Despite the tremendous success of general relativity so far, modified theories of gravity have received increased attention lately, motivated from both theoretical and observational aspects. In ...particular, gravitational wave observations opened new possibilities for testing the viability of such theories in the dynamical and strong-field regime. One could test each modified theory of gravity against observed data one at a time, though perhaps a more efficient approach would be to first probe gravity in a theory-agnostic way and map such information to that on specific theories afterward. One example of such model-independent tests of gravity with gravitational waves is the parametrized post-Einsteinian formalism, in which one introduces generic parameters in the amplitude and phase that capture non-Einsteinian effects. In this paper, we derive gravitational waveforms from inspiraling compact binaries in various modified theories of gravity that violate at least one fundamental pillar in general relativity, such as the strong equivalence principle, Lorentz and parity invariance, and commutativity of spacetime. We achieve this by first deriving relations between corrections to the waveform amplitude/phase and those to the frequency evolution and Kepler’s third law, since the latter two have already been (or can easily be) derived in several example modified theories of gravity. In particular, such an analysis allows us to derive corrections to the waveform amplitude, which extends many of previous works that focused on deriving phase corrections only. Moreover, we derive modified gravitational waveforms in theories with a varying gravitational constant. In particular, we extend the previous work by introducing two different gravitational constants (the conservative one entering in the binding energy and the dissipative one entering in the gravitational wave luminosity) and allowing masses of binary constituents to also vary with time. We also correct some errors in the previous literature. Our results can be used to improve current analyses of testing general relativity with available gravitational wave data as well as to achieve new projected constraints on various modified theories of gravity with future gravitational wave observations.
The gravitational wave observations GW150914 and GW151226 by Advanced LIGO provide the first opportunity to learn about physics in the extreme gravity environment of coalescing binary black holes. ...The LIGO Scientific Collaboration and the Virgo Collaboration have verified that this observation is consistent with Einstein’s theory of general relativity, constraining the presence of certain parametric anomalies in the signal. This paper expands their analysis to a larger class of anomalies, highlighting the inferences that can be drawn on nonstandard theoretical physics mechanisms that could otherwise have affected the observed signals. We find that these gravitational wave events constrain a plethora of mechanisms associated with the generation and propagation of gravitational waves, including the activation of scalar fields, gravitational leakage into large extra dimensions, the variability of Newton’s constant, the speed of gravity, a modified dispersion relation, gravitational Lorentz violation and the strong equivalence principle. Though other observations limit many of these mechanisms already, GW150914 and GW151226 are unique in that they are direct probes of dynamical strong-field gravity and of gravitational wave propagation. We also show that GW150914 constrains inferred properties of exotic compact object alternatives to Kerr black holes. We argue, however, that the true potential for GW150914 to both rule out exotic objects and constrain physics beyond general relativity is severely limited by the lack of understanding of the coalescence regime in almost all relevant modified gravity theories. This event thus significantly raises the bar that these theories have to pass, both in terms of having a sound theoretical underpinning and reaching the minimal level of being able to solve the equations of motion for binary merger events. We conclude with a discussion of the additional inferences that can be drawn if the lower-confidence observation of an electromagnetic counterpart to GW150914 holds true, or such a coincidence is observed with future events; this would provide dramatic constraints on the speed of gravity and gravitational Lorentz violation.
Recently the Event Horizon Telescope Collaboration, with very-long baseline interferometric observations, resolved structure at the scale of ∼5 Schwarzschild radii about the center of M87*, the ...supermassive black hole resident at the center of Messier 87. This important observation has paved the way for testing what is known as the "no-hair" theorem, stating that isolated black holes are described by the Kerr metric, parametrized only by their mass and spin. Generic, parametrized spacetimes beyond Kerr allow one to arbitrarily test the no-hair theorem for deviations from the Kerr result with no prior theoretical knowledge or motivation. In this paper, we present such a new general, stationary, axisymmetric and asymptotically flat black hole solution with separable geodesic equations (thus preserving symmetries of a Kerr black hole), extending the previous work of Johannsen. In this new metric, five free nonlinear functions parameterically deviate from the Kerr result, allowing one to effectively transform to many alternative black hole solutions present in the literature. We then derive analytic expressions for the Keplerian and epicyclic frequencies, the orbital energy and angular momentum, and the location of the innermost stable orbit of circular equatorial particle orbits. We also compute the image of the photon rings in the new spacetime, which correspond to the boundary of the black hole shadow image taken by the Event Horizon Telescope. We finally compare each quantity for the Kerr result against various parametrizations of the metric, finding that, especially for highly rotating black holes, the two solutions disagree significantly. Such a metric parametrization allows one to perform the no-hair tests in a model-independent way, and finally map constraints to specific alternative theories of gravity.
