Nambu-Jona-Lasinio Model in Curved Space-Time

The phase structure of Nambu-Jona-Lasinio model with N-component fermions in curved space-time is studied in the leading order of the 1/N expansion. The effective potential for composite operator $\bar{\psi}\psi$ is calculated by using the normal coordinate expansion in the Schwinger proper-time method. The existence of the first-order phase transition caused by the change of the space-time curvature is confirmed and the dynamical mass of the fermion is calculated as a simultaneous function of the curvature and the four-fermion coupling constant. The phase diagram in the curvature and the coupling constant is obtained.Comment: 8 pages, 3 figures not included, uses LaTeX, HUPD-931

Equilibrium hydrostatic equation and Newtonian limit of the singular f(R) gravity

We derive the equilibrium hydrostatic equation of a spherical star for any gravitational Lagrangian density of the form $L=\sqrt{-g}f(R)$. The Palatini variational principle for the Helmholtz Lagrangian in the Einstein gauge is used to obtain the field equations in this gauge. The equilibrium hydrostatic equation is obtained and is used to study the Newtonian limit for $f(R)=R-\frac{a^{2}}{3R}$. The same procedure is carried out for the more generally case $f(R)=R-\frac{1}{n+2}\frac{a^{n+1}}{R^{n}}$ giving a good Newtonian limit.Comment: Revised version, to appear in Classical and Quantum Gravity