This paper consists of four parts. Part one deals with an investigation of the properties of P-equilibrated, electrically charged neutral quark-star matter at zero and finite temperatures, and the determination of its equation of state. In part two, the properties of sequences of quark stars, divided into strange-and charm-quark stars, depending on quark-flavor content, are investigated. The strange stars are constructed for absolutely stable strange-quark matter, whose energy per baryon number lies below the one in 56Fe. In part three, the electrostatic potential of electrons inside and in the close vicinity outside of strange stars, which is of decisive importance for the possible existence of nuclear crusts on the surfaces of such stars, is computed. It is found that finite temperatures lead to a considerable reduction of the electrostatic electron potential at the surface of a strange star, which is accompanied by a strong reduction of the Coulomb barrier associated with the difference of the electrostatic potential at the surface of the star's strange-matter core and the base of the crust. This finding is of great importance for the stable existence of crusts on strange stars, since the Coulomb barrier plays the important role of preventing atomic nuclei bound in the nuclear crust from coming into contact with the star's strange-matter core, where atomic matter by hypothesis would be converted into strange matter. The structure and stability of quark stars against radial oscillations is discussed in part four, where it is found that charm-quark stars are unstable against radial oscillations. Thus no charm-quark stars (and, as is demonstrated too, no quark-matter stars possessing still higher central mass densities) can exist in nature.PACS number(s):

A collection of modern, field-theoretical equations of state is applied to the investigation of cooling properties of compact stars. These comprise neutron stars as well as hypothetical strange matter stars, made up of absolutely stable 3-flavor strange quark matter. Various uncertainties in the behavior of matter at supernuclear densities, e.g., hyperonic degrees of freedom, behavior of coupling strengths in matter, pion and meson condensation, superfluidity, transition to quark matter, absolute stability of strange quark matter, and last but not least the many-body technique itself are tested against the body of observed cooling data.

We study the properties of neutron stars adopting relativistic equations of state of neutron star matter, calculated in the framework of the relativistic Brueckner-Hartree-Fock approximation for electrically charge neutral neutron star matter in beta-equilibrium. For higher densities more baryons (hyperons etc.) are included by means of the relativistic Hartree-or Hartree-Fock approximation. The special features of the different approximations and compositions are discussed in detail. Besides standard neutron star properties special emphasis is put on the limiting periods of neutron stars, for which the Kepler criterion and gravitation-reaction instabilities are considered. Furthermore the cooling behaviour of neutron stars is investigated, too. For comparison we give also the outcome for some nonrelativistic equations of state. I IntroductionA necessary ingredient for solving the structure equations for (rotating) neutron stars (NS) is the equation of state (EOS) [1]. For NSs the EOS has to cover a wide range of densities ranging from super-nuclear densities (up to 5 to 10 times normal nuclear matter density) in the star's core down to the density of iron at the star's surface. At present, neither heavy-ion reactions nor NS data are capable to determine the EOS accurately, and the behaviour of high-density matter is still an open and one of the most challenging problems in modern physics, containing many ingredients from different branches of physics. The theoretical determination of the EOS over such an enormous range has therefore to rely mainly on theoretical arguments and extrapolations for which no direct experimental confirmation exists. The best one can do in such a situation is a step-by-step improvement of the available models for the EOS. Since the central density of a NS is so extreme, both the Fermi momenta and the effective nucleon mass are of the order of 500 MeV, one should prefer a relativistic description [2]- [9].Neutron star matter differs from the high density systems produced in heavy ion collisions by two essential features: a) Matter in high energy collisions is still governed by the charge symmetric nuclear force while neutron star matter (NSM) is bound by gravity. Since the repulsive Coulomb force is much stronger than the gravitational attraction, NSM is much more asymmetric than "standard" matter. b) The second essential difference is caused by the weak interaction time scale of ∼ 10 −10 s, which is small in comparison with the lifetime of the star, but large in comparison with the characteristic time scale of heavy ion reactions. For that reasons "normal" matter is subject to the constraints of isospin symmetry and strangeness conservation, but NSM has to obey the constraints of charge neutrality and generalized beta-equilibrium with no strangeness conservation. It is obvious from these considerations that NSM is an even more theoretical object than nuclear "normal" matter, with a rather complex structure [2]- [9].Due to these features one can adopt the following structure o...

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