Electromagnetic Fields of Separable Space-Times

Carter derived the forms of the metric and the vector potentials of the space-times in which the relativistic Schrodinger equation for the motion of a charged particle separates. Here we show that on each `spheroidal' surface a rotation rate exists such that relative to those rotating axes the electric and magnetic fields are parallel and orthogonal to the spheroid which is thus an equipotential in those axes. All the finite Carter separable systems without magnetic monopoles or gravomagnetic NUT monopoles have the same gyromagnetic ratio as the Dirac electron.Comment: 9 pages; accepted for publication in Class. Quantum Gra

Observable Properties of Orbits in Exact Bumpy Spacetimes

We explore the properties of test-particle orbits in "bumpy" spacetimes - stationary, reflection-symmetric, asymptotically flat solutions of Einstein equations that have a non-Kerr (anomalous) higher-order multipole-moment structure but can be tuned arbitrarily close to the Kerr metric. Future detectors should observe gravitational waves generated during inspirals of compact objects into supermassive central bodies. If the central body deviates from the Kerr metric, this will manifest itself in the emitted waves. Here, we explore some of the features of orbits in non-Kerr spacetimes that might lead to observable signatures. As a basis for this analysis, we use a family of exact solutions proposed by Manko & Novikov which deviate from the Kerr metric in the quadrupole and higher moments, but we also compare our results to other work in the literature. We examine isolating integrals of the orbits and find that the majority of geodesic orbits have an approximate fourth constant of the motion (in addition to the energy, angular momentum and rest mass) and the resulting orbits are tri-periodic to high precision. We also find that this fourth integral can be lost for certain orbits in some oblately deformed Manko-Novikov spacetimes. However, compact objects will probably not end up on these chaotic orbits in nature. We compute the location of the innermost stable circular orbit (ISCO) and find that the behavior of orbtis near the ISCO can be qualitatively different depending on whether the ISCO is determined by the onset of an instability in the radial or vertical direction. Finally, we compute periapsis and orbital-plane precessions for nearly circular and nearly equatorial orbits in both the strong and weak field, and discuss weak-field precessions for eccentric equatorial orbits.Comment: 42 pages, 20 figures, accepted by Phys. Rev. D, v2 has minor changes to make it consistent with published versio

Cosmology with the lights off: Standard sirens in the Einstein Telescope era

We explore the prospects for constraining cosmology using gravitational-wave (GW) observations of neutron-star binaries by the proposed Einstein Telescope (ET), exploiting the narrowness of the neutron-star mass function. Double neutron-star (DNS) binaries are expected to be one of the first sources detected after "first-light" of Advanced LIGO and are expected to be detected at a rate of a few tens per year in the advanced era. However the proposed ET could catalog tens of thousands per year. Combining the measured source redshift distributions with GW-network distance determinations will permit not only the precision measurement of background cosmological parameters, but will provide an insight into the astrophysical properties of these DNS systems. Of particular interest will be to probe the distribution of delay times between DNS-binary creation and subsequent merger, as well as the evolution of the star-formation rate density within ET's detection horizon. Keeping H_0, \Omega_{m,0} and \Omega_{\Lambda,0} fixed and investigating the precision with which the dark-energy equation-of-state parameters could be recovered, we found that with 10^5 detected DNS binaries we could constrain these parameters to an accuracy similar to forecasted constraints from future CMB+BAO+SNIa measurements. Furthermore, modeling the merger delay-time distribution as a power-law, and the star-formation rate (SFR) density as a parametrized version of the Porciani and Madau SF2 model, we find that the associated astrophysical parameters are constrained to within ~ 10%. All parameter precisions scaled as 1/sqrt(N), where N is the number of cataloged detections. We also investigated how precisions varied with the intrinsic underlying properties of the Universe and with the distance reach of the network (which may be affected by the low-frequency cutoff of the detector).Comment: 24 pages, 11 figures, 6 tables. Minor changes to reflect published version. References updated and correcte

Non-Linear Effects in Non-Kerr spacetimes

There is a chance that the spacetime around massive compact objects which are expected to be black holes is not described by the Kerr metric, but by a metric which can be considered as a perturbation of the Kerr metric. These non-Kerr spacetimes are also known as bumpy black hole spacetimes. We expect that, if some kind of a bumpy black hole exists, the spacetime around it should possess some features which will make the divergence from a Kerr spacetime detectable. One of the differences is that these non-Kerr spacetimes do not posses all the symmetries needed to make them integrable. We discuss how we can take advantage of this fact by examining EMRIs into the Manko-Novikov spacetime.Comment: 8 pages, 3 Figures; to appear in the proceedings of the conference "Relativity and Gravitation: 100 Years after Einstein in Prague" (2012

