Stability analysis in the higher-dimensional einstein/maxwell-scalar theory

Abstract

We have discussed the classical stability in the curved space. From the viewpoint of the stability, we clarified the basic difference between the minimal coupling of gravity with a scalar field and the conformal coupling of gravity with a scalar field. Under Minkowski background, we found that the minimal case is stable, while the conformal case is unstable. To see the effects of the scalar field, we analyze the stability of the Schwarzschild black hole in the BransDicke theory. We found that all non-static perturbations allow the real values of the frequency k, which means that this system is classically stable. Also we analyzed the stability of the Einstein/Maxwell-Scalar system in six dimensions. It is found that the scalar field does not give the instability in the monopole compactification. Further we discussed the stability of tendimensional Einstein/Maxwell and Einstein/Maxwell-Scalar theories with $M_4\times S^2 \times S^2 \times S^2$ compactification. Although these theories are able to accommodate the chiral fermions, we found that this compactification contains tachyonic modes. Finally, the stability of the recent superstring compactification is discussed and the effects of the curvature squared terms on the stability are considered.