Spherically Symmetric Gravitational Collapse of Perfect Fluids

Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change on an initial spacelike hypersurface. Rather than specifying Schwarzschild coordinates for the exterior of the collapsing region, we let the interior dictate the form of the solution in the exterior, and thus both regions are found to be written in one coordinate patch. This not only alleviates the need for complicated matching schemes at the interface, but also finds a new coordinate system for the Schwarzschild spacetime expressed in generalized Painleve-Gullstrand coordinates.Comment: 3 pages, To appear in the proceedings of the eleventh Marcel Grossmann meeting on general relativity (MGXI), 23-29 July, 2006, Berli

Three-dimensional shapelets and an automated classification scheme for dark matter haloes

We extend the two-dimensional Cartesian shapelet formalism to d-dimensions. Concentrating on the three-dimensional case, we derive shapelet-based equations for the mass, centroid, root-mean-square radius, and components of the quadrupole moment and moment of inertia tensors. Using cosmological N-body simulations as an application domain, we show that three-dimensional shapelets can be used to replicate the complex sub-structure of dark matter halos and demonstrate the basis of an automated classification scheme for halo shapes. We investigate the shapelet decomposition process from an algorithmic viewpoint, and consider opportunities for accelerating the computation of shapelet-based representations using graphics processing units (GPUs).Comment: 19 pages, 11 figures, accepted for publication in MNRA

Gravitational collapse of spherically symmetric plasmas in Einstein-Maxwell spacetimes

We utilize a recent formulation of a spherically symmetric spacetime endowed with a general decomposition of the energy momentum tensor [Phys. Rev. D, 75, 024031 (2007)] to derive equations governing spherically symmetric distributions of electromagnetic matter. We show the system reduces to the Reissner-Nordstrom spacetime in general, spherically symmetric coordinates in the vacuum limit. Furthermore, we show reduction to the charged Vaidya spacetime in non-null coordinates when certain equations of states are chosen. A model of gravitational collapse is discussed whereby a charged fluid resides within a boundary of finite radial extent on the initial hypersurface, and is allowed to radiate charged particles. Our formalism allows for the discussion of all regions in this model without the need for complicated matching schemes at the interfaces between successive regions. As further examples we consider the collapse of a thin shell of charged matter onto a Reissner-Nordstrom black hole. Finally, we reduce the entire system of equations to the static case such that we have the equations for hydrostatic equilibrium of a charged fluid.Comment: Accepted for publication in Phys. Rev.

Spherically Symmetric Gravitational Collapse of General Fluids

We express Einstein's field equations for a spherically symmetric ball of general fluid such that they are conducive to an initial value problem. We show how the equations reduce to the Vaidya spacetime in a non-null coordinate frame, simply by designating specific equations of state. Furthermore, this reduces to the Schwarzschild spacetime when all matter variables vanish. We then describe the formulation of an initial value problem, whereby a general fluid ball with vacuum exterior is established on an initial spacelike slice. As the system evolves, the fluid ball collapses and emanates null radiation such that a region of Vaidya spacetime develops. Therefore, on any subsequent spacelike slice there exists three regions; general fluid, Vaidya and Schwarzschild, all expressed in a single coordinate patch with two free-boundaries determined by the equations. This implies complicated matching schemes are not required at the interfaces between the regions, instead, one simply requires the matter variables tend to the appropriate equations of state. We also show the reduction of the system of equations to the static cases, and show staticity necessarily implies zero ``heat flux''. Furthermore, the static equations include a generalization of the Tolman-Oppenheimer-Volkoff equations for hydrostatic equilibrium to include anisotropic stresses in general coordinates.Comment: 11 pages, 3 figures, submitted to Phys. Rev.

Pressure gradients, shell crossing singularities and acoustic oscillations - application to inhomogeneous cosmological models

Inhomogeneous cosmological models have recently become a very interesting alternative to standard cosmology. This is because these models are able to fit cosmological observations without the need for dark energy. However, due to inhomogeneity and pressure-less matter content, these models can suffer from shell crossing singularities. These singularities occur when two shell of dust collide with each other leading to infinite values of the density. In this Letter we show that if inhomogeneous pressure is included then these singularities can be prevented from occurring over the period of structure formation. Thus, a simple incorporation of a gradient of pressure allows for more comprehensive studies of inhomogeneous cosmological models and their application to cosmology.Comment: 5 pages, 3 figures. Accepted for publication in MNRA

Gravitational waves from Sco X-1: A comparison of search methods and prospects for detection with advanced detectors

The low-mass X-ray binary Scorpius X-1 (Sco X-1) is potentially the most luminous source of continuous gravitational-wave radiation for interferometers such as LIGO and Virgo. For low-mass X-ray binaries this radiation would be sustained by active accretion of matter from its binary companion. With the Advanced Detector Era fast approaching, work is underway to develop an array of robust tools for maximizing the science and detection potential of Sco X-1. We describe the plans and progress of a project designed to compare the numerous independent search algorithms currently available. We employ a mock-data challenge in which the search pipelines are tested for their relative proficiencies in parameter estimation, computational efficiency, robust- ness, and most importantly, search sensitivity. The mock-data challenge data contains an ensemble of 50 Scorpius X-1 (Sco X-1) type signals, simulated within a frequency band of 50-1500 Hz. Simulated detector noise was generated assuming the expected best strain sensitivity of Advanced LIGO and Advanced VIRGO ($4 \times 10^{-24}$ Hz$^{-1/2}$). A distribution of signal amplitudes was then chosen so as to allow a useful comparison of search methodologies. A factor of 2 in strain separates the quietest detected signal, at $6.8 \times 10^{-26}$ strain, from the torque-balance limit at a spin frequency of 300 Hz, although this limit could range from $1.2 \times 10^{-25}$ (25 Hz) to $2.2 \times 10^{-26}$ (750 Hz) depending on the unknown frequency of Sco X-1. With future improvements to the search algorithms and using advanced detector data, our expectations for probing below the theoretical torque-balance strain limit are optimistic.Comment: 33 pages, 11 figure

