Astrophysics and Space Science

, 364:188 | Cite as

Possible distribution of mass inside a black hole. Is there any upper limit on mass density?

  • Michal KřížekEmail author


The maximum mass of a neutron star is about three solar masses. In this case the radius of such neutron star is approximately equal to the Schwarzschild radius. Adding a small amount of matter to this star, a black hole arises. Thus its interior could contain a star with neutron or quark density just below the event horizon instead of the proposed point singularity. We also show that the Hawking miniature black hole evaporation is improbable, since it would yield unrealistic mean mass densities.


Black hole Neutron star Relativistic volume Chandrasekhar limit TOV limit 



The author is indebted to Yurii V. Dumin, Attila Mészáros, Vladimír Novotný, Lawrence Somer, and Vladimír Wagner for fruitful discussions and to Filip and Pavel Křížek for drawing the figures. This paper was supported by RVO 67985840 of the Czech Republic.


  1. Abbott, B.P., et al.: GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119, 161101 (2017) ADSCrossRefGoogle Scholar
  2. Akiyama, K., et al.: First M87 Event Horizon Telescope results. I. The shadow of the supermassive black hole. Astrophys. J. Lett. 875, 1–17 (2019) ADSCrossRefGoogle Scholar
  3. Burgio, G.F., et al.: Maximum mass of neutorn stars with a quark core. Phys. Lett. B 526, 19–26 (2002) ADSCrossRefGoogle Scholar
  4. Ellis, H.G.: Gravity inside a nonrotating, homogeneous, spherical body (2012). arXiv:1203.4750v2
  5. Fahr, H.-J., Sokaliwska, M.: The influence of gravitational binding energy on cosmic expansion dynamics: new perspectives for cosmology. Astrophys. Space Sci. 339, 379–387 (2012) ADSCrossRefGoogle Scholar
  6. Fischer, E.: The definition of density in general relativity. Int. J. Astron. Astrophys. 7, 303–312 (2017) CrossRefGoogle Scholar
  7. Florides, P.S.: A new interior Schwarzschild solution. Proc. R. Soc. Lond. A 337, 529–535 (1974) ADSMathSciNetCrossRefGoogle Scholar
  8. Lattimer, J.M., Prakash, M.: The physics of neutron stars. Science 304, 536 (2004) ADSCrossRefGoogle Scholar
  9. Linares, M., Shahbaz, T., Casares, J.: Peering into the dark side: magnesium lines establish a massive neutron star in PSR J2215 + 5135. Astrophys. J. 859(54), 1–14 (2018) Google Scholar
  10. Patrignani, C., et al.: Particle Physics Booklet. University of California, Berkeley (2016) Google Scholar
  11. Peebles, P.J.E.: Principles of Physical Cosmology. Princeton Univ. Press, New Jersey (1993) zbMATHGoogle Scholar
  12. Schödel, R., et al.: A star in a 15.2-years orbit around the supermassive black hole at the centre of the Milky Way. Nature 419, 694–696 (2002) ADSCrossRefGoogle Scholar
  13. Schwarzschild, K.: Über das Gravitationsfeld einer Kugel aus incompressiebler Flüssigkeit nach der Einsteinschen Theorie. Sitz.ber. Preuss. Akad. Wiss. 1, 424–435 (1916). translation: On the gravitational field of a sphere of incompressible liquid, according to Einstein’s theory. The Abraham Zelmanov Journal 1 (2008), 20–32 zbMATHGoogle Scholar
  14. Steiner, A.W., Lattimer, J.M., Brown, E.F.: The neutron star mass-radius relation and the equation of state of dense matter. Astrophys. J. Lett. 765, L1–L5 (2013) ADSCrossRefGoogle Scholar
  15. Stephani, H.: Relativity: An Introduction to Special and General Relativity, 3rd edn. Cambridge Univ. Press, Cambridge (2004) CrossRefGoogle Scholar

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Institute of MathematicsCzech Academy of SciencesPrague 1Czech Republic

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