Abstract
The new possibilities to construct the stable relativistic compact objects were opened by Ni in 2011, after his discovery of new solution of the Einstein field equations for the spherically symmetric distribution of matter. The solution occurs to be the super-class of the well-known Tolman-Oppenheimer-Volkoff solution published in 1939. In the presented work, we consider the equation of state for a radiation fluid and use the Ni’s solution to construct the massive objects consisting of radiation. We describe their fundamental properties. Since there is no upper constraint of energy/mass of the Ni’s object, the formally calculated gravitational mass (from gravitational effects) of these objects can be as high as observed for the super-massive compact objects in the centers of galaxies and even in the most massive quasars. In the solution by Ni, the gravitational acceleration is not linearly proportional to the energy concentrated in the object. Actually, the models indicate that the objects should be extremely luminous, as quasars. The most massive of them can have enough energy to emit the radiation with a quasar luminosity during the age of the universe. And, it is predicted that they must possess an extremely extended “corona” with the gravitational effects resembling those, which are assigned to a dark matter.
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Notes
The conclusion about the “forbidden point” in the center of hollow sphere may not be true. Unfortunately, its proof or disproof is difficult because the GR is non-linear theory. As mentioned, the metrics in the internal cavity of hollow sphere is shaped by the circumambient matter. If there is a particle in the cavity, the metrics is also influenced by it. For a particle of small mass in a relatively large distance from the center, the shaping by the circumambient matter is dominant. If the particle is moved to be closer to the center, its influence on the metrics in the center increases, but that of the circumambient matter remains the same as before. It is possible that there exists a critical, ultra-short distance of the particle from the central point, within which its gravity dominates over the gravity of the circumambient matter. If this appeared to be true, the metrics of the center would be outer-Schwarzchild non-singular metrics with respect to the particle. The singularity would simply disappear after the particle would cross the critical distance. It would be only an abstract singularity existing exclusively in the mathematical description of the metrics of cavity without any particle.
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Acknowledgements
The author acknowledges the partial support of this work by VEGA—the Slovak Grant Agency for Science (grant No. 2/0031/14).
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Neslušan, L. Outline of the concept of stable relativistic radiation sphere. A model of quasar?. Astrophys Space Sci 362, 48 (2017). https://doi.org/10.1007/s10509-017-3027-x
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DOI: https://doi.org/10.1007/s10509-017-3027-x