Abstract: In four dimensions, the most general metric admitting two commuting Killing vectors and a rank-two Killing tensor can be parametrized by ten arbitrary functions of a single variable. We show that picking a special vierbein, reducing the system to eight functions, implies the existence of two geodesic and share-free, null congruences, generated by two principal null directions of the Weyl tensor. Thus, if the spacetime is an Einstein manifold, the Goldberg-Sachs theorem implies it is Petrov type D, and by explicit construction, is in the Carter class. Hence, our analysis provides a straightforward connection between the most general integrable structure and the Carter family of spacetimes.

Abstract: We show that the asymptotically flat hairy black holes, solutions of the Einstein field equations minimally coupled to a scalar field, previously discovered by one of us, present mode instability against linear radial perturbations. It is also shown that the number of unstable modes is finite and their frequencies can be made arbitrarily small.

Abstract: In the standard asymptotic expansion of four-dimensional static asymptotically flat spacetimes, the coefficient of the first subleading term of the lapse function can be identified with the mass of the spacetime. Using the Hamiltonian formalism we show that, in asymptotically locally anti-de Sitter spacetimes endowed with a scalar field, the mass can read off in the same way only when the boundary conditions are compatible with the asymptotic realization of the anti-de Sitter symmetry. Since the mass is determined only by the spatial metric and the scalar field, the above effect appears by considering not only the constraints, but also the dynamic field equations, which relate the spatial metric with the lapse function. In particular, this result implies that some prescriptions for computing the mass of a hairy spacetime are not suitable when the scalar field breaks the asymptotic anti-de Sitter invariance.

Abstract: A new class of vacuum black holes for the most general gravity theory leading to second order field equations in the metric in even dimensions is presented. These space-times are locally anti-de Sitter in the asymptotic region, and are characterized by a continuous parameter that does not enter in the conserve charges, nor it can be reabsorbed by a coordinate transformation: it is therefore a purely gravitational hair. The black holes are constructed as a warped product of a two-dimensional space-time, which resembles the r-t plane of the Banados-Teitelboim-Zanelli black hole, times a warp factor multiplying the metric of a D – 2-dimensional Euclidean base manifold, which is restricted by a scalar equation. It is shown that all the Noether charges vanish. Furthermore, this is consistent with the Euclidean action approach: even though the black hole has a finite temperature, both the entropy and the mass vanish. Interesting examples of base manifolds are given in eight dimensions which are products of Thurston geometries, giving then a nontrivial topology to the black hole horizon. The possibility of introducing a torsional hair for these solutions is also discussed.

Abstract: In this paper we construct asymptotically locally AdS and flat black holes in the presence of a scalar field whose kinetic term is constructed out from a linear combination of the metric and the Einstein tensor. The field equations as well as the energy-momentum tensor are second order in the metric and the field, therefore the theory belongs to the ones defined by Horndeski. We show that in the presence of a cosmological term in the action, it is possible to have a real scalar field in the region outside the event horizon. The solutions are characterized by a single integration constant, the scalar field vanishes at the horizon and it contributes to the effective cosmological constant at infinity. We extend these results to the topological case. The solution is disconnected from the maximally symmetric AdS background, however, within this family there exists a gravitational soliton which is everywhere regular. This soliton is therefore used as a background to define a finite Euclidean action and to obtain the thermodynamics of the black holes. For a certain region in the space of parameters, the thermodynamic analysis reveals a critical temperature at which a Hawking-Page phase transition between the black hole and the soliton occurs. We extend the solution to arbitrary dimensions greater than 4 and show that the presence of a cosmological term in the action allows one to consider the case in which the standard kinetic term for the scalar it is not present. In such a scenario, the solution reduces to an asymptotically flat black hole.

Abstract: The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is generalized to relativistic plasmas in curved spacetime. The connections between plasma elements, which are established by a covariant connection equation, display a particularly complex structure in curved spacetime. Nevertheless, it is shown that these connections can be interpreted in terms of magnetic field lines alone by adopting a 3 + 1 foliation of spacetime.

Abstract: Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated with linear polarization) and dispersion. The particular case of a vacuum-dominated anisotropic Universe, which reproduces a Friedmann-Robertson-Walker Universe (for late times)-while, for earlier times, it matches a Kasner Universe-is studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is then dependent on light polarization, its dispersion, and its non-null geodesic behavior. New results presented here may help to tackle some issues related to the “horizon” problem.

Abstract: From the point of view of elementary particle physics the gravitational constant G is extraordinarily small. This has led to ask whether it could have decayed to its present value from an initial one commensurate with microscopical units. A mechanism that leads to such a decay is proposed herein. It is based on assuming that G may take different values within regions of the universe separated by a novel kind of domain wall, a “G-wall”. The idea is implemented by introducing a gauge potential A, and its conjugate D, which determines the value of G as an integration constant rather than a fundamental constant. The value of G jumps when one goes through a G-wall. The procedure extends one previously developed for the cosmological constant, but the generalization is far from straightforward: (i) The intrinsic geometry of a G-wall is not the same as seen from its two sides, because the second law of black hole thermodynamics mandates that the jump in G must cause a discontinuity in the scale of length. (ii) The size of the decay step in G is controlled by a function G(D) which may be chosen so as to diminish the value of G towards the asymptote G = 0, without fine tuning. It is shown that: (i) The dynamics of the gravitational field with G treated as a dynamical variable, coupled to G-walls and matter, follows from an action principle, which is given. (ii) A particle that impinges on a G-wall may be refracted or reflected. (iii) The various forces between two particles change when a G-wall is inserted in between them. (iv) G-walls may be nucleated trough tunneling and thermal effects. The semiclassical probabilities are evaluated. (v) If the action principle is constructed properly, the entropy of a black hole increases when the value of the gravitational constant is changed through the absorption of a G-wall by the hole.

Abstract: We construct regular configurations of the Einstein-Yang-Mills theory in various dimensions. The gauge field is of meron-type: it is proportional to a pure gauge (with a suitable parameter lambda determined by the field equations). The corresponding smooth gauge transformation cannot be deformed continuously to the identity. In the three-dimensional case we consider the inclusion of a Chern-Simons term into the analysis, allowing lambda to be different from its usual value of 1/2. In four dimensions, the gravitating meron is a smooth Euclidean wormhole interpolating between different vacua of the theory. In five and higher dimensions smooth meron-like configurations can also be constructed by considering warped products of the three-sphere and lower-dimensional Einstein manifolds. In all cases merons (which on flat spaces would be singular) become regular due to the coupling with general relativity. This effect is named “gravitational catalysis of merons”.

Abstract: The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is extended to nonideal relativistic plasmas in curved spacetime. The existence of generalized magnetofluid connections that are preserved by the plasma dynamics is formalized by means of a covariant connection equation that includes different nonideal effects. These generalized connections are constituted by 2-dimensional hypersurfaces, which are linked to an antisymmetric tensor field that unifies the electromagnetic and fluid fields. They can be interpreted in terms of generalized magnetofluid vorticity field lines by considering a 3 + 1 foliation of spacetime and a time resetting projection that compensates for the loss of simultaneity between spatially separated events. The worldshects of the generalized magnetofluid vorticity field lines play a fundamental role in the plasma dynamics by prohibiting evolutions that do not preserve the magnetofluid connectivity.