Leo C. Stein

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Quantitative polarized infrared analysis of trace OH in populations of randomly oriented mineral grains

Abstract Use of infrared spectroscopy as an accurate, quantitative method to measure concentrations of hydrous species in minerals requires consideration of the interactions of anisotropic crystals with infrared light. Ensuring that contributions are identified from species at all orientations in the crystal requires combining three measurements, taken with the electric field polarized along three mutually perpendicular directions. This is typically accomplished by determining the orientation of a crystal in advance, and then sectioning it perpendicular to its principal axes. In many instances, however, natural or experimental samples are not suitable for such handling. Here we demonstrate a method that instead uses at least three randomly sectioned grains, considered to be multiple samples of a homogeneous population. We explain the theory whereby: (1) the orientations of the polarization vectors of measurements taken on these grains are determined by comparison to oriented standards of the same mineral, and (2) the principal-axis spectra of the sample are synthesized from the randomly oriented spectra. By comparison to complementary electron backscatter diffraction (EBSD) data, we demonstrate that determination of orientations using the silicate overtone bands in Fourier-Transform infrared (FTIR) spectra is accurate and precise, with typical angular errors of 6°. We show that this precision is sufficient for the synthetic principal-axis spectra to be essentially indistinguishable from X-ray oriented standard spectra. We demonstrate the application of this technique to determining the OH concentrations in a population of hydrated olivine grains recovered from a high-pressure, high-temperature multi-anvil experiment.

X-Pipeline: an analysis package for autonomous gravitational-wave burst searches

Autonomous gravitational-wave searches—fully automated analyses of data that run without human intervention or assistance—are desirable for a number of reasons. They are necessary for the rapid identification of gravitational-wave burst candidates, which in turn will allow for follow-up observations by other observatories and the maximum exploitation of their scientific potential. A fully automated analysis would also circumvent the traditional by hand setup and tuning of burst searches that is both labourious and time consuming. We demonstrate a fully automated search with X-Pipeline, a software package for the coherent analysis of data from networks of interferometers for detecting bursts associated with gamma-ray bursts (GRBs) and other astrophysical triggers. We discuss the methods X-Pipeline uses for automated running, including background estimation, efficiency studies, unbiased optimal tuning of search thresholds and prediction of upper limits. These are all done automatically via Monte Carlo with multiple independent data samples and without requiring human intervention. As a demonstration of the power of this approach, we apply X-Pipeline to LIGO data to compute the sensitivity to gravitational-wave emission associated with GRB 031108. We find that X-Pipeline is sensitive to signals approximately a factor of 2 weaker in amplitude than those detectable by the cross-correlation technique used in LIGO searches to date. We conclude with comments on the status of X-Pipeline as a fully autonomous, near-real-time-triggered burst search in the current LSC-Virgo Science Run.

Bumpy black holes in alternative theories of gravity

We generalize the bumpy black hole framework to allow for alternative theory deformations. We construct two model-independent parametric deviations from the Kerr metric: one built from a generalization of the quasi-Kerr and bumpy metrics and one built directly from perturbations of the Kerr spacetime in Lewis-Papapetrou form. We find the conditions that these bumps must satisfy for there to exist an approximate second-order Killing tensor so that the perturbed spacetime still possesses three constants of the motion (a deformed energy, angular momentum and Carter constant) and the geodesic equations can be written in first-order form. We map these parametrized metrics to each other via a diffeomorphism and to known analytical black hole solutions in alternative theories of gravity. The parametrized metrics presented here serve as frameworks for the systematic calculation of extreme mass-ratio inspiral waveforms in parametrized non-general relativity theories and the investigation of the accuracy to which space-borne gravitational wave detectors can constrain such deviations.

Black Hole Based Tests of General Relativity

General relativity has passed all solar system experiments and neutron star based tests, such as binary pulsar observations, with flying colors. A more exotic arena for testing general relativity is in systems that contain one or more black holes. Black holes are the most compact objects in the universe, providing probes of the strongest-possible gravitational fields. We are motivated to study strong-field gravity since many theories give large deviations from general relativity only at large field strengths, while recovering the weak-field behavior. In this article, we review how one can probe general relativity and various alternative theories of gravity by using electromagnetic waves from a black hole with an accretion disk, and gravitational waves from black hole binaries. We first review model-independent ways of testing gravity with electromagnetic/gravitational waves from a black hole system. We then focus on selected examples of theories that extend general relativity in rather simple ways. Some important characteristics of general relativity include (but are not limited to) (i) only tensor gravitational degrees of freedom, (ii) the graviton is massless, (iii) no quadratic or higher curvatures in the action, and (iv) the theory is 4 dimensional. Altering a characteristic leads to a different extension of general relativity: (i) scalar-tensor theories, (ii) massive gravity theories, (iii) quadratic gravity, and (iv) theories with large extra dimensions. Within each theory, we describe black hole solutions, their properties, and current and projected constraints on each theory using black hole-based tests of gravity. We close this review by listing some of the open problems in model-independent tests and within each specific theory.

