Finally, results from Gravity Probe-B

Nearly fifty years after its inception, the Gravity Probe B satellite mission delivers the first measurements of how a spinning gyroscope precesses in the gravitational warping of spacetime.Comment: A Viewpoint article, published in Physics 4, 43 (2011), available at http://physics.aps.org/articles/v4/43 Submitted to the arXiv by permission of the American Physical Societ

Constraining Lorentz-violating, Modified Dispersion Relations with Gravitational Waves

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.Comment: 11 pages, 3 figures, 2 tables: title changed slightly, published versio

The 1919 measurement of the deflection of light

The measurement of the deflection of starlight during a total solar eclipse on May 29, 1919 was the first verification of general relativity by an external team of scientists, brought Einstein and his theory to the attention of the general public, and left a legacy of experimental testing that continues today. The discovery of gravitational lenses turned Einstein's deflection into an important tool for astronomy and cosmology. This article reviews the history of the 1919 measurement and other eclipse measurements, describes modern measurements of the effect using radio astronomy, and of its cousin, the Shapiro time delay, and discusses gravitational lenses.Comment: 17 pages, 3 figures. Submitted to Classical and Quantum Gravity for its "Milestones of General Relativity" focus issue to be published during the Centenary Year of G

Dynamic temperature selection for parallel-tempering in Markov chain Monte Carlo simulations

Modern problems in astronomical Bayesian inference require efficient methods for sampling from complex, high-dimensional, often multi-modal probability distributions. Most popular methods, such as Markov chain Monte Carlo sampling, perform poorly on strongly multi-modal probability distributions, rarely jumping between modes or settling on just one mode without finding others. Parallel tempering addresses this problem by sampling simultaneously with separate Markov chains from tempered versions of the target distribution with reduced contrast levels. Gaps between modes can be traversed at higher temperatures, while individual modes can be efficiently explored at lower temperatures. In this paper, we investigate how one might choose the ladder of temperatures to achieve more efficient sampling, as measured by the autocorrelation time of the sampler. In particular, we present a simple, easily-implemented algorithm for dynamically adapting the temperature configuration of a sampler while sampling. This algorithm dynamically adjusts the temperature spacing to achieve a uniform rate of exchanges between chains at neighbouring temperatures. We compare the algorithm to conventional geometric temperature configurations on a number of test distributions and on an astrophysical inference problem, reporting efficiency gains by a factor of 1.2-2.5 over a well-chosen geometric temperature configuration and by a factor of 1.5-5 over a poorly chosen configuration. On all of these problems a sampler using the dynamical adaptations to achieve uniform acceptance ratios between neighbouring chains outperforms one that does not.Comment: 21 pages, 21 figure

Mutual benefit, added value? Doing research in the National Health Service

The National Health Service (NHS) has recently been the focus of government efforts to retain pharmaceutical research in the UK. Efforts to foster new partnerships between health care providers and industry have been framed with suggestions that clinical trials can offer patient benefit within the NHS, cutting across ethical and sociological concerns with the possible tension between doing research and offering care. This paper draws on ethnographic research to explore the sometimes awkward juxtapositions between trial protocols and everyday care, individual health and commercial profit, and thus the distribution of value produced through trials. While researchers appear to find the distinction between research and care useful, at least some of the time, both formal and informal strategies for living with this distinction may have the unintended consequence of making research appear supplementary to rather than simply different from clinical care

Resource Letter PTG-1: Precision Tests of Gravity

This resource letter provides an introduction to some of the main current topics in experimental tests of general relativity as well as to some of the historical literature. It is intended to serve as a guide to the field for upper-division undergraduate and graduate students, both theoretical and experimental, and for workers in other fields of physics who wish learn about experimental gravity. The topics covered include alternative theories of gravity, tests of the principle of equivalence, solar-system and binary-pulsar tests, searches for new physics in gravitational arenas, and tests of gravity in new regimes, involving astrophysics and gravitational radiation.Comment: 9 pages; submitted to American Journal of Physic

