A Metric for Rapidly Spinning Black Holes Suitable for Strong-Field Tests of the No-Hair Theorem

According to the no-hair theorem, astrophysical black holes are uniquely characterized by their masses and spins and are described by the Kerr metric. Several parametric deviations from the Kerr metric have been suggested to study observational signatures in both the electromagnetic and gravitational-wave spectra that differ from the expected Kerr signals. Due to the no-hair theorem, however, such spacetimes cannot be regular everywhere outside the event horizons, if they are solutions to the Einstein field equations; they are often characterized by naked singularities or closed time-like loops in the regions of the spacetime that are accessible to an external observer. For observational tests of the no-hair theorem that involve phenomena in the vicinity of the circular photon orbit or the innermost stable circular orbit around a black hole, these pathologies limit the applicability of the metrics only to compact objects that do not spin rapidly. In this paper, we construct a Kerr-like metric which depends on a set of free parameters in addition to its mass and spin and which is regular everywhere outside of the event horizon. We derive expressions for the energy and angular momentum of a particle on a circular equatorial orbit around the black hole and compute the locations of the innermost stable circular orbit and the circular photon orbit. We demonstrate that these orbits change significantly for even moderate deviations from the Kerr metric. The properties of our metric make it an ideally suited spacetime to carry out strong-field tests of the no-hair theorem in the electromagnetic spectrum using the properties of accretion flows around astrophysical black holes of arbitrary spin.Comment: 11 pages, 7 figures, accepted for publication in PR

Neutron Stars in f(R) Gravity with Perturbative Constraints

We study the structure of neutron stars in f(R) gravity theories with perturbative constraints. We derive the modified Tolman-Oppenheimer-Volkov equations and solve them for a polytropic equation of state. We investigate the resulting modifications to the masses and radii of neutron stars and show that observations of surface phenomena alone cannot break the degeneracy between altering the theory of gravity versus choosing a different equation of state of neutron-star matter. On the other hand, observations of neutron-star cooling, which depends on the density of matter at the stellar interior, can place significant constraints on the parameters of the theory.Comment: Discussion extended, typos corrected, figures revised. Accepted for publication in PR

The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs

The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth of the instability, the mean (averaged over the disc scale-height) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds stresses during the late times of the exponential growth of the instability is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic. Even though we derived these properties of the stress tensors for the exponential growth of the instability in incompressible flows, numerical simulations of shearing boxes show that this characteristic is qualitatively preserved under more general conditions, even during the saturated turbulent state generated by the instability.Comment: 9 pages, 4 figures. Minor revisions. Accepted for publication in MNRA

The MHD Alfven wave oscillation model of kHz Quasi Periodic Oscillations of Accreting X-ray Binaries

We ascribe the interpretation of the twin kilohertz Quasi Periodic Oscillations (kHz QPOs) of X-ray spectra of Low Mass X-Ray Binaries (LMXBs) to MHD Alfven wave oscillations in the different mass density regions of the accreted matter at the preferred radius, and the upper kHz QPO frequency coincides with the Keplerian frequency. The proposed model concludes that the kHz QPO frequencies depend inversely on the preferred radius, and that theoretical relation between the upper frequency (\nt) and the lower frequency (\no) is \no \sim \nt^{2}, which is similar to the measured empirical relation. The separation between the twin frequencies decreases (increases) with increasing kHz QPO frequency if the lower kHz QPO frequency is more (less) than $\sim$ 400 Hz.Comment: Accepted by Astron. & Astrophys., 4 pages, 4 figure

Ranging system which compares an object reflected component of a light beam to a reference component of the light beam

A system is described for measuring the distance to an object by comparing a first component of a light pulse that is reflected off the object with a second component of the light pulse that passes along a reference path of known length, which provides great accuracy with a relatively simple and rugged design. The reference path can be changed in precise steps so that it has an equivalent length approximately equal to the path length of the light pulse component that is reflected from the object. The resulting small difference in path lengths can be precisely determined by directing the light pulse components into opposite ends of a detector formed of a material that emits a second harmonic light output at the locations where the opposite going pulses past simultaneously across one another

Constraining Parity Violation in Gravity with Measurements of Neutron-Star Moments of Inertia

Neutron stars are sensitive laboratories for testing general relativity, especially when considering deviations where velocities are relativistic and gravitational fields are strong. One such deviation is described by dynamical, Chern-Simons modified gravity, where the Einstein-Hilbert action is modified through the addition of the gravitational parity-violating Pontryagin density coupled to a field. This four-dimensional effective theory arises naturally both in perturbative and non-perturbative string theory, loop quantum gravity, and generic effective field theory expansions. We calculate here Chern-Simons modifications to the properties and gravitational fields of slowly spinning neutron stars. We find that the Chern-Simons correction affects only the gravitomagnetic sector of the metric to leading order, thus introducing modifications to the moment of inertia but not to the mass-radius relation. We show that an observational determination of the moment of inertia to an accuracy of 10%, as is expected from near-future observations of the double pulsar, will place a constraint on the Chern-Simons coupling constant of \xi^{1/4} < 5 km, which is at least three-orders of magnitude stronger than the previous strongest bound.Comment: 14 pages, 6 figures, replaced with version accepted for publication in Phys. Rev.

Measuring and modeling optical diffraction from subwavelength features

We describe a technique for studying scattering from subwavelength features. A simple scatterometer was developed to measure the scattering from the single-submicrometer, subwavelength features generated with a focused ion beam system. A model that can describe diffraction from subwavelength features with arbitrary profiles is also presented and shown to agree quite well with the experimental measurements. The model is used to demonstrate ways in which the aspect ratios of subwavelength ridges and trenches can be obtained from scattering data and how ridges can be distinguished from trenches over a wide range of aspect ratios. We show that some earlier results of studies on distinguishing pits from particles do not extend to low-aspect-ratio features

The correlations between the spin frequencies and kHz QPOs of Neutron Stars in LMXBs

We studied the correlations between spin frequencies and kilohertz quasi-periodic oscillations (kHz QPOs) in neutron star low mass X-ray binaries. The updated data of kHz QPOs and spin frequencies are statistically analyzed. We found that when two simultaneous kHz QPOs are present in the power spectrum, the minimum frequency of upper kHz QPO is at least 1.3 times larger than the spin frequency, i.e. \nu_{s}<\nu_{2min}/1.3. We also found that the average kHz QPO peak separation in 6 Atoll sources anti-correlates with the spin frequency in the form \lan\dn\ran = -(0.19\pm0.05)\ns+(389.40\pm21.67)Hz. If we shifted this correlation in the direction of the peak separation by a factor of 1.5, this correlation matches the data points of the two accretion powered millisecond X-ray pulsars, SAX J1808.4-3658 and XTE J1807-294.Comment: 4 pages, 2 figures, accepted for publication in A&