Linking the rates of neutron star binaries and short gamma-ray bursts

Short gamma-ray bursts are believed to be produced by both binary neutron star (BNS) and neutron star-black hole (NSBH) mergers. We use current estimates for the BNS and NSBH merger rates to calculate the fraction of observable short gamma-ray bursts produced through each channel. This allows us to constrain merger rates of BNS to $\mathcal{R}_{\rm{BNS}}=384^{+431}_{-213}{\rm{Gpc}^{-3} \rm{yr}^{-1}}$ ($90\%$ credible interval), a $16\%$ decrease in the rate uncertainties from the second LIGO--Virgo Gravitational-Wave Transient Catalog, GWTC-2. Assuming a top-hat emission profile with a large Lorentz factor, we constrain the average opening angle of gamma-ray burst jets produced in BNS mergers to $\approx 15^\circ$. We also measure the fraction of BNS and NSBH mergers that produce an observable short gamma-ray burst to be $0.02^{+0.02}_{-0.01}$ and $0.01 \pm 0.01$, respectively and find that $\gtrsim 40\%$ of BNS mergers launch jets (90\% confidence). We forecast constraints for future gravitational-wave detections given different modelling assumptions, including the possibility that BNS and NSBH jets are different. With $24$ BNS and $55$ NSBH observations, expected within six months of the LIGO-Virgo-KAGRA network operating at design sensitivity, it will be possible to constrain the fraction of BNS and NSBH mergers that launch jets with $10\%$ precision. Within a year of observations, we can determine whether the jets launched in NSBH mergers have a different structure than those launched in BNS mergers and rule out whether $\gtrsim 80\%$ of binary neutron star mergers launch jets. We discuss the implications of future constraints on understanding the physics of short gamma-ray bursts and binary evolution.Comment: Accepted in Physical Review D: 13 pages, 5 figure

Timing analysis for 20 millisecond pulsars in the Parkes Pulsar Timing Array

We present timing models for 20 millisecond pulsars in the Parkes Pulsar Timing Array. The precision of the parameter measurements in these models has been improved over earlier results by using longer data sets and modelling the non-stationary noise. We describe a new noise modelling procedure and demonstrate its effectiveness using simulated data. Our methodology includes the addition of annual dispersion measure (DM) variations to the timing models of some pulsars. We present the first significant parallax measurements for PSRs J1024-0719, J1045-4509, J1600-3053, J1603-7202, and J1730-2304, as well as the first significant measurements of some post-Keplerian orbital parameters in six binary pulsars, caused by kinematic effects. Improved Shapiro delay measurements have resulted in much improved pulsar mass measurements, particularly for PSRs J0437-4715 and J1909-3744 with $M_p=1.44\pm0.07$ $M_\odot$ and $M_p=1.47\pm0.03$ $M_\odot$ respectively. The improved orbital period-derivative measurement for PSR J0437-4715 results in a derived distance measurement at the 0.16% level of precision, $D=156.79\pm0.25$ pc, one of the most fractionally precise distance measurements of any star to date.Comment: 21 pages, 5 figures, 7 tables. Accepted for publication in MNRA

Gender-Related Differences in the Prevalence of Cardiovascular Disease Risk Factors and their Correlates in Urban Tanzania.

\ud Urban areas in Africa suffer a serious problem with dual burden of infectious diseases and emerging chronic diseases such as cardiovascular diseases (CVD) and diabetes which pose a serious threat to population health and health care resources. However in East Africa, there is limited literature in this research area. The objective of this study was to examine the prevalence of cardiovascular disease risk factors and their correlates among adults in Temeke, Dar es Salaam, Tanzania. Results of this study will help inform future research and potential preventive and therapeutic interventions against such chronic diseases. The study design was a cross sectional epidemiological study. A total of 209 participants aged between 44 and 66 years were included in the study. A structured questionnaire was used to evaluate socioeconomic and lifestyle characteristics. Blood samples were collected and analyzed to measure lipid profile and fasting glucose levels. Cardiovascular risk factors were defined using World Health Organization criteria. The age-adjusted prevalence of obesity (BMI > or = 30) was 13% and 35%, among men and women (p = 0.0003), respectively. The prevalence of abdominal obesity was 11% and 58% (p < 0.0001), and high WHR (men: >0.9, women: >0.85) was 51% and 73% (p = 0.002) for men and women respectively. Women had 4.3 times greater odds of obesity (95% CI: 1.9-10.1), 14.2-fold increased odds for abdominal adiposity (95% CI: 5.8-34.6), and 2.8 times greater odds of high waist-hip-ratio (95% CI: 1.4-5.7), compared to men. Women had more than three-fold greater odds of having metabolic syndrome (p = 0.001) compared to male counterparts, including abdominal obesity, low HDL-cholesterol, and high fasting blood glucose components. In contrast, female participants had 50% lower odds of having hypertension, compared to men (95%CI: 0.3-1.0). Among men, BMI and waist circumference were significantly correlated with blood pressure, triglycerides, total, LDL-, and HDL-cholesterol (BMI only), and fasting glucose; in contrast, only blood pressure was positively associated with BMI and waist circumference in women. The prevalence of CVD risk factors was high in this population, particularly among women. Health promotion, primary prevention, and health screening strategies are needed to reduce the burden of cardiovascular disease in Tanzania.\u