WEAK-FIELD LIMIT OF THE CONFORMAL THEORY OF GRAVITY AND GALACTIC ROTATION CURVES

Анотація

We study the weak-field limit of the static spherically symmetric solution of the locally conformally invariant theory, which is regarded as an alternative to Einstein's general relativity theory in explaining the at galactic rotation curves. In contrast with the previous works, we consider the physically relevant case where the scalar field that breaks conformal symmetry and generates fermion masses is nonzero. In the physical gauge, in which this scalar field is constant in space-time, the solution reproduces the weak-field limit of the Schwarzschild-(anti) de Sitter solution modified by an additional term that, depending on the sign of the Weyl term in the action, is either oscillatory or exponential as a function of the radial distance. Such behaviour reflects the presence of, correspondingly, either a tachyon or a massive ghost in the spectrum, which is a drawback of the theory under discussion.