عالم زوجي ضد المادة المظلمة والطاقة المظلمة والثابت الكوني

univers jumeaux contre matiere sombre matiere noire et constante cosmologique

22. **Black holes do not exist. **

Where the black hole model does come from ? From the null second member field equation. Paradoxically such very dense object rises from an equation which was initially built to describe empty regions of the Universe. The Kerr metric does not bring so much : the object becomes more complex, that’s all. Rotation brings an azimutal frame-dragging phenomenon, which means that the speed of light is different if one looks forward or backward with respect to the spinning movement. Whatever is the technique you choose, the things become frankly pathological when you pass the horizon and get in. At the centre lies “the singularity”. Let us start with an exercise. Consider the 2d metric (a). If we consider r as a radial distance and j as a polar angle, we get problems for r < Rs. But if we introduce the change (b) the expression of the metric becomes (c). All pathologies disappear. Moreover this surface can be imbedded in R3 : the meridian equation is (d). See figure 25 where we have figured a geodesic. This illustrates the fact that a pathology can depend on a wrong choice of coordinates and on a wrong choice of topology.

In the 3d example we have computed (plane) geodesics ( see figure 26 ) which are projected on the initial (r,q,j) representation space. We get a “throat sphere” linking two Euclidean 3d spaces. There is nothing inside. Space for r < Rs has no physical meaning. If we would try to compute geodesics in that place, we would find an imaginary solution.

Fig. 25 : 2d metric of a surface with a “bridge” linking two folds.

Fig. 26 : 3d metric hypersurface with a “space bridge”. Geodesics.

Classically, one introduce a proper time s (j) and a “time-coordinate t (i). Then the study of radial geodesics gives two differential equations (k) and (l), whose solutions correspond to curves (m), fig. 6.2, reference [52].

The curves shown on figure (m) are the basis of the black hole model. One identifies the coordinate t to the proper time of a “distant observer” so that the free fall time of a test particle, towards the Schwarzshild Sphere become infinite for him. Let us show that this is completely due to this peculiar choice of time coordinate. In [54] 1925 Eddington suggested a new time-marker (p).

Following, the study of corresponding radial geodesics.

We use Lagrange equations. On the right we see that the speed of light, following radial paths has two values. ( nu = - 1 ) corresponds to centripetal paths : the speed has a constant value – c. Similarly (left) the transit time from a distant point to the Schwarzschild sphere depends on the orientation of the paths. Centripetal ( nu = - 1 ) free fall time is achieved in finite time interval Dt . Oppositely a centrifugal path ( nu = + 1 ), starting from the Schwarzschild sphere gives an infinite time interval, so that the Schwarzschild sphere works like a one-way membrane. This corresponds to a radial frame-dragging effect. This is not a reason to reject this interpretation of the Schwarzschild geometry. In effect we find a similar phenomenon in the Kerr metric ( azimutal frame-dragging). Next, the classical expression of the Kerr metric. We see that we get two distinct values for azimutal speed of light. Depends if we consider light following the rotation or going backwards.

We can give a new interpretation of the Schwarzschild geometry, through a space-bridge linking two folds F and F. If the fold F corresponds to the twin fold, the time coordinate t = - t ( T-symmetry). From section 19 we know that this T-symmetry goes with a mass-inversion, so that when a positive mass passes through the Schwarzschild sphere, considered as a throat surface, the sign of it becomes negative. The conjugated geometry, as presented in section 13 corresponds to change Rs into – Rs. Then we introduce the following Eddington-like time marker change :

Still using Lagrange’s equation we study the radial geodesics system and build a link between the two folds.

But the inverse paths requires an infinite time, so that it is a one-way passage from a Universe to the other. Here again we find a frame-dragging effect, in the opposite direction.

During the transit the proper time flow is unchanged : ds > O . This makes the black hole model questionable. In effect, according to this new interpretation of the Schwarzschild geometry such space bridge can swallow in a very short time ( » 10-4 sec) unlimited amounts of matter. By the way, an analysis based on the Kerr metric, although a little bit more complicated gives similar results.

Following, the solution of the geodesic systems.

How to figure such paths ? We can use the initial ( r , q , j ) representation space. Then we get the above system of differential equations and the schema of figure 27 .

Fig.27 : Income and outcome geodesics.

The geodesic seems to “bounce” on the Schwarzschild sphere, as shown of figure 28 too.

** **

But all that comes from such naïve Euclidean representation of the path. Using the following change of space marker :

The expression of joint metrics become :

Fig. 29 : Didactic image of a fast flow space bridge.

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