# 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).

## Geometry-Generating Function

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.

## Remarks

• 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.

## Conclusions

• 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 experimental test.

• 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