SUN - BLACK HOLE - LIGHT OF BALL OR OR NORMAL SUN

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The black hole in the Kerr solution rotates. Its axis of rotation determines a particular direction in space, so that space-time turns out to be curved differently depending on the angle to the axis of rotation. The geometry of the space is axisymmetric, and not spherically symmetric as in the black Schwarzschild hole. This complication leads to radical changes in the character of circular orbits of light rays.

To understand the location of the orbits of light around the Kerr black hole, imagine that we are looking along the axis of rotation towards the black hole on the rays of light that go to it in the equatorial plane.

Orbits around the light of the Kerr black hole (in its equatorial plane).

Fig.4 Orbits around the light of the Kerr black hole (in its equatorial plane). Those rays of light that travel far from a rotating black hole deviate only to small angles. A beam of light approaching a hole with the desired value of the impact parameter can travel in a circular orbit around this hole. But in the equatorial plane there are two unstable circular orbits of light. The outer orbit contains rays with reverse rotation, while the inner orbit contains rays with an inverse rotation.

As can be seen from Fig. 4, rays of light passing far from the hole (i.e. for large impact parameter values) deviate only slightly. When the impact parameter has a strictly defined value, a ray of light, and in this case can go in a circular orbit around the black hole. However, now there are two possibilities. If a ray of light approaches a black hole on one side, it can be caught in an unstable circular orbit through which it turns in the direction opposite to the direction of rotation of the hole. Such a circular orbit with reverse rotation is located at a greater distance from the black hole than the photon sphere in the Schwarzschild case.

If, however, the ray of light approaches a black hole on the other side, it can be captured in an unstable circular orbit, but now the beam is reversed in the same direction as the hole itself rotates. Such a circular orbit with a direct rotation is located much closer to the hole - closer than the photon sphere in the Schwarzschild case.

Analysis of the behavior of light rays in the equatorial plane shows that there are two circular orbits - the inner one, along which light turns to the same side as the black hole rotates, and the outer one, along which the light turns in the opposite direction. We can say that when the Schwarz-Schild black hole acquires a moment of momentum, the photon sphere "splits" into two. Between the orbits with forward and reverse rotation in the equatorial plane, there are many unstable circular orbits for light rays. These orbits correspond to the light rays coming to the black hole from different directions, not lying in the equatorial plane.

In order to understand what happens outside the equatorial plane, consider the light rays approaching the black hole parallel to its axis of rotation. Figure 5 shows the trajectories of such rays in the vicinity of the limiting black hole (M = a), calculated by C T. Cunningham.

Orbits of light around the Kerr black hole (parallel to the axis of rotation).

Fig.5 Orbits of light around the Kerr black hole (parallel to the axis of rotation). Those rays of light that travel far from a rotating black hole deviate only to small angles. For a beam of light coming to a hole parallel to its axis of rotation, there is only one possible circular orbit. (The diagram is constructed for the limiting Kerr solution when M = a.)

If Figure 4 shows a "top view", namely orbits lying in the equatorial plane, then Fig. 5 is a "side view" of the orbits of light rays in a plane passing through an axis around which a black hole rotates.

As always, the rays of light, passing far from the black hole, deviate only at small angles. Rays whose impact parameters are smaller (that is, which pass closer to the axis of rotation) are deflected more strongly. Now among all the values ​​of the impact parameter there is only one, at which light is captured into a circular orbit around the hole (Fig. 5). Thus, for rays approaching a black hole parallel to its rotation axis, there is only one unstable circular orbit. This orbit is from the black hole at distances intermediate between the distances for the orbits in the equatorial plane with forward and reverse rotation.

So, around the black hole there are many different unstable circular orbits of light rays. The furthest of them is a circular orbit with reverse rotation in the equatorial plane. The closest is a circular orbit with a direct rotation, again in the equatorial plane. Between these two limits there are various possible orbits of light rays that have approached the black hole at different angles. For each given angle there will be orbits, with both forward and reverse rotation, except for those rays that came parallel to the axis of rotation. For a beam of light that has approached a black hole parallel to its axis of rotation, there is only one circular orbit.

If the black hole rotates slowly, then the spread of circular orbits is small. All possible orbits are located near each other above the outer horizon of events at distances close to the position of the Schwarzschild photon sphere (which would exist if the hole did not rotate). With a faster rotation of the black hole, the distance between the orbits in the equatorial plane with forward and reverse rotation becomes larger. Accordingly, the spread of the radii of circular orbits increases. The greatest possible dispersion occurs for the limiting Kerr black hole (when M = a).

Spread of circular orbits of light near a rapidly rotating black hole.

