an outer angular velocities, corresponding to the before mention double coordinate transformation.

The energy density for this consideration can now be calculated from

for the momentum tensors we have:

T22=[1/a]*T00

T33=[1/a]*T00.

In order to calculated divergence in the separate moment tensors one can use partial differention, denoted by dq in the following example dq*T11/dq*T22=f({1/T22},T33). It is also plain to see here that R00-T00>0, which shows qed that such a space is indeed non Schwarzchild in nature. Although this spacetime in non Schwarzchild it still remains symmetrical with a=0, e.g. one can reduce the proposed Kerr spacetime by considering a function of order 1-f(x,r). This construction would be far more realistic if some arbitrary coordinate k rotated into k', however this was meant to construct a proof of concept and not to create more of a mess!

The proposition rest on the assertion that the overlapping frame dragging creating a compressed gravitational wave...

note: page is currently under construction analysis are not final, the calculations have not been checked, and until more work is done, should only be considered as a proposition....

©2001: Edward Halerewicz, Jr.