排斥物质
排斥物质（第4页）
6）对观测到的强引力透镜效应的另一种解释。
负引力透镜。
...当一个（正）质量m存在于褶皱F中时，它会改变褶皱F的几何结构。如参考文献[6]首次所展示的，褶皱F相邻部分的几何结构，解方程：
(19) S = 0
可以用施瓦茨希尔德解来描述：
(20)
其中常数v为负数。
(21)
...质量m存在于褶皱F中，它吸引质量m*，排斥另一褶皱F中的质量，其测地线为双曲线型。
(22)
可以计算零测地线。
j = 极坐标。q = 1/r。b和h是轨迹参数。零测地线为：
(22)
光线路径为双曲线型，对应图6。我们得到了负引力透镜。
图6：在褶皱F中由于位于褶皱F中的质量m*的存在而产生的负引力透镜。
...在图7中，我们以示意图的方式展示了光线路径，这些路径由于褶皱F中非均匀质量分布r的作用而聚焦，从而增强了由于星系产生的正引力透镜。如果光子穿过均匀介质，其轨迹是直线。
图7：由于星系和周围排斥物质的共同作用而弯曲的光线路径示意图。
...传统上，人们将观测到的强引力透镜效应视为我们宇宙中存在吸引物质的证据。我们建议这可能主要是由于基本不可见的排斥物质，这些物质包围着可见结构（更准确地说，是这些排斥物质的梯度，在星系附近）。
结论。
...我们认为宇宙是两种物质群体（正常物质m和排斥物质m*）相互作用的场所，系统的动力学对应于：
-
m吸引m
-
m吸引m
-
m和m*相互排斥
根据牛顿（和反牛顿）定律。因此，排斥物质的行为就像它拥有负质量（和负能量）一样。我们构建了一个位于某种“洞”中的星系模型，该“洞”被周围的排斥物质环境所包围并限制。我们证明，此时可以得到令人满意的旋转曲线。
...我们通过引入一个新的几何框架避免了负质量和负能量的问题：宇宙由两个褶皱组成，被认为是“骨架流形”的双叶覆盖，提供了一个将两个共轭点（M, M*）联系起来的对合映射。褶皱F的几何由度规g描述，褶皱F的几何由度规g描述。这两个度规通过一组耦合的场方程联系起来。从几何角度看，位于一个褶皱中的任何结构在另一个褶皱中都是不可见的。我们构建了一个宇宙学模型，假设两个宇宙是均匀和各向同性的。在辐射时期，我们假设质量密度ρ和ρ以及压强p和p分别相等。此时模型就等同于标准模型。当物质（和排斥物质）在两个褶皱中占主导地位时（我们假设两个世界同时发生解耦），两个演化过程不同：一个宇宙（假设是我们的宇宙）比另一个宇宙膨胀得更快。排斥物质世界对我们宇宙演化的影响类似于在爱因斯坦场方程中引入宇宙常数，这使得我们可以将宇宙的年龄与最近的哈勃常数测量结果相匹配。当当前质量密度比ρ*/ρ = 64时，我们得到的宇宙年龄为157亿年。
...由于几何上不可见的周围排斥物质的梯度而产生的负引力透镜，可以产生与由于吸引物质产生的引力透镜相同的效果。
参考文献。
[1] M. Myamoto 和 R. Nagai, Publ. Astron. Soc. Japan 27, 583, 1975
[2] S. Chandrasekhar : Ellipsoidal Figures of Equilibrium. Yale University Press, New Haven 和 London, 1969
[3] J. Binney 和 S. Tremaine, Galactic Dynamics, Princeton University Press, Princeton, 1987.
[4] Bahcall J.N. & Soneira R.M., APJ. S 44, p. 73, 1980
[5] Bahcall J.N., Flynn A. 和 Gould A., APJ 389, p. 234, 1992
[6] Petit J.P. : The missing mass effect. Il Nuovo Cimento B, 第109卷，1994年7月，第697–710页
[7] Petit J.P. : Twin Universe Cosmology. Astr. And Sp. Sc. 226, 273–307, 1995
致谢：
作者感谢J.M. Souriau教授的有益建议和评论。
本研究由法国CNRS和A. Dreyer专利与开发公司资助。
1998年密封提交至巴黎科学院。
原始版本（英文）
repulsive dark matter
Repulsive dark matter (p4)
6) An alternative interpretation of the observed strong gravitational lensing effects.
