Instability of the massive Klein-Gordon field on the Kerr spacetime

We investigate the instability of the massive scalar field in the vicinity of a rotating black hole. The instability arises from amplification caused by the classical superradiance effect. The instability affects bound states: solutions to the massive Klein-Gordon equation which tend to zero at infinity. We calculate the spectrum of bound state frequencies on the Kerr background using a continued fraction method, adapted from studies of quasinormal modes. We demonstrate that the instability is most significant for the $l = 1$, $m = 1$ state, for $M \mu \lesssim 0.5$. For a fast rotating hole ($a = 0.99$) we find a maximum growth rate of $\tau^{-1} \approx 1.5 \times 10^{-7} (GM/c^3)^{-1}$, at $M \mu \approx 0.42$. The physical implications are discussed.Comment: Added references. 27 pages, 7 figure

Quasi two-level PWM operation of a nine-arm modular multilevel converter for six-phase medium-voltage motor drives

This paper proposes a hybrid converter for medium-voltage six-phase machine drive systems that mixes the operation of a traditional two-level voltage-source inverter and the modular multilevel converter (MMC) to enable operation over a wide frequency range. Topologically, the proposed converter consists of nine arms resembling two sets of three-phase MMCs with three common arms, yielding a nine-arm MMC with a 25% reduction in the number of employed arms compared to a traditional dual three-phase MMC. The multilevel property of a standard MMC is emulated in the proposed converter, however on a two-level basis, resulting in a stepped two-level output voltage waveform. The proposed converter has a reduced footprint with advantages of small voltage steps, modular structure, and ease of scalability. Further, it is able to drive high-power six-phase machines within low operating frequencies at the rated torque. The operating principle of the converter is elaborated, and its modulation scheme is discussed. The features of the proposed converter are verified through simulations and experimentally

Analysis and assessment of modular multilevel converter internal control schemes

Adoption of distributed submodule (SM) capacitors in a modular multilevel converter (MMC) necessitates complex controllers to ensure the stability of its internal dynamics. This paper presents comprehensive analysis and assessment of different proportional resonant (PR)-based control schemes proposed to stabilize the internal dynamics and ensure ac and dc sides power quality of the MMC within a dc transmission system. With the consideration of passive component tolerances, different energy and voltage based control schemes under various conditions are analyzed. It has been established that without vertical voltage balance control, unequal passive component values in the upper and lower arms of the same phase-leg may cause: unbalanced fundamental currents in the arms, unequal dc voltage across the arms, and fundamental oscillations in the common-mode currents that lead to fundamental frequency ripple in the dc link current. The theoretical analysis that explains this mechanism is presented, and is used to show that vertical voltage balancing is necessary for the nullification of arm voltage difference and suppression of odd oscillations caused by capacitive/inductive asymmetry between arms of the same phase-leg. Simulations support the theoretical analysis and the effectiveness of voltage balancing in ensuring correct operation, independent of tolerances of the MMC passive elements and operating conditions. A new direct method for elimination of fundamental oscillations in the common-mode and dc link current is proposed. Experimental results from a singlephase MMC prototype validate the presented theoretical discussions and simulations

Kerr-Gauss-Bonnet Black Holes: An Analytical Approximation

Gauss-Bonnet gravity provides one of the most promising frameworks to study curvature corrections to the Einstein action in supersymmetric string theories, while avoiding ghosts and keeping second order field equations. Although Schwarzschild-type solutions for Gauss-Bonnet black holes have been known for long, the Kerr-Gauss-Bonnet metric is missing. In this paper, a five dimensional Gauss-Bonnet approximation is analytically derived for spinning black holes and the related thermodynamical properties are briefly outlined.Comment: 5 pages, 1 figur

Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.Comment: 16 pages, 6 Figures. Submitted to General Relativity and Gravitatio

A novel converter station structure for improving multi-terminal HVDC system resiliency against AC and DC faults

In an effort to minimize the power disruption between a dc grid and ac grids that host power converters during ac and dc network faults, this paper proposes a novel converter station structure to improve ac and dc fault ride-through performance of the multi-terminal HVDC grid. The proposed structure consists of two independent ac and dc interfacing circuits, which are a half-bridge modular multilevel converter and a cascaded H-bridge (CHB) based energy storage system. Taking the advantages of high controllability and flexibility of the independent CHB converter and ease of integrating energy modules, a decoupled power relationship between the ac and dc sides is achieved, which is important for enhancing ac and dc fault performance. Operation of the proposed converter station under normal conditions and during ac and dc faults is explained, with the control system presented. Simulation validation of the proposed structure on a three-terminal HVDC grid confirms the enhanced performance, including the continuous operation during ac and dc faults with negligible power transfer disruption

TeV-Scale Black Hole Lifetimes in Extra-Dimensional Lovelock Gravity

We examine the mass loss rates and lifetimes of TeV-scale extra dimensional black holes (BH) in ADD-like models with Lovelock higher-curvature terms present in the action. In particular we focus on the predicted differences between the canonical and microcanonical ensemble statistical mechanics descriptions of the Hawking radiation that results in the decay of these BH. In even numbers of extra dimensions the employment of the microcanonical approach is shown to generally lead to a significant increase in the BH lifetime as in case of the Einstein-Hilbert action. For odd numbers of extra dimensions, stable BH remnants occur when employing either description provided the highest order allowed Lovelock invariant is present. However, in this case, the time dependence of the mass loss rates obtained employing the two approaches will be different. These effects are in principle measurable at future colliders.Comment: 27 pages, 9 figs; Refs. and discussion adde

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals. This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.Comment: to be published in Physical Review B (1 march 2000

The All-Data-Based Evolutionary Hypothesis of Ciliated Protists with a Revised Classification of the Phylum Ciliophora (Eukaryota, Alveolata)

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Loop quantum gravity: the first twenty five years

This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.Comment: 24 pages, 3 figure