Wheeler's approach to finding exact solutions in Lovelock gravity has been predominantly applied to static spacetimes. This has led to a Birkhoff's theorem for arbitrary base manifolds in dimensions higher than four. In this work, we generalize the method and apply it to a stationary metric. Using this perspective, we present a Taub-NUT solution in eight-dimensional Lovelock gravity coupled to Maxwell fields. We use the first-order formalism to integrate the equations of motion in the torsionfree sector. The Maxwell field is presented explicitly with general integration constants, while the background metric is given implicitly in terms of a cubic algebraic equation for the metric function. We display precisely how the NUT parameter generalizes Wheeler polynomials in a highly nontrivial manner.
Recent work has shown the existence of a unique nonlinear extension of electromagnetism which preserves conformal symmetry and allows for the freedom of duality rotations. Moreover, black holes and gravitational waves have been found to exist in this nonlinearly extended electrovacuum. We generalise these dyonic black holes in two major ways: with the relaxation of their horizon topology and with the inclusion of magnetic mass. Motivated by recent attention to traversable wormholes, we use this new family of Taub-NUT spaces to construct AdS wormholes. We explore some thermodynamic features by using a semi-classical approach. Our results show that a phase transition between the nut and bolt configurations arises in a similar way to the Maxwellian case.
Topological excitations of gauge fields exhibit a discrete behavior, which arises from the global structure. We calculate the Chern numbers of higher dimensional Taub-NUT and Taub-Bolt instantons and find the winding numbers, which classify the U(1)−bundles that harbor Maxwell dyons. Our results can be written in general for any even dimension and apply for many different theories of gravity. We illustrate this point by focusing on Lovelock gravity. The magnetic flux is found to be a pure topological excitation whereas the electric flux is indirectly indexed by the magnetic counterpart. We argue that this last result is a consequence of the path integral approach to quantum gravity.MSC: 32L81, 51P05, 55R15, 58J28, 81T70
We calculate the Chern numbers of SU(2)-homogeneous Einstein-Maxwell gravitational instantons with boundary at infinity. By restating these numbers as Chern-Simons invariants on the boundary apparent conflicting results emerge. We resolve this issue examining the topological stability of the self-gravitating Abelian fields. No quantization carrying physical meaning is found when the background is a Taub-NUT space. However the magnetic charge of dyons on Taub-Bolt spaces is found to be of topological quantum nature. In this framework electric charge is quantized by a consistency condition.MSC: 83C45, 53Z05
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