An effective chiral Lagrangian in heavy-fermion formalism whose parameters are constrained by kaon-nucleon and kaon-nuclear interactions next to the leading order in chiral expansion is used to describe kaon condensation in dense "neutron star" matter. The critical density is found to be robust with respect to the parameters of the chiral Lagrangian and comes out to be ρ c ∼ (3 − 4)ρ 0 . Once kaon condensation sets in, the system is no longer composed of neutron matter but of nuclear matter. Possible consequences on stellar collapse with the formation of compact "nuclear stars" or light-mass black holes are pointed out.

The main objective of this work is to explore the evolution in the structure of the quark-antiquark bound states in going down in the chirally restored phase from the so-called "zero binding points" T zb to the QCD critical temperature T c at which the Nambu-Goldstone and Wigner-Weyl modes meet. In doing this, we adopt the idea recently introduced by Shuryak and Zahed for charmed cc, light-quark qq mesons π, σ, ρ, A 1 and gluons that at T zb , the quark-antiquark scattering length goes through ∞ at which conformal invariance is restored, thereby transforming the matter into a near perfect fluid behaving hydrodynamically, as found at RHIC. We show that the binding of these states is accomplished by the combination of (i) the color Coulomb interaction, (ii) the relativistic effects, and (iii) the interaction induced by the instanton-antiinstanton molecules. The spin-spin forces turned out to be small. While near T zb all mesons are large-size nonrelativistic objects bound by Coulomb attraction, near T c they get much more tightly bound, with many-body collective interactions becoming important and making the σ and π masses approach zero (in the chiral limit). The wave function at the origin grows strongly with binding, and the near-local four-Fermi interactions induced by the instanton molecules play an increasingly more important role as the temperature moves downward toward T c .

We investigate the soft X-ray transients with black hole primaries, which may have been the sources of gamma-ray bursts (GRBs) and hypernovae earlier in their evolution. For systems with evolved donors, we are able to reconstruct the pre-explosion periods and find that the black hole mass increases with the orbital period of the binary. This correlation can be understood in terms of angular momentum support in the helium star progenitor of the black hole, if the systems with shorter periods had more rapidly rotating primaries prior to their explosion; centrifugal support will then prevent more of its mass from collapsing into the black hole on a dynamical time. This trend of more rapidly rotating stars in closer binaries is usual in close binaries and in the present case can be understood in terms of spin-up during spiral-in and subsequent tidal coupling. We investigate the relation quantitatively and obtain reasonable agreement with the observed mass-period correlation. An important ingredient is the fact that the rapidly rotating new black hole powers both a GRB and the hypernova explosion of the remaining envelope, so that the material initially prevented from falling into the black hole will be expelled rather than accreted. For systems in which the donor is now and will remain in main sequence, we cannot reconstruct the pre-explosion period in detail, because some of their history has been erased by angular momentum loss through magnetic braking and gravitational waves. We can, however, show that their periods at the time of black hole formation were most likely 0.4-0.7 days, somewhat greater than their present periods. Furthermore, their black holes would have been expected to accrete $1 M of material from the donor during their previous evolution. Comparison with predictions suggests that little mass will be lost in the explosion for the relatively high pre-explosion periods of these binaries. A natural consequence of the He star rotation is that black holes formed in the shorter period (before explosion) soft X-ray transients acquire significant Kerr parameters. This makes them good sources of power for GRBs and hypernovae, via the Blandford-Znajek mechanism, and thus supports our model for the origin of GRBs in soft X-ray transients.