Generalized Kerr spacetime with an arbitrary mass quadrupole moment: geometric properties versus particle motion
An exact solution of Einstein's field equations in empty space first found in 1985 by Quevedo and Mashhoon is analyzed in detail. This solution generalizes Kerr spacetime to include the case of matter with an arbitrary mass quadrupole moment and is specified by three parameters, the mass M, the angular momentum per unit mass a and the quadrupole parameter q. It reduces to the Kerr spacetime in the limiting case q = 0 and to the Erez–Rosen spacetime when the specific angular momentum a vanishes. The geometrical properties of such a solution are investigated. Causality violations, directional singularities and repulsive effects occur in the region close to the source. Geodesic motion and accelerated motion are studied on the equatorial plane which, due to the reflection symmetry property of the solution, also turns out to be a geodesic plane.
Pulsar timing in extreme mass ratio binaries: a general relativistic approach
The detection of a pulsar (PSR) in a tight, relativistic orbit around a supermassive or intermediate mass black hole - such as those in the Galactic centre or in the centre of Globular clusters - would allow for precision tests of general relativity (GR) in the strong-field, non-linear regime. We present a framework for calculating the theoretical time-frequency signal from a PSR in such an Extreme Mass Ratio Binary (EMRB). This framework is entirely relativistic with no weak-field approximations and so able to account for all higher-order strong-field gravitational effects, relativistic spin dynamics, the convolution with astrophysical effects and the combined impact on the PSR timing signal. Specifically we calculate both the spacetime path of the pulsar radio signal and the complex orbital and spin dynamics of a spinning pulsar around a Kerr black hole, accounting for spacetime curvature and frame dragging, relativistic and gravitational time delay, gravitational light bending, temporal and spatial dispersion induced by the presence of plasma along the line of sight and relativistic aberration. This then allows for a consistent time-frequency solution to be generated. Such a framework is key for assessing the use of PSR as probes of strong field GR, helping to inform the detection of an EMRB system hosting a PSR and, most essentially, for providing an accurate theoretical basis to then compare with observations to test fundamental physics.
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.