Gravitational waves from the inspiral of a compact object into a massive, axisymmetric body with arbitrary multipole moments

Enhanced Extreme Mass Ratio Inspiral Rates and Intermediate Mass Black Holes

Extreme mass ratio inspirals (EMRIs) occur when stellar-mass compact objects begin a gravitational wave (GW) driven inspiral into massive black holes. EMRI waveforms can precisely map the surrounding spacetime, making them a key target for future space-based GW interferometers such as LISA, but their event rates and parameters are massively uncertain. One of the largest uncertainties is the ratio of true EMRIs (which spend at least thousands of orbits in the LISA band) and direct plunges, which are in-band for at most a handful of orbits and are not detectable in practice. In this Letter, we show that the traditional dichotomy between EMRIs and plunges-EMRIs originate from small semimajor axes, plunges from large-does not hold for intermediate-mass black holes with masses M_{•}≲10^{5}M_{⊙}. In this low-mass regime, a plunge always has an O(1) probability of failing and transitioning into a novel "cliffhanger" EMRI. Cliffhanger EMRIs are more easily produced for larger stellar-mass compact objects, and are less likely for smaller ones. This new EMRI production channel can dominate volumetric EMRI rates n[over ˙]_{EMRI} if intermediate-mass black holes are common in dwarf galactic nuclei, potentially increasing n[over ˙]_{EMRI} by an order of magnitude.

Geodesics and gravitational waves in chaotic extreme-mass-ratio inspirals: the curious case of Zipoy-Voorhees black-hole mimickers

Due to the growing capacity of gravitational-wave astronomy and black-hole imaging, we will soon be able to emphatically decide if astrophysical dark objects lurking in galactic centers are black holes. Sgr A*, one of the most prolific astronomical radio sources in our galaxy, is the focal point for tests of general relativity. Current mass and spin constraints predict that the central object of the Milky Way is supermassive and slowly rotating, thus can be conservatively modeled as a Schwarzschild black hole. Nevertheless, the well-established presence of accretion disks and astrophysical environments around supermassive compact objects can significantly deform their geometry and complicate their observational scientific yield. Here, we study extreme-mass-ratio binaries comprised of a minuscule secondary object inspiraling onto a supermassive Zipoy-Voorhees compact object; the simplest exact solution of general relativity that describes a static, spheroidal deformation of Schwarzschild spacetime. We examine geodesics of prolate and oblate deformations for generic orbits and reevaluate the non-integrability of Zipoy-Voorhees spacetime through the existence of resonant islands in the orbital phase space. By including radiation loss with post-Newtonian techniques, we evolve stellar-mass secondary objects around a supermassive Zipoy-Voorhees primary and find clear imprints of non-integrability in these systems. The peculiar structure of the primary, allows for, not only typical single crossings of transient resonant islands, that are well-known for non-Kerr objects, but also inspirals that transverse through several islands, in a brief period of time, that lead to multiple glitches in the gravitational-wave frequency evolution of the binary. The detectability of glitches with future spaceborne detectors can, therefore, narrow down the parameter space of exotic solutions that, otherwise, can cast identical shadows with black holes.

Circular Geodesics in a New Generalization of q-Metric

This paper introduces an alternative generalization of the static solution with quadrupole moment, the q-metric, that describes a deformed compact object in the presence of the external fields characterized by multipole moments. In addition, we also examine the impact of the external fields up to quadrupole on the circular geodesics and the interplay of these two quadrupoles on the place of the innermost stable circular orbit (ISCO) in the equatorial plane.

Gravitational Wave Glitches in Chaotic Extreme-Mass-Ratio Inspirals

The Kerr geometry admits the Carter symmetry, which ensures that the geodesic equations are integrable. It is shown that gravitational waveforms associated with extreme-mass-ratio inspirals involving a nonintegrable compact object display "glitch" phenomena, where the frequencies of gravitational waves increase abruptly, when the orbit crosses certain spacetime regions known as Birkhoff islands. The presence or absence of these features in data from upcoming space-borne detectors will therefore allow not only for tests of general relativity but also of fundamental spacetime symmetries.

