| Abstrakt: |
We have determined the first and second order radial and time symmetric variations of the mass-energy of spherically symmetric isentropic perfect fluids in the framework of the scalar-tensor theories of gravitation. The results are then used to study the conditions for the total mass-energy to be a minimum under variations which conserve the total number of baryons of the system, and these conditions are interpreted as necessary for the dynamical stability of static configurations subjected to the above perturbations. The post-Newtonian approximation is performed, and we obtain a stability criterion in the Chandrasekhar form,  > 4/3 + 2Kst(GM/R) ≡ υc, υ → 4/3, where  is the pressure averaged adiabatic index,M andR are the total mass and the radius of the configuration respectively, andKst is a constant that depends on the density distribution, the scalar field,ø, coupling functionω(ø), anddω/dø. The value ofKst, is compared to that in Einstein's general relativity and in the Jordan-Brans-Dicke theory. This is done for the specific scalar-tensor theories of Barker, Schwinger, and for models with curvature coupling. |
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