Prospects for detection of gravitational waves from intermediate-mass-ratio inspirals

Testing General Relativity with Gravitational Waves: An Overview

The detections of gravitational-wave (GW) signals from compact binary coalescence by ground-based detectors have opened up the era of GW astronomy. These observations provide opportunities to test Einstein’s general theory of relativity at the strong-field regime. Here we give a brief overview of the various GW-based tests of General Relativity (GR) performed by the LIGO-Virgo collaboration on the detected GW events to date. After providing details for the tests performed in four categories, we discuss the prospects for each test in the context of future GW detectors. The four categories of tests include the consistency tests, parametrized tests for GW generation and propagation, tests for the merger remnant properties, and GW polarization tests.

The missing link in gravitational-wave astronomy: A summary of discoveries waiting in the decihertz range

Since 2015 the gravitational-wave observations of LIGO and Virgo have transformed our understanding of compact-object binaries. In the years to come, ground-based gravitational-wave observatories such as LIGO, Virgo, and their successors will increase in sensitivity, discovering thousands of stellar-mass binaries. In the 2030s, the space-based LISA will provide gravitational-wave observations of massive black holes binaries. Between the ∼ 10 -103 Hz band of ground-based observatories and the ∼ 1 0 - 4 -10- 1 Hz band of LISA lies the uncharted decihertz gravitational-wave band. We propose a Decihertz Observatory to study this frequency range, and to complement observations made by other detectors. Decihertz observatories are well suited to observation of intermediate-mass ( ∼ 1 0 2 -104 M ⊙) black holes; they will be able to detect stellar-mass binaries days to years before they merge, providing early warning of nearby binary neutron star mergers and measurements of the eccentricity of binary black holes, and they will enable new tests of general relativity and the Standard Model of particle physics. Here we summarise how a Decihertz Observatory could provide unique insights into how black holes form and evolve across cosmic time, improve prospects for both multimessenger astronomy and multiband gravitational-wave astronomy, and enable new probes of gravity, particle physics and cosmology.

Testing the Binary Black Hole Nature of a Compact Binary Coalescence

We propose a novel method to test the binary black hole nature of compact binaries detectable by gravitational wave (GW) interferometers and, hence, constrain the parameter space of other exotic compact objects. The spirit of the test lies in the "no-hair" conjecture for black holes where all properties of a Kerr black hole are characterized by its mass and spin. The method relies on observationally measuring the quadrupole moments of the compact binary constituents induced due to their spins. If the compact object is a Kerr black hole (BH), its quadrupole moment is expressible solely in terms of its mass and spin. Otherwise, the quadrupole moment can depend on additional parameters (such as the equation of state of the object). The higher order spin effects in phase and amplitude of a gravitational waveform, which explicitly contains the spin-induced quadrupole moments of compact objects, hence, uniquely encode the nature of the compact binary. Thus, we argue that an independent measurement of the spin-induced quadrupole moment of the compact binaries from GW observations can provide a unique way to distinguish binary BH systems from binaries consisting of exotic compact objects.

Measuring Intermediate-Mass Black-Hole Binaries with Advanced Gravitational Wave Detectors

We perform a systematic study to explore the accuracy with which the parameters of intermediate-mass black-hole binary systems can be measured from their gravitational wave (GW) signatures using second-generation GW detectors. We make use of the most recent reduced-order models containing inspiral, merger, and ringdown signals of aligned-spin effective-one-body waveforms to significantly speed up the calculations. We explore the phenomenology of the measurement accuracies for binaries with total masses between 50M(⊙) and 500M(⊙) and mass ratios between 0.1 and 1. We find that (i) at total masses below ∼200M(⊙), where the signal-to-noise ratio is dominated by the inspiral portion of the signal, the chirp mass parameter can be accurately measured; (ii) at higher masses, the information content is dominated by the ringdown, and total mass is measured more accurately; (iii) the mass of the lower-mass companion is poorly estimated, especially at high total mass and more extreme mass ratios; and (iv) spin cannot be accurately measured for our injection set with nonspinning components. Most importantly, we find that for binaries with nonspinning components at all values of the mass ratio in the considered range and at a network signal-to-noise ratio of 15, analyzed with spin-aligned templates, the presence of an intermediate-mass black hole with mass >100M(⊙) can be confirmed with 95% confidence in any binary that includes a component with a mass of 130M(⊙) or greater.

Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors

We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10-5 - 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.

Transient resonances in the inspirals of point particles into black holes

We show that transient resonances occur in the two-body problem in general relativity for spinning black holes in close proximity to one another when one black hole is much more massive than the other. These resonances occur when the ratio of polar and radial orbital frequencies, which is slowly evolving under the influence of gravitational radiation reaction, passes through a low order rational number. At such points, the adiabatic approximation to the orbital evolution breaks down, and there is a brief but order unity correction to the inspiral rate. The resonances cause a perturbation to orbital phase of order a few tens of cycles for mass ratios ∼10(-6), make orbits more sensitive to changes in initial data (though not quite chaotic), and are genuine nonperturbative effects that are not seen at any order in a standard post-Newtonian expansion. Our results apply to an important potential source of gravitational waves, the gradual inspiral of white dwarfs, neutron stars, or black holes into much more massive black holes. Resonances' effects will increase the computational challenge of accurately modeling these sources.

Second-order gravitational self-force

Using a rigorous method of matched asymptotic expansions, I derive the equation of motion of a small, compact body in an external vacuum spacetime through second order in the body's mass (neglecting effects of internal structure). The motion is found to be geodesic in a certain locally defined regular geometry satisfying Einstein's equation at second order. I outline a method of numerically obtaining both the metric of that regular geometry and the complete second-order metric perturbation produced by the body.

Periastron advance in black-hole binaries

The general relativistic (Mercury-type) periastron advance is calculated here for the first time with exquisite precision in full general relativity. We use accurate numerical relativity simulations of spinless black-hole binaries with mass ratios 1/8≤m(1)/m(2)≤1 and compare with the predictions of several analytic approximation schemes. We find the effective-one-body model to be remarkably accurate and, surprisingly, so also the predictions of self-force theory [replacing m(1)/m(2)→m(1)m(2)/(m(1)+m(2))(2)]. Our results can inform a universal analytic model of the two-body dynamics, crucial for ongoing and future gravitational-wave searches.

Intermediate-mass-ratio black-hole binaries: numerical relativity meets perturbation theory

We study black-hole binaries in the intermediate-mass-ratio regime 0.01≲q≲0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading (ℓ, m) modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO and VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully nonlinear numerical simulations.

Intermediate-mass-ratio black-hole binaries: numerical relativity meets perturbation theory

We study black-hole binaries in the intermediate-mass-ratio regime 0.01≲q≲0.1 with a new technique that makes use of nonlinear numerical trajectories and efficient perturbative evolutions to compute waveforms at large radii for the leading and nonleading (ℓ, m) modes. As a proof-of-concept, we compute waveforms for q=1/10. We discuss applications of these techniques for LIGO and VIRGO data analysis and the possibility that our technique can be extended to produce accurate waveform templates from a modest number of fully nonlinear numerical simulations.

Carter-like constants of the motion in Newtonian gravity and electrodynamics

For a test body orbiting an axisymmetric body in Newtonian gravitational theory with mass m and multiple moments Q_{l} (and for a charge in orbit about a charge distribution with the same multipole moments) we show that there exists, in addition to the energy and angular momentum component along the symmetry axis, a conserved quantity analogous to the Carter constant of Kerr spacetimes for rotating black holes in general relativity, if the odd-l moments vanish, and the even-l moments satisfy Q_{2l}=m(Q_{2}/m);{l}. Strangely, this is precisely the relation among mass moments enforced by the no-hair theorems of rotating black holes. By contrast, if Newtonian gravity is supplemented by a multipolar gravitomagnetic field, whose leading term represents frame dragging, we are unable to find an analogous Carter-like constant. This further highlights the special nature of the Kerr geometry.