Pion condensation of quark matter in the static Einstein universe

In the framework of an extended Nambu--Jona-Lasinio model we are studying pion condensation in quark matter with an asymmetric isospin composition in a gravitational field of the static Einstein universe at finite temperature and chemical potential. This particular choice of the gravitational field configuration enables us to investigate phase transitions of the system with exact consideration of the role of this field in the formation of quark and pion condensates and to point out its influence on the phase portraits. We demonstrate the effect of oscillations of the thermodynamic quantities as functions of the curvature and also refer to a certain similarity between the behavior of these quantities as functions of curvature and finite temperature. Finally, the role of quantum fluctuations for spontaneous symmetry breaking in the case of a finite volume of the universe is shortly discussed.Comment: RevTex4; 15 pages, 10 figure

The gravitational coupling between longitudinal segments of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

The gravitational interaction is derived between a solid longitudinal segment cut from a cylinder of uniform density, and an external point mass. The derivation is expressed p(2p+m+1)(m)(cos theta), and the parametric form of the coupling coefficients K-2p,K-m,K-alpha(psi) is presented. This theory is applied to the gravitational interaction between a point mass and a finite hollow cylinder, where the cylinder bears a number of 'flats' cut into its outer surface. The 'flats' are imagined to be regularly spaced in azimuth around the cylinder, each flat being treated as the removal of a solid segment from the full cylinder. Such forms of test mass have been proposed for the satellite test of the equivalence principle (STEP) experiment, since the masses may then be prevented from rotating in azimuth-a factor which is considered to be essential for this experiment. The gravitational theory developed here is applied to such STEP test masses, and two 'low gravitational susceptibility' designs for test-mass pairs are considered, having four and six 'flats', respectively. An expression for the axial force on such masses is derived which is more than 10(5) times faster to compute than a Monte Carlo integration of similar accuracy, by virtue of which it is shown that a design with six or more 'flats' is to be preferred. This theory is shown to have much wider applicability to gravitational problems involving general segmented cylindrical bodies, including square- and hexagonal-section prisms of finite length (hollow or solid)

Optimization of the geometry for dipole-dipole and dipole-monopole experiments, using the gravitational interaction between a point-source and a finite cylinder

The torsion balance has been used frequently in the search for weak gravitational-like forces. A major problem in the design of these experiments is the optimization of the geometry of the cylindrical masses that have been used. Starting from the formula for simple Newtonian gravitational interaction, the general formulae for treating both ''dipole-dipole'' and ''dipole-monopole'' interactions for cylindrically shaped bodies are derived. These formulae are used to optimize the shape of both the attracting and balance masses. The interaction forces are derived using only 3D integration-rather than the usual 6D integration carried out over the volumes of both interacting bodies. This has resulted in considerably reduced computational time, and thereby the attainment of high accuracy in the optimization

Spherical harmonic representation of the gravitational coupling between a truncated sector of a hollow cylinder and an arbitrary gravitational source: Relevance to the STEP experiment

The gravitational interaction between grooves machined in a hollow cylindrical mass of uniform density, and an external point mass, is derived in terms of the Associated Legendre functions, and the parametric form of the coupling coefficients is presented. The cross-sections of the grooves, which are regularly spaced in azimuth, are in the form of truncated sectors of the cylinder's end-faces. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, for which four grooves have been assumed, and an expression for the axialforce is derived which is more than 104 times faster to compute than a Monte-Carlo integration of similar accuracy. Following this analysis it is suggested that the STEP test-masses should carry at least 6 grooves. This theory has wider application to gravitational problems involving general sectored cylindrical bodies

Gravitational modelling of the test masses for STEP and LISA

The test masses for the proposed STEP (satellite test of the equivalence principle) experiment can be influenced, adversely, by time-varying gravitational coupling to other masses within the spacecraft. The liquid helium in the spacecraft's Dewar is a severe potential source of this effect, since its influence is at the same frequency as any actual equivalence principal violation. The pairs of STEP test masses must be made differentially immune to this effect, and a measure of this immunity can be quantified in terms of a 'differential acceleration susceptibility', defined as .R; ; '/ D 1az=a. Here 1az and a are the differential-axial and commonmode accelerations, respectively, of the two masses, for a perturbing source at relative position .R; ; '/. This work presents the results of analyses for STEP's test masses having either four or six flats, included to prevent them from rolling in azimuth .'/. Different schemes for minimizing .R; ; '/ are discussed in detail, and it is shown that the gravitational effect of the flats may be balanced between the inner and outer masses, leading to a 'fully-balanced' pair. However, it is concluded that such a scheme is not practical, and the 'susceptibility' may be minimized, alternatively, by choosing six flats rather than four. It is noted that the gravitational theory used here may be applied to six- or four-sided bodies, including cubic test masses-as proposed for LISA

Analytical evaluation of short-range forces in cylindrical geometry

This paper concerns the potential field for Yukawa-type forces in a cylindrical geometry. A set of formulae is derived for a cylindrical body in order to reduce the integration over the body from 3D (or 6D for a pair of interacting bodies) to either a 1D integration, or an analytical formula. Using these formulae we consider analytically the potential field of two Yukawa force terms, and reanalyse Long's and Spero et al's experiments for the inverse-square law test. The results show that the - graph produces similar results to the case where a single Yukawa term is considered. The theory can also be applied to other problems in short-range force experiments that involve cylindrically shaped bodies as the test masses

Differential gravitational coupling between cylindrically-symmetric, concentric test masses and an arbitrary gravitational source: relevance to the STEP experiment

The gravitational interaction between a point mass and a finite, hollow, thick-walled cylinder is calculated, the axial force is derived, and the parametric form of the coupling coefficients k2p is presented. This theory is applied to the test-masses for the Satellite Test of the Equivalence Principle (STEP) experiment, and an equation is derived for the differential gravitational coupling to these masses which is more than 105 times faster to compute than a Monte-Carlo integration of similar accuracy

Optimization of immunity to helium tidal influences for the STEP experiment test masses

This paper describes an optimization strategy for the design of the three pairs of test masses in the STEP (satellite test of the equivalence principle) experiment. Using these designs, the allowable helium tidal amplitude is calculated for a STEP accelerometer sensitivity of , based on a worst case distribution of the liquid helium in the satellite's dewar. It is found that the hybrid belted/straight-cylinder geometry can be dimensioned such that the quadrupole moment and differential hexadecapole moment are identically zero. The resulting test mass designs are technically feasible. Some practical problems relating to their manufacture are discussed