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Condensates in the Cosmos: Quantum Stabilization of the Collapse of Relativistic Degenerate Stars to Black Holes

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According to prevailing theory, relativistic degenerate stars with masses beyond the Chandrasekhar and Oppenheimer–Volkoff (OV) limits cannot achieve hydrostatic equilibrium through either electron or neutron degeneracy pressure and must collapse to form stellar black holes. In such end states, all matter and energy within the Schwarzschild horizon descend into a central singularity. Avoidance of this fate is a hoped-for outcome of the quantization of gravity, an as-yet incomplete undertaking. Recent studies, however, suggest the possibility that known quantum processes may intervene to arrest complete collapse, thereby leading to equilibrium states of macroscopic size and finite density. I describe here one such process which entails pairing (or other even-numbered association) of neutrons (or constituent quarks in the event of nucleon disruption) to form a condensate of composite bosons in equilibrium with a core of degenerate fermions. This process is analogous to, but not identical with, the formation of hadron Cooper pairs that give rise to neutron superfluidity and proton superconductivity in neutron stars. Fermion condensation to composite bosons in a star otherwise destined to collapse to a black hole facilitates hydrostatic equilibrium in at least two ways: (1) removal of fermions results in a decrease in the Fermi level which stiffens the dependence of degeneracy pressure on fermion density, and (2) phase separation into a fermionic core surrounded by a self-gravitating condensate diminishes the weight which must be balanced by fermion degeneracy pressure. The outcome is neither a black hole nor a neutron star, but a novel end state, a “fermicon star,” with unusual physical properties.

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References

  • Whitney B. (2005). Nature 437: 37

    Article  ADS  Google Scholar 

  • Krumholz M.R., McKee C.F., Klein R.I. (2005). Nature 438: 332

    Article  ADS  Google Scholar 

  • C. E. Rolfs and W. S. Rodney, Cauldrons in the Cosmos: Nuclear Astrophysics (University of Chicago Press, Chicago, 1988), p. 117.

  • S. Chandrasekhar, M.N.R.A.S. 95, 91 (1931); Ap. J. 74, 81 (1931).

  • Oppenheimer J.R., Volkoff G.M. (1939). Phys. Rev. 55: 374

    Article  MATH  ADS  Google Scholar 

  • C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, San Francisco, 1973), p. 823. Note that the authors employ so-called “natural units” in which \({G = c = \hbar =1}\) . The Schwarzschild radius is then 2M where M is the stellar mass.

  • Whitehead A.N. (1953). Alfred North Whitehead: An Anthology. Macmillan, New York

    Google Scholar 

  • Silverman M.P. (2004). Int. J. Mod. Phys. D 13: 2281

    Article  MATH  ADS  Google Scholar 

  • Silverman M.P. (2005). Int. J Mod. Phys. D 14: 2285

    Article  MATH  ADS  Google Scholar 

  • Hawking S.W. (1974). Nature 248: 30

    Article  ADS  Google Scholar 

  • M. Bojowald et al., Phys. Rev. Lett. 95, 091302-1 (2005).

  • C. A. Regal et al., Phys. Rev. Lett. 92, 040403 (2004).

  • Grimm R.(2005). Nature 453: 1035

    Article  ADS  Google Scholar 

  • Zwierlein M.W. et al. (2005). Nature 453: 1047

    Article  ADS  Google Scholar 

  • J. Kinast et al. Phys. Rev. Lett. 92: 150402-1 (2004).

  • Levi B.G. (2003). Phys. Today 56: 18

    Google Scholar 

  • Pitaevskii L., Stringari S. (2002). Science 298: 2144

    Article  Google Scholar 

  • O’Hara K.M. et al. (2002). Science 298: 2179

    Article  ADS  Google Scholar 

  • J. Kinast et al.(2005). Science 307: 1296

    Article  ADS  Google Scholar 

  • Pines D., Alpar M.A.(1985). Nature 316: 27

    Article  ADS  Google Scholar 

  • B. Link, Phys. Rev. Lett. 91, 101101 (2003).

    Google Scholar 

  • M. P. Silverman, Gravity Research Foundation 2006 Honorable Mention Award Essay.

  • M. P. Silverman , quantum stabilization of relativistic degenerate stars and galactic dark matter,” Lecture presented at the Conference on Relativistic Dynamics of Particles and Fields, University of Connecticut, Storrs, 2006.

  • A. G. W. Cameron, Can. J. Phys. 35, 1021 (1957); Ap. J. 129, 676 (1959); Ap. J. 130, 884 (1959).

  • Ingrosso G., Grasso D, Ruffini R. (1991). Astron Astrophys. 248: 481

    ADS  Google Scholar 

  • Li G.Q., Lee C.-H., Brown G.E. (1997). Phys. Rev. Lett. 79: 5214

    Article  ADS  Google Scholar 

  • M. P. Silverman, “Fermion condensation in a stellar black hole,” Gravity Research Foundation 2006(Honorable Mention Essay); Int. J. Mod. Phys. D (to be published).

