We study the parameter space of D-dimensional cosmological Einstein gravity together with quadratic curvature terms. In D > 4 there are in general two distinct (anti)-de Sitter vacua. We show that for appropriate choice of the parameters there exists a critical point for one of the vacua, for which there are only massless tensor, but neither massive tensor nor scalar, gravitons. At criticality, the linearized excitations have vanishing energy (as do black hole solutions). A further restriction of the parameters gives a one-parameter cosmological Einstein plus Weyl 2 model with a unique vacuum, whose Λ is determined.

No! We show that the field equations of Einstein–Gauss–Bonnet theory defined in generic $$D>4$$D>4 dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to $$D=4$$D=4. Therefore, the recently introduced four-dimensional, novel, Einstein–Gauss–Bonnet theory does not admit an intrinsically four-dimensional definition, in terms of metric only, as such it does not exist in four dimensions. The solutions (the spacetime, the metric) always remain $$D>4$$D>4 dimensional. As there is no canonical choice of 4 spacetime dimensions out of D dimensions for generic metrics, the theory is not well defined in four dimensions.

In a recent Letter [1], a general covariant fourdimensional modified gravity that propagates only a massless spin-2 graviton and bypasses Lovelock's theorem [2] was claimed to exist. Here we show that this claim is not correct. The suggested theory is a limit of the Einstein-Gauss-Bonnet theory with the field equations lim D→4

It is a known fact that the Kerr-Schild type solutions in general relativity satisfy both exact and linearized Einstein field equations. We show that this property remains valid also for a special class of the Kerr-Schild metrics in arbitrary dimensions in generic quadratic curvature theory. In addition to the anti-de Sitter (AdS) wave (or Siklos) metric which represents plane waves in an AdS background, we present here a new exact solution, in this class, to the quadratic gravity in D dimensions which represents a spherical wave in an AdS background. The solution is a special case of the Kundt metrics belonging to spacetimes with constant curvature invariants. © 2012 American Physical Society

We construct the conserved charge of generic gravity theories built on arbitrary contractions of the Riemann tensor (but not on its derivatives) for asymptotically (anti)-de Sitter spacetimes. Our construction is a generalization of the Abbott-Deser-Tekin charges of linear and quadratic gravity theories in cosmological backgrounds. As an explicit example we find the energy and angular momentum of the Banados-Teitelboim-Zanelli black hole in the (2 þ 1)-dimensional Born-Infeld gravity.