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

Constraining f(R) Gravity as a Scalar Tensor Theory

We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass or by exploiting the so-called chameleon effect. However, in both cases, it appears likely that any late-time cosmic acceleration will be observationally indistinguishable from acceleration caused by a cosmological constant. We also explore further observational constraints from, e.g., big bang nucleosynthesis and inflation.Comment: 15 pages, 5 figure

A Parameter-Free Tour of the Binary Black Hole Population

The continued operation of the Advanced LIGO and Advanced Virgo gravitational-wave detectors is enabling the first detailed measurements of the mass, spin, and redshift distributions of the merging binary black hole population. Our present knowledge of these distributions, however, is based largely on strongly parameteric models; such models typically assume the distributions of binary parameters to be superpositions of power laws, peaks, dips, and breaks, and then measure the parameters governing these "building block" features. Although this approach has yielded great progress in initial characterization of the compact binary population, the strong assumptions entailed leave it often unclear which physical conclusions are driven by observation and which by the specific choice of model. In this paper, we instead model the merger rate of binary black holes as an unknown autoregressive process over the space of binary parameters, allowing us to measure the distributions of binary black hole masses, redshifts, component spins, and effective spins with near-complete agnosticism. We find the primary mass spectrum of binary black holes to be doubly-peaked, with a fairly flat continuum that steepens at high masses. We identify signs of unexpected structure in the redshift distribution of binary black holes: a uniform-in-comoving volume merger rate at low redshift followed by a rise in the merger rate beyond redshift $z\approx 0.5$. Finally, we find that the distribution of black hole spin magnitudes is unimodal and concentrated at small but non-zero values, and that spin orientations span a wide range of spin-orbit misalignment angles but are also unlikely to be truly isotropic.Comment: 24 pages, 14 figures; code can be found at http://github.com/tcallister/autoregressive-bbh-inference and data can be download from https://zenodo.org/record/761609

Post-Newtonian expansion for Gauss-Bonnet Gravity

The Parametrized Post-Newtonian expansion of gravitational theories with a scalar field coupled to the Gauss-Bonnet invariant is performed and confrontation of such theories with Solar system experiments is discussed.Comment: 4 pages; typos corrected, published versio

Instrumental Stakeholder Theory Makes Ethically Based Relationship Building Palatable to Managers Focused on the Bottom Line

We appreciate the opportunity to engage in this dialogue with Weitzner and Deutsch (2019) to clarify the meaning and intent of some of the arguments found in our article, “How Applying Instrumental Stakeholder Theory Can Provide Sustainable Competitive Advantage” (Jones, Harrison, & Felps, 2018). We are grateful for the high praise from the authors regarding the rigor and logic of our applications of resource-based criteria to instrumental stakeholder theory (IST). We begin this response by highlighting a few areas of agreement, followed by some points where we disagree

How Applying Instrumental Stakeholder Theory Can Provide Sustainable Competitive Advantage

Instrumental stakeholder theory considers the performance consequences for firms of highly ethical relationships with stakeholders, characterized by high levels of trust, cooperation, and information sharing. While research suggests performance benefits, an obvious question remains: If instrumental stakeholder theory-based stakeholder treatment is so valuable, why isn\u27t it the dominant mode of relating to stakeholders? We argue that the existing instrumental stakeholder theory literature has three shortcomings that limit its ability to explain variance in performance. (1) Little theory exists around how instrumental stakeholder theory-based stakeholder management could provide sustainable competitive advantage. (2) The literature has largely neglected the potential downsides (i.e., costs) associated with pursuing these sorts of stakeholder relationships. (3) There is a paucity of theory on the contexts in which the incremental benefits of instrumental stakeholder theory-based stakeholder relationships are most likely to exceed the costs. As our primary contribution, we develop a theoretical path from a communal sharing relational ethics strategy--characterized by an intention to rely on relational contracts, joint wealth creation, high levels of mutual trust and cooperation, and communal sharing of property--to a close relationship capability, which we argue is valuable, rare, and difficult to imitate and, thus, a potential source of sustainable competitive advantage. We also consider the potential costs of achieving this capability and identify contexts in which the resulting relationships are likely to have the greatest net value

Digging the population of compact binary mergers out of the noise

Coalescing compact binaries emitting gravitational wave (GW) signals, as recently detected by the Advanced LIGO-Virgo network, constitute a population over the multi-dimensional space of component masses and spins, redshift, and other parameters. Characterizing this population is a major goal of GWobservations and may be approached via parametric models.We demonstrate hierarchical inference for such models with a method that accounts for uncertainties in each binary merger’s individual parameters, for mass-dependent selection effects, and also for the presence of a second population of candidate events caused by detector noise. Thus, the method is robust to potential biases from a contaminated sample and allows us to extract information from events that have a relatively small probability of astrophysical origin

Unifying cosmological and recent time variations of fundamental couplings

A number of positive and null results on the time variation of fundamental constants have been reported. It is difficult to judge whether or not these claims are mutually consistent, since the observable quantities depend on several parameters, namely the coupling strengths and masses of particles. The evolution of these coupling-parameters over cosmological history is also a priori unknown. A direct comparison requires a relation between the couplings. We explore several distinct scenarios based on unification of gauge couplings, providing a representative (though not exhaustive) sample of such relations. For each scenario we obtain a characteristic time dependence and discuss whether a monotonic time evolution is allowed. For all scenarios, some contradictions between different observations appear. We show how a clear observational determination of non-zero variations would test the dominant mechanism of varying couplings within unified theories.Comment: Formatting changes and minor typos, equivalent to published version. 35 pages (11pt article format), 8 figure