  • M. P. Silverman, “Condensates in the cosmos: quantum stabilization of degenerate stars and dark matter,” presented at 2006 Biennial Meeting of the International Association for Relativistic Dynamics, University of Connecticut, Storrs CT, 12–14 June 2006.

  • L. Landau and L. Lifshitz, op. cit. 170.

  • Silverman M.P., Mallett R.L., Gen. Relat. (2002). Gravit 34: 633

    Article  MATH  Google Scholar 

  • Silverman M.P. (2002). A Universe of Atoms, An Atom in the Universe. Springer, New York

    Google Scholar 

  • Zwierlein M.W., Schunck C.H., A. Schirotzek, W. Ketterle (2006). Nature 442: 54

    Article  ADS  Google Scholar 

  • Gross E.P., Nuovo Cimento 20, 454 (1961); J. Math. Phys.4: 195 (1963).

    Google Scholar 

  • Pitaevskii L.P. (1961). Sov. Phys. JETP 13: 451

    MathSciNet  Google Scholar 

  • Pitaevskii L.P., Stringari S. (2003). Bose-Einstein Condensation. Oxford, New York

    MATH  Google Scholar 

  • Foot C.J. (2005). Atomic Physics. Oxford, New York, 234–235.

    Google Scholar 

  • Greiner W., Neise L., Stocker H. (1994) Thermodynamics and Statistical Mechanics. Springer, New York, 320.

    Google Scholar 

  • Pethick C.J., Smith H. (2002). Bose–Einstein Condensation in Dilute Gases. Cambridge University Press, New York, 21.

    Google Scholar 

  • A. Bulgac, Drut J.E., and P. Magierski, Phys. Rev. Lett. 96: 090404 (2006).

    Google Scholar 

  • Greiner W. et al (1995). Thermodynamics and Statistical Mechanics. Springer, New York, 358.

    MATH  Google Scholar 

  • Misner C., Thorne K., Wheeler J. (1973). Gravitation. Freeman, San Francisco, 604.

    Google Scholar 

  • Harrison B., Thorne K., Wakano M., Wheeler J. (1965). Gravitational Theory and Gravitational Collapse. University of Chicago Press, Chicago, 99.

    Google Scholar 

  • In this regard it is interesting to note that Schroedinger initially failed in describing the hydrogen atom by a relativistic quantum theory, but succeeded brilliantly only when forced to revert to what at the time may have seemed to him a less inclusive nonrelativistic approach.

  • Schwarzschild M. (1958). Structure and Evolution of the Stars. Dover, New York, 96.

    Google Scholar 

  • Schaab C. et al. (1998). Astron. Astrophysics 335: 596

    ADS  Google Scholar 

  • C. J. Pethick and H. Smith, op. cit. 106.

  • Gravitational potential energy is not included in the chemical potential, because, in accordance with the equivalence principle, one can always consider chemical equilibrium in a local Lorentz frame where gravity vanishes.

  • J. J. More, B. S. Garbow, and K. E. Hillstrom, User’s Guide to Minpack I, Argonne National Laboratory publication ANL-80–74 (1980), cited in Mathcad Plus 6 User’s Guide(MathSoft Inc, Cambridge MA, 1996), p. 601.

  • H. Heiselberg, Phys. Rev. A 63, 043506 (2001).

    Google Scholar 

  • If the hypothesized fermion condensation process did not occur, and a neutron star collapsed to the density in which the mean interparticle separation is the Compton wavelength \({\mathchar'26\mkern-10mu\lambda_{n}}\) , then the Fermi parameter would be \({y_F =\left( {3\pi ^2} \right)^{1/3}\sim 3.094}\) , which is highly relativistic.

  • K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Denschlag, A. Daley, A. Kantian, H. Buechler, and P. Zoller, Nature 441, 853 (2006).

    Google Scholar 

  • Several quark stars may possibly have been found by the Chandra and Hubble space telescopes; see (a) J. Drake et al., Ap. J. 572, 996 (2002), and (b) R. X. Xu, Ap. J.570, L65 (2002).

  • Glendenning N.K. (1992). Phys Rev. D 46: 1274

    Article  ADS  Google Scholar 

  • Duncan R.C., Shapiro S.L., Wasserman I. (1983). Ap. J. 267: 358

    Article  ADS  Google Scholar 

  • Silverman M.P. (2004). Int. J. Mod. Phys. D 13: 2281

    Article  MATH  ADS  Google Scholar 

  • L. Chandrasekhar, “Our song,” in Black Holes and Relativistic Stars, R. M. Walded. (University of Chicago Press, Chicago, 1998), p. 274.

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Silverman, M.P. Condensates in the Cosmos: Quantum Stabilization of the Collapse of Relativistic Degenerate Stars to Black Holes. Found Phys 37, 632–669 (2007). https://doi.org/10.1007/s10701-007-9121-0

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