Fabrizio Canfora

Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes

Abstract We present a self-gravitating, analytic and globally regular Skyrmion solution of the Einstein–Skyrme system with winding number w = ± 1 , in presence of a cosmological constant. The static spacetime metric is the direct product R × S 3 and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback with unit topological charge. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX with time-dependent scale and squashing coefficients. Remarkably, the Skyrme equations are still identically satisfied for all values of these parameters. Thus, the complete set of field equations for the Einstein–Skyrme–Λ system in the topological sector reduces to a pair of coupled, autonomous, nonlinear differential equations for the scale factor and a squashing coefficient. These equations admit analytic bouncing cosmological solutions in which the universe contracts to a minimum non-vanishing size, and then expands. A non-trivial byproduct of this solution is that a minor modification of the construction gives rise to a family of stationary, regular configurations in General Relativity with negative cosmological constant supported by an SU ( 2 ) nonlinear sigma model. These solutions represent traversable AdS wormholes with NUT parameter in which the only “exotic matter” required for their construction is a negative cosmological constant.

Nonlinear superposition law and Skyrme crystals

Exact configurations of the four dimensional Skyrme model are presented. The static configurations have the profile which behaves as a kink and, consequently, the corresponding energy momentum tensor describes a domain wall. Furthermore, a class of exact time periodic Skyrmions is discovered. Within such class, it is possible to disclose a remarkable phenomenon which is a genuine effect of the Skyrme term. For a special value of the frequency the Skyrmions admit a non linear superposition principle. One can combine two or more exact elementary Skyrmions (which may depend in a non trivial way on all the space like coordinates) into a new exact composite Skyrmion. Due to such superposition law, despite the explicit presence of non linear effects in the energy momentum tensor, the interaction energy between the elementary Skyrmions can be computed exactly. The relations with the appearance of Skyrme crystals is discussed.

Hedgehog ansatz and its generalization for self-gravitating Skyrmions

The hedgehog ansatz for spherically symmetric spacetimes in self-gravitating nonlinear sigma models and Skyrme models is revisited and its generalization for nonspherically symmetric spacetimes is proposed. The key idea behind our construction is that, even if the matter fields depend on the Killing coordinates in a nontrivial way, the corresponding energy-momentum tensor can still be compatible with spacetime symmetries. Our generalized hedgehog ansatz reduces the Skyrme equations to coupled differential equations for two scalar fields together with several constraint equations between them. Some particular field configurations satisfying those constraints are presented in several physically important spacetimes, including stationary and axisymmetric spacetimes. Incidentally, new exact solutions are obtained under the standard hedgehog ansatz, one of which represents a global monopole inside a black hole with the Skyrme effect.

Exact multisoliton solutions in the four-dimensional Skyrme model

Exact analytic solutions of the Skyrme model defined on a spherically symmetric

Generalized hedgehog ansatz and Gribov copies in regions with nontrivial topologies

R^{(1,1)} \times S^2

Black holes with primary hair in gauged N = 8 supergravity

geometry, chosen to mimic finite volume effects, are presented. The static and spherically symmetric configurations have non-trivial winding number and finite soliton mass. These configurations possess an extra topological charge, allowing for a novel BPS bound which can be saturated, unlike what happens in the standard case. Such solutions include exact multi-Skyrmions of arbitrary winding number, composed by interacting elementary Skyrmions. The values of the coupling constants and the compression modulus are found in good agreement with experiments by fitting the masses

Gribov pendulum in the Coulomb gauge on curved spaces

M_N

Black holes with gravitational hair in higher dimensions

and

BTZ-like black holes in even dimensional Lovelock theories

M_\Delta

General relativity with small cosmological constant from spontaneous compactification of Lovelock theory in vacuum

.