Neutron stars and quark stars are not only characterized by their mass and radius but also by how fast they spin, through their moment of inertia, and how much they can be deformed, through their ...Love number and quadrupole moment. These depend sensitively on the star's internal structure and thus on unknown nuclear physics. We find universal relations between the moment of inertia, the Love number, and the quadrupole moment that are independent of the neutron and quark star's internal structure. These can be used to learn about neutron star deformability through observations of the moment of inertia, break degeneracies in gravitational wave detection to measure spin in binary inspirals, distinguish neutron stars from quark stars, and test general relativity in a nuclear structure—independent fashion.
One of largest uncertainties in nuclear physics is the relation between the pressure and density of supranuclear matter: the equation of state. Some of this uncertainty may be removed through future ...gravitational wave observations of neutron star binaries by extracting the tidal deformabilities (or Love numbers) of neutron stars, a novel way to probe nuclear physics in the high-density regime. Previous studies have shown that only a certain combination of the individual (quadrupolar) deformabilities of each body (the so-called chirp tidal deformability) can be measured with second-generation, gravitational wave interferometers, such as Adv. LIGO, due to correlations between the individual deformabilities. To overcome this, we search for approximately universal (i.e. approximately equation-of-state independent) relations between two combinations of the individual tidal deformabilities, such that once one of them has been measured, the other can be automatically obtained and the individual ones decoupled through these relations. We find an approximately universal relation between the symmetric and the anti-symmetric combination of the individual tidal deformabilities that is equation-of-state-insensitive to 20% for binaries with masses less than 1.7M⊙. We show that these relations can be used to eliminate a combination of the tidal parameters from the list of model parameters, thus breaking degeneracies and improving the accuracy in parameter estimation. A simple (Fisher) study shows that the universal binary Love relations can improve the accuracy in the extraction of the symmetric combination of tidal parameters by as much as an order of magnitude, making the overall accuracy in the extraction of this parameter slightly better than that of the chirp tidal deformability. These new universal relations and the improved measurement accuracy on tidal parameters not only are important to astrophysics and nuclear physics, but also impact our ability to probe extreme gravity with gravitational waves and cosmology.
Neutron stars are ideal astrophysical sources to probe general relativity due to their large compactnesses and strong gravitational fields. For example, binary pulsar and gravitational wave ...observations have placed stringent bounds on certain scalar-tensor theories in which a massless scalar field is coupled to the metric through matter. A remarkable phenomenon of neutron stars in such scalar-tensor theories is spontaneous scalarization, where a normalized scalar charge remains of order unity even if the matter-scalar coupling vanishes asymptotically far from the neutron star. While most works on scalarization of neutron stars focus on numerical analysis, this paper aims to derive accurate scalar charges analytically. To achieve this, we consider a simple energy density profile of the Tolman VII form and work in a weak-field expansion. We solve the modified Tolman-Oppenheimer-Volkoff equations order by order and apply a Padé resummation to account for higher order effects. We find that our analytic scalar charges (in terms of the stellar compactness) beautifully model those computed numerically. We also find a quasiuniversal relation between the scalar charge and stellar binding energy that is insensitive to the underlying equations of state. A comparison of analytic scalar charges for Tolman VII and constant density stars mathematically supports this quasiuniversal relation. The analytic results found here provide physically motivated, ready to use accurate expressions for scalar charges.
Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars, allowing one to probe equations of state for matter at supranuclear densities. Here we design ...new parametrizations for hybrid hadron-quark equations of state, which give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star-neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within ∼3% for both slowly and rapidly rotating configurations, implying that these relations can be used to perform equation-of-state independent tests of general relativity and to break degeneracies in gravitational waveforms for hybrid stars in the third family as well.
Gravitational-wave sources can serve as standard sirens to probe cosmology by measuring their luminosity distance and redshift. Such standard sirens are also useful to probe theories beyond general ...relativity with a modified gravitational-wave propagation. Many of previous studies on the latter assume multimessenger observations so that the luminosity distance can be measured with gravitational waves while the redshift is obtained by identifying sources' host galaxies from electromagnetic counterparts. Given that gravitational-wave events of binary neutron star coalescences with associated electromagnetic counterpart detections are expected to be rather rare, it is important to examine the possibility of using standard sirens with gravitational-wave observations alone to probe gravity. In this paper, we achieve this by extracting the redshift from the tidal measurement of binary neutron stars that was originally proposed within the context of gravitational-wave cosmology (another approach is to correlate "dark sirens" with galaxy catalogs that we do not consider here). We consider not only observations with ground-based detectors (e.g., Einstein Telescope) but also multiband observations between ground-based and space-based (e.g., DECIGO) interferometers. We find that such multiband observations with the tidal information can constrain a parametric non-Einsteinian deviation in the luminosity distance (due to the modified friction in the gravitational wave evolution) more stringently than the case with electromagnetic counterparts by a factor of a few. We also map the above-projected constraints on the parametric deviation to those on specific theories and phenomenological models beyond general relativity to put the former into context.
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