Negative gravitational lensing.
...When a (positive) mass m* is present in the fold F*, it shapes the geometry in the fold F*. As presented first in reference [6] the geometry in the adjacent portion of the fold F , solution of the equation :
(19) S = 0
can be described by a Schwarzschild solution :
(20)
where the constant v is negative.
(21)
...The mass m*, present in the fold F*, where it attracts a mass m*, repels a mass of the other fold F, the geodesic being hyperbola-like.
(22)
The null geodesics can be calculated.
j = polar coordinate. q = 1/r . b and h are trajectory parameters. The null geodesics are :
(22)
The light pathes, hyperbola like, correspond to figure 6. We get a negative gravitational lensing.
Figure 6 : Negative gravitational lensing, in the fold F due to the presence of a mass m, located in the fold F.**
...In figure 7 we have schematically figured light paths, focussed by the action of a non-homogeneous mass distribution r* of the fold F*, reinforcing the positive gravitational lensing due to the galaxy. The photon trajectory is straight if it travels through an homogenous medium.
Fig. 7 : Schematic ligth paths bending, due to the combined actions of the galaxy and surrounding repulsive dark matter.
...Classically one considers the observed strong gravitational lensing effects as a proof of the existence of attractive dark matter in our Universe. We suggest this could be mainly due to basically invisible repulsive dark matter, surrounding the visible structures (more precisely to the gradient of the repulsive dark matter, at the vicinity of the galaxies).
Conclusion.
...We consider the Universe as the site of interaction of two populations : normal matter m and repulsive dark matter m*, the dynamics of the system corresponding to :
-
m attracts m
-
m* attracts m* - m and m* mutually repel
through newtonian (and anti-newtonian) laws. Then the repulsive dark matter behaves as if it owned negative mass (and negative energy). We build a model of a galaxy located is some sort of a hole, in a surrounding repulsive dark matter environment, which confines it. We show that we refind good looking rotation curves.
...We avoid the problem of the negative mass and negative energy, introducing a new geometric framework, the Universe being composed of two folds, considered as the two-fold cover of a "skeleton manifold", which provides an involutive mapping linking two conjugated points (M,M*). The geometry of the fold F is described by a metric g and the one of the fold F* by a metric g*. Both are linked through a system of two coupled field equations. On geometrical grounds, any structure located in a fold is invisible from the second one. We build a cosmological model, assuming that the two universes are homogeneous and isotropic. During the radiative era we assume the mass densities r and r* and the pressures p and p* are respectively equal. Then the model identifies to the standard one. When matter (and repulsive dark matter) dominate in both folds (we assume decoupling occurs at the same moment in both worlds), the two evolutions are different. One universe (supposed to be ours) expands faster than the other one. The impact of the repulsive dark matter world on the evolution of ours is similar to the introduction of a cosmological constant in the Einstein field equation, so that it makes it possible to adjust the age of the Universe to recent measures of the Hubbles constant. With a todays mass-density ratio r*/r = 64 we find an age equal to 15.7 billions years.
...Negative gravitational lensing, due to the gradient of geometrically invisible surrounding repulsive dark matter may induce the same effect as the gravitational lensing attributed to attractive dark matter.
References.
[1] M.Myamoto and R.Nagai Publ. Astrom. Soc. Japan 27, 583, 1975
[2] S.Chandrasekhar : "Ellipsoidal Figures of Equilibrium". Yale University Press, New Haven and London, 1969
[3] J.Binney and S.Tremaine, "Galactic Dynamics", Princeton University Press, Princeton, 1987.
[4] Bahcall J.N & Soneira R.M. APJ. S** 44** p. 73 1980
[5] Bahcall J.N. , Flynn A and Gould A. APJ 389 p.234 1992
[6] Petit J.P.: The missing mass effect. Il Nuovo Cimento B Vol. 109 July 1994, pp. 697-710
[7] Petit J.P. : Twin Universe Cosmology. Astr. And Sp. Sc. **226 **: 273-307, 1995
Achnowledgements :
The author thanks Pr. J.M.Souriau for useful advices and comments.
This work is supported by the french CNRS and by the A. Dreyer Brevets et Développement company.
Déposé sous pli cacheté à l'Académie des Sciences de Paris, 1998.