Fig. 6 Spread of circular orbits of light near a rapidly rotating black hole. All possible circular orbits of light near the Kerr black hole (for a ~ 90% M) lie within the boundaries shown here. Each ray of light traveling in a circular orbit is highly curved, remaining on the surface of an ellipsoid within the specified boundaries.

For a visual representation of the scatter of circular orbits of light - near a rotating black hole, it is most convenient to depict the enveloping surface of all such orbits, consisting of two parts - the outer and the inner ones.

In Fig. 6 shows the cross-section of the envelope surface of all possible circular orbits around a rapidly rotating Kerr hole (a ~ 90% M). Each ray of light moves in a very complex manner along the surface of the elliptical ring within these boundaries. If the angular momentum of the black hole is lost as the rotation slows down, the volume enclosed between the parts of the envelope surface must also decrease. When the rotation is completely stopped, the entire envelope surface becomes the photon sphere of the Schwarzschild black hole.

So far we have only touched on what happens outside the Kerr black hole.

To get acquainted with the geometry inside such a hole, imagine that we sent a light beam with an impact distance less than that required for capture into a circular orbit. Figure 7 shows light rays that approach the Kerr black hole parallel to its axis of rotation, the value of the impact parameter being less than required to capture the beam into a circular orbit. Fig. 7 and is based on Cunningham calculations. Let us note the important fact that the trajectories of these light rays near the center of the black hole turn and go from the singularity. If away from the Kerr black hole gravity causes attraction and drags all the bodies inward, then near the singularity it acts as a repulsion force and tends to push them out! Those rays of light that are aimed directly at the ring, deviate the most - such rays literally bounce off a black hole. This "repulsive" nature of the Kerr singularity means that at some distance from the center of the hole the gravitational repulsion balances the gravitational attraction.

Trajectories of light rays inside the Kerr black hole.

Fig. 7 Trajectories of light rays inside the Kerr black hole. Those rays of light that are directed at a rotating black hole with a smaller value of the impact parameter than for a circular orbit fall into the hole. The type of trajectories of light rays deep inside the hole shows that the singularity repels the light rays. Near the singularity, the rays of light experience the effect of antigravity. (The scheme is constructed for the limiting Kerr solution when M = a.)

Hence, circular orbits of light will again appear in this neutral region! Figure 8 shows the boundaries of all possible circular orbits of light deep below the inner horizon of events. Unlike the outer light orbits around the black hole, in the inner region there can be not only unstable but also stable orbits. Therefore, the singularity of the Kerr black hole is surrounded by light rays.

To explore the deepest areas of the Kerr black hole, imagine that we send rays of light parallel to the axis of rotation and very close to it, so that the value of the impact parameter for these light rays is less than what is needed to hit the ring singularity. Therefore, the rays of light, moving along the axis of rotation or close to it, will pass through the ring into the negative space.

Let us consider the passage of light rays through the singularity, first of all, that the rays deviate away from the edges of the ring.

The spread of pendular circular orbits of light in a negative space (r <0)

Fig. 8. The spread of pendular circular orbits of light in a negative space (r <0). All possible pendulum circular orbits near the singularity of the Kerr black hole (for a = 90% M) lie within the boundaries shown in the diagram. Inside this area of ​​negative space, light rays bounce back and forth along an ellipsoidal surface.

This is due to gravitational repulsion near the singularity. A part of the rays of the set according to Fig. 7 can dive for a moment into a negative space and return from there. They form circular pendular orbits in the negative space of the Kerr black hole (Fig. 8).

Finally, consider the ray of light that comes to the Kerr singularity from the negative universe. Those of them that go along the axis of rotation or very close to it, directly fall into the positive space through the annular singularity. However, as shown in Fig. 9, all rays of light, which when approaching a black hole with large values ​​of the impact parameter, repel it. When viewed from a negative space, the hole turns out to be a source of anti-gravity. She pushes everything away from herself and attracts nothing . This is why the negative universe is sometimes called the "world of antigravitation."

The rays of light coming from the negative space.

Fig.9 The rays of light coming from the negative space. Approaching the rotating black hole from the negative space, the rays of light are repelled by this hole. In a negative space, a rotating black hole is the source of antigravity. (The scheme is constructed for the limiting Kerr solution when M = a.)

Now, after we have considered in detail the course of the various trajectories of light rays near the Kerr black hole, we can imagine what a rotating black hole will look like for a remote astronomer. On what side astronomers from the Earth would not watch, from the space station - from any direction and distance a black hole - the Sun will outwardly look like a glowing ball.

Conclusion 1. Material objects, accelerating to the speed of light when falling onto a black hole - the Sun, turn into energy - radiation according to the Einstein formula e = mc2 and create, according to Kerry's solution for black holes, a glowing sphere with a radius of 696 thousand km., That is our The usual Sun.

Authors: Gordeev SI, Voloshina VN 28-07-2003



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