Distinguishing Fuzzballs from Black Holes through Their Multipolar Structure

Within general relativity, the unique stationary solution of an isolated black hole is the Kerr spacetime, which has a peculiar multipolar structure depending only on its mass and spin. We develop a general method to extract the multipole moments of arbitrary stationary spacetimes and apply it to a large family of horizonless microstate geometries. The latter can break the axial and equatorial symmetry of the Kerr metric and have a much richer multipolar structure, which provides a portal to constrain fuzzball models phenomenologically. We find numerical evidence that all multipole moments are typically larger (in absolute value) than those of a Kerr black hole with the same mass and spin. Current measurements of the quadrupole moment of black-hole candidates could place only mild constraints on fuzzballs, while future gravitational-wave detections of extreme mass-ratio inspirals with the space mission LISA will improve these bounds by orders of magnitude.

On relativistic multipole moments of stationary space-times

Among the known exact solutions of Einstein's vacuum field equations the Manko-Novikov and the Quevedo-Mashhoon metrics might be suitable ones for the description of the exterior gravitational field of some real non-collapsed body. A new proposal to represent such exterior field is the stationary q-metric. In this contribution, we computed by means of the Fodor-Hoenselaers-Perjés formalism the lowest 10 relativistic multipole moments of these metrics. Corresponding moments were derived for the static vacuum solutions of Gutsunayev-Manko and Hernández-Martín. A direct comparison between the multipole moments of these non-isometric space-times is given.

Comparison of vacuum static quadrupolar metrics

We investigate the properties of static and axisymmetric vacuum solutions of Einstein equations which generalize the Schwarzschild spherically symmetric solution to include a quadrupole parameter. We test all the solutions with respect to elementary and asymptotic flatness and curvature regularity. Analysing their multipole structure, according to the relativistic invariant Geroch definition, we show that all of them are equivalent up to the level of the quadrupole. We conclude that the q-metric, a variant of the Zipoy-Voorhees metric, is the simplest generalization of the Schwarzschild metric, containing a quadrupole parameter.

Rotating stars in relativity

Rotating relativistic stars have been studied extensively in recent years, both theoretically and observationally, because of the information they might yield about the equation of state of matter at extremely high densities and because they are considered to be promising sources of gravitational waves. The latest theoretical understanding of rotating stars in relativity is reviewed in this updated article. The sections on equilibrium properties and on nonaxisymmetric oscillations and instabilities in f-modes and r-modes have been updated. Several new sections have been added on equilibria in modified theories of gravity, approximate universal relationships, the one-arm spiral instability, on analytic solutions for the exterior spacetime, rotating stars in LMXBs, rotating strange stars, and on rotating stars in numerical relativity including both hydrodynamic and magnetohydrodynamic studies of these objects.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

Gravitational-Wave Tests of General Relativity with Ground-Based Detectors and Pulsar-Timing Arrays

This review is focused on tests of Einstein's theory of general relativity with gravitational waves that are detectable by ground-based interferometers and pulsar-timing experiments. Einstein's theory has been greatly constrained in the quasi-linear, quasi-stationary regime, where gravity is weak and velocities are small. Gravitational waves will allow us to probe a complimentary, yet previously unexplored regime: the non-linear and dynamical strong-field regime. Such a regime is, for example, applicable to compact binaries coalescing, where characteristic velocities can reach fifty percent the speed of light and gravitational fields are large and dynamical. This review begins with the theoretical basis and the predicted gravitational-wave observables of modified gravity theories. The review continues with a brief description of the detectors, including both gravitational-wave interferometers and pulsar-timing arrays, leading to a discussion of the data analysis formalism that is applicable for such tests. The review ends with a discussion of gravitational-wave tests for compact binary systems.

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.

Revising the multipole moments of numerical spacetimes and its consequences

Identifying the relativistic multipole moments of a spacetime of an astrophysical object that has been constructed numerically is of major interest, both because the multipole moments are intimately related to the internal structure of the object, and because the construction of a suitable analytic metric that mimics a numerical metric should be based on the multipole moments of the latter one in order to yield a reliable representation. In this Letter, we show that there has been a widespread delusion in the way the multipole moments of a numerical metric are read from the asymptotic expansion of the metric functions. We show how one should read correctly the first few multipole moments (starting from the quadrupole mass moment) and how these corrected moments improve the efficiency of describing the metric functions with analytic metrics that have already been used in the literature, as well as other consequences of using the correct moments.

