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.Abstract The energy release L s on the surface of a neutron star (NS) with a weak magnetic field and the energy release L d in the surrounding accretion disk depend on two independent parameters that determine its state (for example, mass M and cyclic rotation frequency f ) and is proportional to the accretion rate. We derive simple approximation formulas illustrating the dependence of the efficiency of energy release in an extended disk and in a boundary layer near the NS surface on the frequency and sense of rotation for various NS equations of state. Such formulas are obtained for the quadrupole moment of a NS, for a gap between its surface and a marginally stable orbit, for the rotation frequency in an equatorial Keplerian orbit and in the marginally stable circular orbit, and for the rate of NS spinup via disk accretion. In the case of NS and disk counterrotation, the energy release during accretion can reach 0.67Ṁc2 . The sense of NS rotation is a factor that strongly affects the observed ratio of nuclear energy release during bursts to gravitational energy release between bursts in X-ray bursters. The possible existence of binary systems with NS and disk counterrotation in the Galaxy is discussed. Based on the static criterion for stability, we present a method of constructing the dependence of gravitational mass M on Kerr rotation parameter j and on total baryon mass (rest mass) m for a rigidly rotating neutron star. We show that all global NS characteristics can be expressed in terms of the function M(j, m) and its derivatives. We determine parameters of the equatorial circular orbit and the marginally stable orbit by using M(j, m) and an exact solution of the Einstein equations in a vacuum, which includes the following three parameters: gravitational mass M, angular momentum J, and quadrupole moment Φ 2 . Depending on Φ 2 , this solution can also be interpreted as a solution that describes the field of either two Kerr black holes or two Kerr disks.

The method developed by one of the authors for the construction of exact solutions of the Einstein-Maxwell equations by setting the behaviour of the Ernst potentials on the symmetry axis is discussed in full detail. Some new results regarding the solution of the integral equations and the construction of the 3*3 matrix potential H are presented. Two new examples of the application of the method are considered, one of which is the stationary vacuum solution for a rotating mass, and the second one is the four-parameter metric which can be used for the description of the exterior field of a charged magnetized spinning source.

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