Nonlinear perturbations of Reissner-Nordström black holes
We develop a nonlinear perturbation theory of Reissner-Nordstr\"om black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial sector. Gravitational part of these equations is similar to Regge-Wheeler and Zerilli equations with source and additional coupling to the electromagnetic sector. We construct solutions to the inhomogeneous part of wave equations in terms of sources for Einstein-Maxwell equations. We discuss $\ell=0$ and $ \ell=1$ cases separately.
Master Equations for Perturbations of Generalised Static Black Holes with Charge in Higher Dimensions
We extend the formulation for perturbations of maximally symmetric black holes in higher dimensions developed by the present authors in a previous paper to a charged black hole background whose horizon is described by an Einstein manifold. For charged black holes, perturbations of electromagnetic fields are coupled to the vector and scalar modes of metric perturbations non-trivially. We show that by taking appropriate combinations of gauge-invariant variables for these perturbations, the perturbation equations for the Einstein-Maxwell system are reduced to two decoupled second-order wave equations describing the behaviour of the electromagnetic mode and the gravitational mode, for any value of the cosmological constant. These wave equations are transformed into Schrodinger-type ODEs through a Fourier transformation with respect to time. Using these equations, we investigate the stability of generalised black holes with charge. We also give explicit expressions for the source terms of these master equations with application to the emission problem of gravitational waves in mind.
Compact Circularly Polarized Composite Cavity-Backed Crossed Dipole for GPS Applications
In this paper, we present a circularly polarized (CP) composite cavity-backed crossed dipole antenna for global positioning system (GPS) applications. We produce the CP radiation by crossing two dipoles through a 90° phase delay line of a vacant-quarter printed ring, which also has a broadband impedance matching characteristic. Two techniques, insertion of meander lines in the dipole arm and arrowhead-shaped trace at its end, are employed to reduce the sizes of the primary radiation element. The compact radiator is backed by a cavity reflector to achieve a wide CP radiation beamwidth. The proposed antenna exhibits a measured bandwidth of 1.450～1.656 GHz for a voltage standing wave ratio (VSWR) < 2 and 1.555～1.605 GHz for AR < 3-dB. At 1.575 GHz, the antenna has a gain of 7 dBic, a frontto-back ratio of 27 dB, AR of 1.18 dB, and 3-dB AR beamwidths of 130° and 132° in the x-z and y-z planes, respectively.