Curvature scalar instability inf(R)gravity

Curvature scalar instability in f(R) gravity

An instability in the presence of matter in theories of gravity which include a 1/R correction in the gravitational action has been found by Dolgov and Kawasaki. In the present paper this instability is discussed for f(R) gravity in general. We focus on the Palatini formalism of the theory and it is shown that no such instability occurs in this version of f(R) gravity. The reasons for the appea...

Positive Scalar Curvature

One of the striking initial applications of the Seiberg-Witten invariants was to give new obstructions to the existence of Riemannian metrics of positive scalar curvature on 4– manifolds. The vanishing of the Seiberg–Witten invariants of a manifold admitting such a metric may be viewed as a non-linear generalization of the classic conditions [12, 11] derived from the Dirac operator. If a manifo...

Curvature instability in membranes

2014 A simple, thermodynamical model was proposed some time ago [1, 2] to describe the physical properties of various systems for which the curvature elastic energy plays an important role. The basis of this model is provided by the notions of effective rigidity and spontaneous curvature. Here we consider the case of bilayer membranes and generalize the model for situations where small adsorbed...

PRESCRIBING SCALAR CURVATURE ON Sn

on S for n ≥ 3. In the case R is rotationally symmetric, the well-known Kazdan-Warner condition implies that a necessary condition for (1) to have a solution is: R > 0 somewhere and R′(r) changes signs. Then, (a) is this a sufficient condition? (b) If not, what are the necessary and sufficient conditions? These have been open problems for decades. In Chen & Li, 1995, we gave question (a) a nega...

Positive Scalar Curvature and Surgery