Towards a Theory of Bipolar Gravity (BG)
Paul R. Gerber
Gerber Molecular Design, Forten 649, CH-8873 Amden, Switzerland
The motivation for this work is the evidence that the assumption of
matter-antimatter repulsion (MAR) could remove several of the very basic problems
encountered in current cosmology
(see companion note).
The geometry-generating function, G, is a scalar function from which the geometry
of space can be derived. It's gradient serves to generate the deviation of the
metric tensor from a flat unit tensor. This deviation is simply the (symmetric)
tensor product of the gradient of G with itself. For a single mass point at the
origin, G takes the form
G(r) = 2s(r/s-1)1/2,
where s is the Schwarzschild radius. In the black-hole range (r<s) this formula
does not make sense at presence. A small calculation yields the well known metric
tensor for the Schwarzschild geometry, in particular the radial element
grr = 1 + drG drG = (1-s/r)-1,
dr being the partial derivative with respect to r.
- G provides a simple way to generate the geometries of several mass points by
simple additions. Again the black-hole regions are to be
excluded and should not overlap.
- The geometry-generating function of a point of antimatter
has simply a negative sign. However, the bilinear rule of generating the metric
tensor leads to the identical geometry as for a matter point.
- The geometry of a matter point and its antimatter point, each at a distance d/2
from, and opposite to the origin differs from the corresponding arrangement of
two matter points. For distances r>>d the matter-antimatter case yields a
dipolar-type geometry, while the matter-matter case leads to a monopolar
Schwarzschild geometry with a doubled Schwarzschild radius. A complete overlap
of the matter and antimatter points restores a flat geometry, though, the details
of the overlapping process are beyond mathematical treatment in both cases
when d becomes smaller than 2s.
- Clearly, the compensation in the matter-antimatter case implies that matter
and antimatter must repel each other, since a test mass does not feel Newtons
attraction in the far range. For mixtures of matter and antimatter points the
test mass would just experience the surplus of the one or the other in the
mixture provided the test mass is in the far range.
- A further consequence is, that zero rest-mass particles do not generate
gravity at all. However, the null geodesics of the geometry determine their
paths. This opens up the question, whether light is really soaked up by
a black hole. I personally would prefer the alternative that total reflection
takes place at the Schwarzschild surface.
- For our local matter-alone island (Virgo supercluster), where all the tests of
General Relativity (GR) have been performed, there is essentially no difference
between BG and GR. The only difference is the exclusion of massless particles
from the generation of gravity (geometry), for which I'm not aware of any
- However, in Cosmos, one is no longer forced to postulate a baryogenesis
process any more. Bipolar Gravity leads to a dramatically different view of
cosmological development. This is the subject of a different note:
Cosmology as Matter-Antimatter Phase Separation
- In addition, BG may have important consequences for a quantum theory of
Gravitation, because it would allow for dipolar radiation, in principle.
Amden, January 19, 2011