Gravitational waves from intermediate-mass-ratio inspirals for ground-based detectors

We explore the prospects for Advanced LIGO to detect gravitational waves from neutron stars and stellar mass black holes spiraling into intermediate-mass ($M\sim 50 M_\odot$ to $350 M_\odot$) black holes. We estimate an event rate for such \emph{intermediate-mass-ratio inspirals} (IMRIs) of up to $\sim 10$--$30 \mathrm{yr}^{-1}$. Our numerical simulations show that if the central body is not a black hole but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat then the waves will likely be tri-periodic, as for a black hole. We report generalizations of a theorem due to Ryan (1995) which suggest that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) a full map of the central body's metric, full details of the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. We estimate that Advanced LIGO can measure or constrain deviations of the central body from a Kerr black hole with modest but interesting accuracy.Comment: Accepted for publication in Physical Review Letter

Group equivariant neural posterior estimation

Simulation-based inference with conditional neural density estimators is a powerful approach to solving inverse problems in science. However, these methods typically treat the underlying forward model as a black box, with no way to exploit geometric properties such as equivariances. Equivariances are common in scientific models, however integrating them directly into expressive inference networks (such as normalizing flows) is not straightforward. We here describe an alternative method to incorporate equivariances under joint transformations of parameters and data. Our method -- called group equivariant neural posterior estimation (GNPE) -- is based on self-consistently standardizing the "pose" of the data while estimating the posterior over parameters. It is architecture-independent, and applies both to exact and approximate equivariances. As a real-world application, we use GNPE for amortized inference of astrophysical binary black hole systems from gravitational-wave observations. We show that GNPE achieves state-of-the-art accuracy while reducing inference times by three orders of magnitude

Ultimate gravitational mass defect

We present a new type of gravitational mass defect in which an infinite amount of matter may be bounded in a zero ADM mass. This interpolates between effects typical of closed worlds and T-spheres. We consider the Tolman model of dust distribution and show that this phenomenon reveals itself for a solution that has no origin on one side but is closed on the other side. The second class of examples corresponds to smooth gluing T-spheres to the portion of the Friedmann-Robertson-Walker solution. The procedure is generalized to combinations of smoothly connected T-spheres, FRW and Schwarzschild metrics. In particular, in this approach a finite T-sphere is obtained that looks for observers in two R-regions as the Schwarzschild metric with two different masses one of which may vanish.Comment: 9 pages. 1 reference added. To appear in Gen. Rel. Gra

A complex increase in hepatitis C virus in a correctional facility: bumps in the road

Objective: The prevalence of hepatitis C virus (HCV) in correctional facilities in Australia among people who inject drugs is 60%, with disproportionate effects observed in Aboriginal and Torres Strait Islander people. Following the micro-elimination of HCV in a Queensland correctional facility (QCF), newly acquired cases began to increase in mid-2019. Here we discuss the public health response to increasing HCV in a QCF. Methods: Enhanced surveillance was performed to obtain contextual outbreak data on risk factors including injecting drug use, sharing of personal hygiene equipment and do-it-yourself-tattooing. Results: In the sixteen months, there were 250 notifications of new and re-infected HCV infections in prisoners in the QCF. Qualitative data revealed the leading factor in transmission to be injecting drug use. Conclusions: Drivers for increased HCV transmission in correctional facilities include boredom, waiting lists for opioid substitution programs, changes in injecting behaviours and sharing of injecting paraphernalia. Point-of-care testing combined with education and the development of a needle and syringe program may be promising ways forward for managing HCV in correctional facilities. Implications for public health: Correctional facilities are key locations to target sexually transmitted infection (STI) and blood-borne virus (BBV) testing and treatment as well as health promotion to improve the health of inmates and the communities they return to

Extreme mass ratio inspiral rates: dependence on the massive black hole mass

We study the rate at which stars spiral into a massive black hole (MBH) due to the emission of gravitational waves (GWs), as a function of the mass M of the MBH. In the context of our model, it is shown analytically that the rate approximately depends on the MBH mass as M^{-1/4}. Numerical simulations confirm this result, and show that for all MBH masses, the event rate is highest for stellar black holes, followed by white dwarfs, and lowest for neutron stars. The Laser Interferometer Space Antenna (LISA) is expected to see hundreds of these extreme mass ratio inspirals per year. Since the event rate derived here formally diverges as M->0, the model presented here cannot hold for MBHs of masses that are too low, and we discuss what the limitations of the model are.Comment: Accepted to CQG, special LISA issu

Spherical Universes with Anisotropic Pressure

Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, tau, experienced by the dust particles. The general solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed.Comment: 24 pages, 11 figures, accepted for publication in Classical and Quantum Gravit