Isolated and Binary Neutron Stars in Dynamical Chern-Simons Gravity

We study isolated and binary neutron stars in dynamical Chern-Simons gravity. This theory modifies the Einstein-Hilbert action through the introduction of a dynamical scalar field coupled to the Pontryagin density. We here treat this theory as an effective model, working to leading order in the Chern-Simons coupling. We first construct isolated neutron star solutions in the slow-rotation expansion to quadratic order in spin. We find that isolated neutron stars acquire a scalar dipole charge that corrects its spin angular momentum to linear order in spin and corrects its mass and quadrupole moment to quadratic order in spin, as measured by an observer at spatial infinity. We then consider neutron stars binaries that are widely separated and solve for their orbital evolution in this modified theory. We find that the evolution of post-Keplerian parameters is modified, with the rate of periastron advance being the dominant correction at first post-Newtonian order. We conclude by applying these results to observed pulsars with the aim to place constraints on dynamical Chern-Simons gravity. We find that the modifications to the observed mass are degenerate with the neutron star equation of state, which prevents us from testing the theory with the inferred mass of the millisecond pulsar J1614-2230. We also find that the corrections to the post-Keplerian parameters are too small to be observable today even with data from the double binary pulsar J0737-3039. Our results suggest that pulsar observations are not currently capable of constraining dynamical Chern-Simons gravity, and thus, gravitational-wave observations may be the only path to a stringent constraint of this theory in the imminent future.

THREE-HAIR RELATIONS FOR ROTATING STARS: NONRELATIVISTIC LIMIT

The gravitational field outside of astrophysical black holes is completely described by their mass and spin frequency, as expressed by the no-hair theorems. These theorems assume vacuum spacetimes, and thus they apply only to black holes and not to stars. Despite this, we analytically find that the gravitational potential of arbitrarily rapid, rigidly rotating stars can still be described completely by only their mass, spin angular momentum, and quadrupole moment. Although these results are obtained in the nonrelativistic limit (to leading order in a weak-field expansion of general relativity, GR), they are also consistent with fully relativistic numerical calculations of rotating neutron stars. This description of the gravitational potential outside the source in terms of just three quantities is approximately universal (independent of equation of state). Such universality may be used to break degeneracies in pulsar and future gravitational wave observations to extract more physics and test GR in the strong-field regime.

Numerical binary black hole mergers in dynamical Chern-Simons gravity: Scalar field

Testing general relativity in the nonlinear, dynamical, strong-field regime of gravity is one of the major goals of gravitational wave astrophysics. Performing precision tests of general relativity (GR) requires numerical inspiral, merger, and ringdown waveforms for binary black hole (BBH) systems in theories beyond GR. Currently, GR and scalar-tensor gravity are the only theories amenable to numerical simulations. In this article, we present a well-posed perturbation scheme for numerically integrating beyond-GR theories that have a continuous limit to GR. We demonstrate this scheme by simulating BBH mergers in dynamical Chern-Simons gravity (dCS), to linear order in the perturbation parameter. We present mode waveforms and energy fluxes of the dCS pseudoscalar field from our numerical simulations. We find good agreement with analytic predictions at early times, including the absence of pseudoscalar dipole radiation. We discover new phenomenology only accessible through numerics: a burst of dipole radiation during merger. We also quantify the self-consistency of the perturbation scheme. Finally, we estimate bounds that GR-consistent LIGO detections could place on the new dCS length scale, approximately l ≲ O(10)km.

Challenging the presence of scalar charge and dipolar radiation in binary pulsars

Corrections to general relativity that introduce long-ranged scalar fields which are nonminimally coupled to curvature typically predict that neutron stars possess a nontrivial scalar field profile anchored to the star. An observer far from a star is most sensitive to the spherically symmetric piece of this profile that decays linearly with the inverse of the distance to the source, the so-called scalar monopole charge, which is related to the emission of dipolar radiation from compact binary systems. The presence of dipolar radiation has the potential to rule out or very strongly constrain extended theories of gravity. These facts may lead people to believe that gravitational theories that introduce long-ranged scalar fields have already been constrained strongly from binary pulsar observations. Here we challenge this “lore” by investigating the decoupling limit of Gauss-Bonnet gravity as an example, in which the scalar field couples linearly to the Gauss-Bonnet density in the action. We prove a theorem that neutron stars in this theory cannot possess a scalar charge, due to the topological nature of the Gauss-Bonnet density. Thus Gauss-Bonnet gravity evades the strong binary pulsar constraints on dipole radiation. We discuss the astrophysical systems which will yield the best constraints on Gauss-Bonnet gravity and related quadratic gravity theories. To achieve this we compute the scalar charge in quadratic gravity theories by performing explicit analytic and numerical matching calculations for slowly rotating neutron stars. In generic quadratic gravity theories, either neutron star–binary or neutron star–black hole systems can be used to constrain the theory, but because of the vanishing charge, Gauss-Bonnet gravity evades the neutron star–binary constraints. However, in contrast to neutron stars, black holes in Gauss-Bonnet gravity do anchor scalar charge, because of the difference in topology. The best constraints on Gauss-Bonnet gravity will thus come from accurate black hole observations, for example through gravitational waves from inspiraling binaries or the timing of pulsar–black hole binaries with radio telescopes. We estimate these constraints to be a factor of 10 better than the current estimated bound, and also include estimated constraints on generic quadratic gravity theories from pulsar timing.

Why I-Love-Q: Explaining why universality emerges in compact objects

similar to each other to explain the universality observed. Second, we study the impact on the universality of approximating stellar isodensity contours as self-similar ellipsoids. An analytical calculation in the non-relativistic limit reveals that the shape of the ellipsoids per se does not aect the universal relations much, but relaxing the selfsimilarity assumption can completely destroy it. Third, we investigate the eccentricity proles of rotating relativistic stars and nd that the ellipticity is roughly constant, with variations of roughly (20{30)% in the region that matters to the universal relations. Fourth, we repeat the above analysis for dierentially-rot ating, non-compact, regular stars and nd that this time the ellipticity is not constant, with variations that easily exceed 100%, and moreover, universality is lost. These ndings suggest that universality arises as an emergent approximate symmetry: as one ows in the stellarstructure phase space from non-compact star region to the relativistic star region, the eccentricity variation inside stars decreases, leading to approximate self-similarity in their isodensity contours, which then leads to the universal behavior observed in their exterior multipole moments.