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What has the gravitational lens become?


Gravitational lenses are induced by massive objects. They can appear under varius forms, especially in the form of "caustic".
In some of its effects, gravitational optics is very close to conventional optics. It is through this phenomenon of caustic that exoplanets can be detected.


Detection of an exoplanet

During the transit of a planet through a caustic generated by the mass of its star, its light is amplified and this variation of luminosity, although weak, is measurable.

Thus, January 25th, 2006, ESO announces the discovery of exoplannet OGLE-2005-BLG-390 by observing the luminosity change due to the passage of this planet in a caustic due to microlensing associated with its star.



  • Could we see the same phenomenon between a super massive black hole and the stars that revolve around?

  • Then would we also see some visible deformations of the stars elliptic trajectories by these lens effects?

  • Were these phenomena already observed?


In the the Milky Way Center, Saggitarius A would host a Black Hole 4 million solar masses.
The black hole was "confirmed" by

  1. X ray luminosity variations of Saggitarius A which would be explained by the accretion of matter (accretion disc) to the black hole.

  2. Some 511 Kev emissions, evident marks of the presence of antimatter.


Source: ESO

Around this black hole revolve numerous stars which it was possible to observe the movements (infrared light).
A Mpeg animation is available by clicking on the picture opposite.
These are the elliptical trajectories and velocities of these stars that have enabled mass measurement of Saggitarius A.

It is found that:

  1. The trajectories of stars are perfectly elliptic.

  2. None of this star seems to manifest in their trajectories, a significant brightness variation may reveal the passage in a caustic and therefore the presence of a gravitational lens.

What have become the caustics ?


A three dimensionnal reconstruction of the trajectories of these stars, realized in the mpeg format by l'UCLA Division of Astronomy and Astrophysics, is available by clicking on the image opposite.

This reconstruction also shows the perfect elliptic orbits.

Note that, due to the laws of relativity, additional observations should reveal important variation of the perihelion of these stars. These variations should confirm the mass of the Black Hole.

The 1st law of Képler and its generalization

Star Orbiting Massive Milky Way Centre

In the heliocentric reference frame, the orbit of each planet is an ellipse with one focus is occupied by the sun.
We can express this by saying that otherwise the sun and the planets are rotating around their common center of gravity, which is located near the center of the Sun, so inside it.
The same goes for stars rotating in the galactic center.
But for two objects, having masses of the same order, the centre of gravity is situated outside of these two objects.
Both foci can be very close, they can even merge. (Circular orbits).
Everything takes place as if these two objects turned around a virtual object at their centre of gravity.
If you add a star they always revolve around their common center of gravity. Then adding N stars, we have a set of stars that always revolve around their common center of gravity, ie around a virtual object!

The star cluster, M 13

We then have the illusion of the presence of a super massive object at the center of a star cluster. (Open or globular clusters)

A Virtual Massive Object would thus manifest itself in the centre of the Milky Way.

Can a virtual object of 4 million solar masses induce a gravitational lens?

Yes because the apparent gravitational field is the same as if this mass were physically present in the center of the star cluster. The trajectories and speeds of stars demonstrate this.

Let us note that the mass-luminosity relation of this virtual object would be unconventional !

This does not remind you of dark matter story?

Question :

Is there a black hole in the center of globular clusters?

Considering the ages of the known globular clusters (10 billion years), the density of stars and the probability of star collisions, a black hole should be present in the majority of them. But it seems  not be the case.

A Virtual Massive Object would manifest it in globular clusters?

  • Detection of the the Xray discovered is not the proof of the existence of a Black Hole. There are other possibilities.

  • Neither is the 511 Kev radiation a proof of the presence of a Black Hole. Other causes are possible.

  • The gravitational Field being equivalent in both cases, a variation of the périhélions of the orbits would also not be a proof in favour of the Black Hole.

  • For the same reason, gravitational lens effects would not also be a proof.

In all globular clusters and in all galactic centres we can be in the same ambiguous situation.

But indeed we are in the presence of a

But this does not mean that Black Holes don't exist:

  §  In the case of Sgr A* The ambiguity had already been lifted October 16, 2002 in a publication of the ESO:
The motion of a star around the central black hole in the milky way. The star "S2", which can be seen against the following path passed in 2002 with a speed of 5000 km/s to 17 light-hours of Sgr A * (less than three times the Sun-Pluto distance). This measure clearly shows that it is indeed a black hole, and not a globular cluster. (Source: Dr. Suzy Collin Zahn in an article published in Astronomy N° 70 / March 2014 - pages 20-29 (SAF).

And in other galaxies ?

Source: ESO
Trajectoires des étoiles autour de Sgr A


  1. The central black hole of our Galaxy.
  2. Detection of hard X-ray emission from the Galactic  nuclear region with INTEGRAL.
  3. The source of antimatter from the galactic center.
  4. Early SPI/INTEGRAL measurements of galactic 511 keV line. emission from positron  annihilation.
  5. Early SPI/INTEGRAL contraints on the morphology of the 511 keV line emission in the 4th galactic quadrant.
  6. Hypernovae/GRB in the Galactic Center as possible sources of Galactic Positrons.

Creation date: 06/14/2007
Last release: 10.04.2016 (P. Schuler)

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