On incorporating post-Newtonian effects in N-body dynamics

The increasing role of general relativity in the dynamics of stellar systems with central massive black holes and in the evolution of hierarchical triple systems inspires a close examination of how post-Newtonian effects are incorporated into N-body dynamics. The majority of approaches incorporate relativity by adding to the Newtonian N-body equations the standard two-body post-Newtonian terms for a given star around the black hole or for the close binary in a triple system. We argue that, for calculating the evolution of such systems over timescales comparable to the relativistic pericenter advance timescale, it is essential to include "cross terms" in the equations of motion. These are post-Newtonian terms that represent a coupling between the potential of the central black hole and the potential due to other stars in the system. For hierarchical triple systems, these are couplings between the potential of the inner binary and that of the distant third body. Over pericenter precession timescales, the effects of such terms can actually be "boosted" to amplitudes of Newtonian order. We write down the post-Newtonian N-body equations of motion including a central black hole in a truncated form that includes all the relevant cross terms, in a format ready to use for numerical implementation. We do the same for hierarchical triple systems, and illustrate explicitly the effects of cross terms on the orbit-averaged equations of evolution for the orbit elements of the inner binary for the special case where the third body is on a circular orbit. We also describe the inspiration for this investigation: the motion of a test body about a central body with a Newtonian quadrupole moment, including the relativistic pericenter advance, whose correct solution for the conserved total Newtonian energy requires including PN cross terms between the mass monopole and quadrupole potentials.Comment: 15 pages, added discussion and references, version accepted by Phys. Rev.

Capture of non-relativistic particles in eccentric orbits by a Kerr black hole

We obtain approximate analytic expressions for the critical value of the total angular momentum of a non-relativistic test particle moving in the Kerr geometry, such that it will be captured by the black hole. The expressions apply to arbitrary orbital inclinations, and are accurate over the entire range of angular momentum for the Kerr black hole. The expressions can be easily implemented in N-body simulations of the evolution of star clusters around massive galactic black holes, where such captures play an important role.Comment: 8 pages, 1 figure, published versio

Orbital flips in hierarchical triple systems: relativistic effects and third-body effects to hexadecapole order

We analyze the secular evolution of hierarchical triple systems in the post-Newtonian approximation to general relativity. We expand the Newtonian three-body equations of motion in powers of the ratio $a/A$, where $a$ and $A$ are the semimajor axis of the inner binary's orbit and of the orbit of the third body relative to the center of mass of the inner binary, respectively. The leading order "quadrupole" terms, of order $(a/A)^3$ relative to the $1/a^2$ acceleration within the inner binary, are responsible for the well-known Kozai-Lidov oscillations of orbital inclination and eccentricity. The octupole terms, of order $(a/A)^4$ have been shown to allow the inner orbit to "flip" from prograde relative to the outer orbit to retrograde and back, and to permit excursions to very large eccentricities. We carry the expansion of the equations of motion to hexadecapole order, corresponding to contributions of order $(a/A)^5$. We also include the leading orbital effects of post-Newtonian theory, namely the pericenter precessions of the inner and outer orbits. Using the Lagrange planetary equations for the orbit elements of both binaries, we average over orbital timescales, obtain the equations for the secular evolution of the elements through hexadecapole order, and employ them to analyze cases of astrophysical interest. We find that, for the most part, the orbital flips found at octupole order are robust against both relativistic and hexadecapole perturbations. We show that, for equal-mass inner binaries, where the octupole terms vanish, the hexadecapole contributions can alone generate orbital flips and excursions to very large eccentricities.Comment: 16 pages, 11 figures, typos corrected; matches published versio

Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. V. Evidence for the strong equivalence principle to second post-Newtonian order

Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, non-spinning but arbitrarily shaped bodies. In particular we study the contributions of the internal structure of the bodies (such as self-gravity) that would diverge if the size of the bodies were to shrink to zero. Using a set of virial relations accurate to the first post-Newtonian order that reflect the stationarity of each body, and redefining the masses to include 1PN and 2PN self-gravity terms, we demonstrate the complete cancellation of a class of potentially divergent, structure-dependent terms that scale as s^{-1} and s^{-5/2}, where s is the characteristic size of the bodies. This is further evidence of the Strong Equivalence Principle, and supports the use of post-Newtonian approximations to derive equations of motion for strong-field bodies such as neutron stars and black holes. This extends earlier work done by Kopeikin.Comment: 14 pages, submitted to Phys. Rev. D; small changes to coincide with published versio