Charging axisymmetric space-times with cosmological constant

Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.Comment: 15 pages, v2: typos correcte

Switched Control of Electron Nuclear Spin Systems

In this article, we study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static B_0 field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control on nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation on the nuclear spins, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations can be used to synthesize any unitary transformation on the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins

Exact relativistic treatment of stationary counter-rotating dust disks III. Physical Properties

This is the third in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which can be interpreted as counter-rotating disks of dust. We discuss the physical properties of a class of solutions to the Einstein equations for disks with constant angular velocity and constant relative density which was constructed in the first part. The metric for these spacetimes is given in terms of theta functions on a Riemann surface of genus 2. It is parameterized by two physical parameters, the central redshift and the relative density of the two counter-rotating streams in the disk. We discuss the dependence of the metric on these parameters using a combination of analytical and numerical methods. Interesting limiting cases are the Maclaurin disk in the Newtonian limit, the static limit which gives a solution of the Morgan and Morgan class and the limit of a disk without counter-rotation. We study the mass and the angular momentum of the spacetime. At the disk we discuss the energy-momentum tensor, i.e. the angular velocities of the dust streams and the energy density of the disk. The solutions have ergospheres in strongly relativistic situations. The ultrarelativistic limit of the solution in which the central redshift diverges is discussed in detail: In the case of two counter-rotating dust components in the disk, the solutions describe a disk with diverging central density but finite mass. In the case of a disk made up of one component, the exterior of the disks can be interpreted as the extreme Kerr solution.Comment: 30 pages, 20 figures; to appear in Phys. Rev.

Gravitating Fluxbranes

We consider the effect that gravity has when one tries to set up a constant background form field. We find that in analogy with the Melvin solution, where magnetic field lines self-gravitate to form a flux-tube, the self-gravity of the form field creates fluxbranes. Several exact solutions are found corresponding to different transverse spaces and world-volumes, a dilaton coupling is also considered.Comment: 14 pages, 5 figure

Wave equations for the perturbations of a charged black hole

A pair of simple wave equations is presented for the symmetric gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled, and the other has a source term given by the solution of the first equation. The derivation is presented in full detail for either axially symmetric or stationary perturbations, and is quite straightforward. This result is expected to have important applications in astrophysical models.Comment: 4 page

Pair creation of black holes joined by cosmic strings

We argue that production of charged black hole pairs joined by a cosmic string in the presence of a magnetic field can be analyzed using the Ernst metric. The effect of the cosmic string is to pull the black holes towards each other, opposing to the background field. An estimation of the production rate using the Euclidean action shows that the process is suppressed as compared to the formation of black holes without strings.Comment: 7 pages, LaTeX. Minor typos corrected

Black Hole Pair Creation and the Entropy Factor

It is shown that in the instanton approximation the rate of creation of black holes is always enhanced by a factor of the exponential of the black hole entropy relative to the rate of creation of compact matter distributions (stars). This result holds for any generally covariant theory of gravitational and matter fields that can be expressed in Hamiltonian form. It generalizes the result obtained previously for the pair creation of magnetically charged black holes by a magnetic field in Einstein--Maxwell theory. The particular example of pair creation of electrically charged black holes by an electric field in Einstein--Maxwell theory is discussed in detail.Comment: (12 pages, ReVTeX) Revised version of "Pair Creation of Electrically Charged Black Holes". New section shows that the BH pair creation rate is enhanced by a factor $\exp(BH entropy)$ for any Hamiltonian gravity + matter theor

Determining parameters of the Neugebauer family of vacuum spacetimes in terms of data specified on the symmetry axis

We express the complex potential E and the metrical fields omega and gamma of all stationary axisymmetric vacuum spacetimes that result from the application of two successive quadruple-Neugebauer (or two double-Harrison) transformations to Minkowski space in terms of data specified on the symmetry axis, which are in turn easily expressed in terms of multipole moments. Moreover, we suggest how, in future papers, we shall apply our approach to do the same thing for those vacuum solutions that arise from the application of more than two successive transformations, and for those electrovac solutions that have axis data similar to that of the vacuum solutions of the Neugebauer family. (References revised following response from referee.)Comment: 18 pages (REVTEX

Active Management of Low-Voltage Networks for Mitigating Overvoltages Due to Photovoltaic Units

In this paper, the overvoltage problems that might arise from the integration of photovoltaic (PV) panels into low-voltage (LV) distribution networks is addressed. A distributed scheme is proposed that adjusts the reactive and active power output of inverters to prevent or alleviate such problems. The proposed scheme is model-free and makes use of limited communication between the controllers in the form of a distress signal only during emergency conditions. It prioritizes the use of reactive power, while active power curtailment is performed only as a last resort. The behavior of the scheme is studied using dynamic simulations on a single LV feeder and on a larger network composed of 14 LV feeders. Its performance is compared with a centralized scheme based on the solution of an optimal power flow (OPF) problem, whose objective function is to minimize the active power curtailment. The proposed scheme successfully mitigates overvoltage situations due to high PV penetration and performs almost as well as the OPF-based solution with significantly less information and communication requirements