Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars

Affiliation(s)

Department of Physics, University of Connecticut, Storrs, CT.

Department of Physics, Trinity College, Hartford, CT.

Department of Physics, University of Connecticut, Storrs, CT.

Department of Physics, Trinity College, Hartford, CT.

ABSTRACT

Research by one of the authors suggested that the critical mass of constant-density neutron stars will be greater than eight solar masses when the majority of their neutrons group into bosons that form a Bose-Einstein condensate, provided the bosons interact with each other and have scattering lengths on the order of a picometer. That analysis was able to use Newtonian theory for the condensate with scattering lengths on this order, but general relativity provides a more fundamental analysis. In this paper, we determine the equilibrium states of a static, spherically-symmetric variable-density mixture of a degenerate gas of noninteracting neutrons and a Bose-Einstein condensate using general relativity. We use a Klein-Gordan Lagrangian density with a Gross-Pitaevskii term for the condensate and an effective field for the neutrons. We show that a new class of compact stars can exist with masses above the Oppenheimer-Volkoff limit, provided the scattering length of the bosons is large enough. These stars have no internal singularities, obey causality, and demonstrate a quantum mechanism consistent with general relativity that could prevent collapsed stars from becoming black holes.

Research by one of the authors suggested that the critical mass of constant-density neutron stars will be greater than eight solar masses when the majority of their neutrons group into bosons that form a Bose-Einstein condensate, provided the bosons interact with each other and have scattering lengths on the order of a picometer. That analysis was able to use Newtonian theory for the condensate with scattering lengths on this order, but general relativity provides a more fundamental analysis. In this paper, we determine the equilibrium states of a static, spherically-symmetric variable-density mixture of a degenerate gas of noninteracting neutrons and a Bose-Einstein condensate using general relativity. We use a Klein-Gordan Lagrangian density with a Gross-Pitaevskii term for the condensate and an effective field for the neutrons. We show that a new class of compact stars can exist with masses above the Oppenheimer-Volkoff limit, provided the scattering length of the bosons is large enough. These stars have no internal singularities, obey causality, and demonstrate a quantum mechanism consistent with general relativity that could prevent collapsed stars from becoming black holes.

Cite this paper

D. Cox, R. Mallett and M. Silverman, "Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars,"*Journal of Modern Physics*, Vol. 3 No. 7, 2012, pp. 561-569. doi: 10.4236/jmp.2012.37077.

D. Cox, R. Mallett and M. Silverman, "Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars,"

References

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[1] J. R. Oppenheimer and G. M. Volkoff, “On Massive Neutron Cores,” Physical Review, Vol. 55, No. 4, 1939, pp. 374-381. doi:10.1103/PhysRev.55.374

[2] F. Weber, R. Negreiros, P. Rosenfield and M. Stejner, “Pulsars as Astrophysical Laboratories for Nuclear and Particle Physics,” Progress in Particle and Nuclear Physics, Vol. 59, No. 1, 2007, pp. 94-113. doi:10.1016/j.ppnp.2006.12.008

[3] C. Bailyn, R. K. Jain, P. Coppi and J. A. Orosz, “The Mass Distribution of Stellar Black Holes,” Astrophysical Journal, Vol. 499, 1998, pp. 367-374.

[4] W. M. Farr, N. Sravan, A. Cantell, L. Kreidberg, C. D. Bailyn, I. Mandel and V. Kalogera, “The Mass Distribution of Stellar-Mass Black Holes,” Astrophysical Journal, Vol. 741, No. 103, 2011.

[5] M. P. Silverman, “Condensates in the Cosmos: Quantum Stabilization of the Collapse of Relativistic Degenerate Stars to Black Holes,” Foundations of Physics, Vol. 37, 2007.

[6] P. B. Demorest, T. Pennucci, S. M. Ransom, M. S. E. Roberts and J. W. T. Hessels, “Two-Solar-Mass Neutron Star Measured Using Shapiro Delay,” Nature, Vol. 467, 2010, pp. 1081-1083.

[7] C. A. Regal, M. Greiner and D. S. Jin, “Observation of Resonance Condensation of Fermionic Atom Pairs,” Physical Review Letters, Vol. 92, 2004, p. 403.

[8] J. Kinast, S. L. Hemmer, G. E. Gehm, A. Turlapov and J. E. Thomas, “Evidence for Superfluidity in a Resonantly Interacting Fermi Gas,” Physical Review Letters, Vol. 92, 2004, p. 150402.

[9] R. Grimm, “Low-Temperature Physics: A Quantum Re- volution,” Nature, Vol. 435, No. 7045, 2005, pp. 1035- 1036. doi:10.1038/4351035a

[10] M. W. Zwierlein, J. R. Abo-Shaeer, A. Schirotzek, C. H. Schunck and W. Ketterle, “Vortices and Superfluidity in a Strongly Interacting Fermi Gas,” Nature, Vol. 435, 2005, pp. 1047-1051. doi:10.1038/nature03858

[11] L. P. Pitaevskii and S. Stringari, “The Quest for Superfluidity in Fermi Gases,” Science, Vol. 298, 2002, pp. 2144-2146. doi:10.1126/science.1080087

[12] W. Greiner, B. Müller and J. Rafelski, “Quantum Electrodynamics of Strong Fields, Texts and Monographs in Physics,” Springer-Verlag, Berlin, 1985.

[13] A. Messiah, “Quantum Mechanics,” Dover Publications, New York, 1999.

[14] L. D. Landau and E. M. Lifshitz, “Classical Theory of Fields,” Butterworth-Heinemann, 2000, p. 292.

[15] M. Colpi, S. L. Shapiro and I. Wasserman, “Boson Stars: Gravitational Equilibria of Self-Interacting Scalar Fields,” Physical Review Letters, Vol. 57, No. 20, 1986, pp. 2485-2488.

[16] R. Ruffini and S. Bonazzola, “Systems of Selfgravitating Particles in General Relativity and the Concept of an Equation of State,” Physical Review, Vol. 187, No. 5, 1969, pp. 1767-1783. doi:10.1103/PhysRev.187.1767

[17] F. Schwabl, “Statistical Mechanics,” Springer, Berlin, 2000.

[18] R. C. Tolman, “Relativity Thermodynamics and Cosmology,” Clarendon Press, Oxford, 1934.

[19] R. Adler, M. Bazin and M. Schiffer, “Introduction to General Relativity,” 2nd Edition, McGraw-Hill Book Company, New York, 1975.