Self-consistent orbital evolution of a particle around a Schwarzschild black hole

The motion of a charged particle is influenced by the self-force arising from the particle's interaction with its own field. In a curved spacetime, this self-force depends on the entire past history of the particle and is difficult to evaluate. As a result, all existing self-force evaluations in curved spacetime are for particles moving along a fixed trajectory. Here, for the first time, we overcome this long-standing limitation and present fully self-consistent orbits and waveforms of a scalar charged particle around a Schwarzschild black hole.

How to observe a non-Kerr spacetime using gravitational waves

We present a generic criterion which can be used in gravitational-wave data analysis to distinguish an extreme-mass-ratio inspiral into a Kerr background spacetime from one into a non-Kerr spacetime. We exploit the fact that when an integrable system, such as the system that describes geodesic orbits in a Kerr spacetime, is perturbed, the tori in phase space which initially corresponded to resonances disintegrate so as to form Birkhoff chains on a surface of section. The KAM curves of the islands in such a chain share the same ratio of frequencies, even though the frequencies themselves vary from one KAM curve to another inside an island. However the KAM curves, which do not lie in a Birkhoff chain, do not share this characteristic property. Such a temporal constancy of the ratio of frequencies during the evolution of the gravitational-wave signal will signal a non-Kerr spacetime.

Physics, Astrophysics and Cosmology with Gravitational Waves

Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.

The black hole symphony: probing new physics using gravitational waves

The next decade will very likely see the birth of a new field of astronomy as we become able to directly detect gravitational waves (GWs) for the first time. The existence of GWs is one of the key predictions of Einstein's theory of general relativity, but they have eluded direct detection for the last century. This will change thanks to a new generation of laser interferometers that are already in operation or which are planned for the near future. GW observations will allow us to probe some of the most exotic and energetic events in the Universe, the mergers of black holes. We will obtain information about the systems to a precision unprecedented in astronomy, and this will revolutionize our understanding of compact astrophysical systems. Moreover, if any of the assumptions of relativity theory are incorrect, this will lead to subtle, but potentially detectable, differences in the emitted GWs. Our observations will thus provide very precise verifications of the theory in an as yet untested regime. In this paper, I will discuss what GW observations could tell us about known and (potentially) unknown physics.

Probes and Tests of Strong-Field Gravity with Observations in the Electromagnetic Spectrum

Neutron stars and black holes are the astrophysical systems with the strongest gravitational fields in the universe. In this article, I review the prospect of using observations of such compact objects to probe some of the most intriguing general relativistic predictions in the strong-field regime: the absence of stable circular orbits near a compact object and the presence of event horizons around black-hole singularities. I discuss the need for a theoretical framework, within which future experiments will provide detailed, quantitative tests of gravity theories. Finally, I summarize the constraints imposed by current observations of neutron stars on potential deviations from general relativity.

Kerr black holes are not unique to general relativity

Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this Letter, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.

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

We explore prospects for detecting gravitational waves from stellar-mass compact objects spiraling into intermediate mass black holes (BHs) M approximately 50M to 350M) with ground-based observatories. We estimate a rate for such intermediate-mass-ratio inspirals of <or= 1-30 yr(-1) in Advanced LIGO. We show that if the central body is not a BH but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat, then the waves will likely be triperiodic, as for a BH. We suggest that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) details of the central body's metric, the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. We estimate that advanced ground-based detectors can constrain central body deviations from a BH with interesting accuracy.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and other binary pulsar systems have yielded other tests, especially of strong-field effects. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.

Gravitational self-force on a particle orbiting a Kerr black hole

We present a practical method for calculating the gravitational self-force, as well as the electromagnetic and scalar self-forces, for a particle in a generic orbit around a Kerr black hole. In particular, we provide the values of all the regularization parameters needed for implementing the (previously introduced) mode-sum regularization method. We also address the gauge-regularization problem, as well as a few other issues involved in the calculation of gravitational radiation reaction in Kerr spacetime.

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of special relativity, and the gravitational redshift experiment. Future tests of EEP and of the inverse square law will search for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light defl ection the Shapiro time delay, the perihelion advance of Mercury, and the Nordtvedt effect in lunar motion. Gravitational wave damping has been detected in an amount that agrees with general relativity to half a percent using the Hulse-Taylor binary pulsar, and new binary pulsar systems may yield further improvements. When direct observation of gravitational radiation from astrophysical sources begins, new tests of general relativity will be possible.