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We study the dynamical breaking of chiral and color symmetries of dense quarkmatter in the ultrastatic hyperbolic spacetime $R\otimes H^3$ in the frameworkof an extended Nambu--Jona-Lasinio model. On the basis of analyticalexpressions for chiral and color condensates as functions of curvature andtemperature, the phenomenon of dimensional reduction and gravitationalcatalysis of symmetry breaking in strong gravitational field is demonstrated inthe regime of weak coupling constants. In the case of strong couplings it isshown that curvature leads to small corrections to the flat-space values ofcondensate and thus enhances the symmetry breaking effects. Finally, usingnumerical calculations phase transitions under the influence of chemicalpotential and negative curvature are considered and the phase portrait of thesystem is constructed.

Gravitational catalysis of chiral and color symmetry breaking of quark matter in hyperbolic space