Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars
- 1 Department of Physics, University of Connecticut, Storrs, CT
- 2 Department of Physics, University of Connecticut, Storrs, CT
- 3 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.
- 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
- 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
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- R. Grimm, “Low-Temperature Physics: A Quantum Re- volution,” Nature, Vol. 435, No. 7045, 2005, pp. 1035- 1036. doi:10.1038/4351035a
- 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
- 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
- W. Greiner, B. Müller and J. Rafelski, “Quantum Electrodynamics of Strong Fields, Texts and Monographs in Physics,” Springer-Verlag, Berlin, 1985.
- A. Messiah, “Quantum Mechanics,” Dover Publications, New York, 1999.
- L. D. Landau and E. M. Lifshitz, “Classical Theory of Fields,” Butterworth-Heinemann, 2000, p. 292.
- 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.