Energy in ghost-free massive gravity theory

The detailed calculations of the energy in the ghost-free massive gravity theory is presented. The energy is defined in the standard way within the canonical approach, but to evaluate it requires resolving the Hamiltonian constraints, which are known, in general, only implicitly. Fortunately, the constraints can be explicitly obtained and resolved in the spherically symmetric sector, which allows one to evaluate the energy. It turns out that the energy is positive for globally regular and asymptotically flat fields constituting the "physical sector" of the theory. In other cases the energy can be negative and even unbounded from below, which suggests that the theory could be still plagued with ghost instability. However, a detailed inspection reveals that the corresponding solutions of the constraints are either not globally regular or not asymptotically flat. Such solutions cannot describe initial data triggering ghost instability of the physical sector. This allows one to conjecture that the physical sector could actually be protected from the instability by a potential barrier separating it from negative energy states.Comment: 35 pages, minor improvements, an appendix adde

De Sitter vacua in ghost-free massive gravity theory

We present a simple procedure to obtain all de Sitter solutions in the ghost-free massive gravity theory by using the Gordon ansatz. For these solutions the physical metric can be conveniently viewed as describing a hyperboloid in 5D Minkowski space, while the flat reference metric depends on the Stuckelberg field $T(t,r)$ that satisfies the equation $(\partial_t{T})^2-(\partial_r T)^2=1$. This equation has infinitely many solutions, hence there are infinitely many de Sitter vacua with different physical properties. Only the simplest solution with $T=t$ has been previously studied since it is manifestly homogeneous and isotropic, but it is unstable. However, other solutions could be stable. We require the timelike isometry to be common for both metrics, and this gives physically distinguished solutions since only for them the canonical energy is time-independent. We conjecture that these solutions minimize the energy and are therefore stable. We also show that in some cases solutions can be homogeneous and isotropic in a non-manifest way such that their symmetries are not obvious. All of this suggests that the theory may admit viable cosmologies.Comment: 14 pages, 1 figure, references adde

Odd-Parity Negative Modes of Einstein-Yang-Mills Black Holes and Sphalerons

An analytical proof of the existence of negative modes in the odd--parity perturbation sector is given for all known non-abelian Einstein--Yang--Mills black holes. The significance of the normalizability condition in the functional stability analysis is emphasized. The role of the odd--parity negative modes in the sphaleron interpretation of the Bartnik--McKinnon solutions is discussed.Comment: (minor typographical errors fixed, to appear in Phys.Lett.B

Giant wormholes in ghost-free bigravity theory

We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we call W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.Comment: 26 pages, 6 figures, section 8.2 describing the W1b wormhole geometry is considerably modifie