In a recent series of papers we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instanc
e, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we here focus on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modified Regge-Wheeler equation, while the polar perturbations are of mixed scalar-tensor character and are described by a system of two coupled wave equations. When applied to these equations, the eikonal machinery leads to axial modes that deviate from the general relativistic results at quadratic order in the Gauss-Bonnet coupling constant. We show that this result is in agreement with an analysis of unstable circular null orbits around blackholes in this theory, allowing us to establish the geometrical optics-null geodesic correspondence for the axial modes. For the polar modes the small-coupling approximation forces us to consider the ordering between eikonal and small-coupling perturbative parameters; one of which we show, by explicit comparison against numerical data, yields the correct identification of the quasinormal modes of the scalar-tensor coupled system of wave equations. These corrections lift the general relativistic degeneracy between scalar and tensorial eikonal quasinormal modes at quadratic order in Gauss-Bonnet coupling in a way reminiscent of the Zeeman effect. In general, our analytic, eikonal quasinormal mode frequencies (normalized to the General Relativity ones) agree with numerical results with an error of $sim 10%$ in the regime of small coupling constant. (abridged)
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 propag
ation. Many of previous studies on the latter assume multi-messenger 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 multi-band observations between ground-based and space-based (e.g. DECIGO) interferometers. We find that such multi-band 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.
Gravitational-wave sources offer us unique testbeds for probing strong-field, dynamical and nonlinear aspects of gravity. In this chapter, we give a brief overview of the current status and future prospects of testing General Relativity with gravitat
ional waves. In particular, we focus on three theory-agnostic tests (parameterized tests, inspiral-merger-ringdown consistency tests, and gravitational-wave propagation tests) and explain how one can apply such tests to example modified theories of gravity. We conclude by giving some open questions that need to be resolved to carry out more accurate tests of gravity with gravitational waves.
Gravitational waves from the explosive merger of distant black holes are encoded with details regarding the complex extreme-gravity spacetime present at their source. Famously described by the Kerr spacetime metric for rotating black holes in general
relativity, what if effects beyond this theory are present? One way to efficiently test this hypothesis is to first obtain a metric which parametrically deviates from the Kerr metric in a model-independent way. Given such a metric, one can then predict the ensuing corrections to both the inspiral and ringdown portions of the gravitational waveform for black holes present in the new spacetime. With these tools in hand, one can then test gravitational wave signals for such effects by two different methods, (i) inspiral-merger-ringdown consistency test, and (ii) parameterized test. In this paper, we demonstrate the exact recipe one needs to do just this. We first derive parameterized corrections to the waveform inspiral, ringdown, and remnant properties for a generic non-Kerr spacetime and apply this to two example beyond-Kerr spacetimes each parameterized by a single non-Kerr parameter. We then predict the beyond-Kerr parameter magnitudes required in an observed gravitational wave signal to be statistically inconsistent with the Kerr case in general relativity. We find that the two methods give very similar bounds. The constraints found with existing gravitational-wave events are comparable to those from x-ray observations, while future gravitational-wave observations using Cosmic Explorer (Laser Interferometer Space Antenna) can improve such bounds by two (three) orders of magnitude.
Gravitational waves from extreme gravity events such as the coalescence of two black holes in a binary system fill our observable universe, bearing with them the underlying theory of gravity driving their process. One compelling alternative theory of
gravity -- known as Einstein-dilaton Gauss-Bonnet gravity motivated by string theory -- describes the presence of an additional dilaton scalar field coupled directly to higher orders of the curvature, effectively describing a fifth force interaction and the emission of scalar dipole radiation between two scalarized black holes. Most previous studies focused on considering only the leading correction to the inspiral portion of the binary black hole waveforms. In our recent paper, we carried out inspiral-merger-ringdown consistency tests in this string-inspired gravity by including corrections to both the inspiral and ringdown portions, as well as those to the mass and spin of remnant black holes, valid to quadratic order in spin. We here extend the analysis by directly computing bounds on the theoretical coupling constant using the full inspiral-merger-ringdown waveform rather than treating the inspiral and merger-ringdown portions separately. We also consider the corrections valid to quartic order in spin to justify the validity of black holes slow-rotation approximation. We find the quasinormal mode corrections to the waveform to be particularly important for high-mass events such as GW170729, in which the dilaton fields small-coupling approximation fails without such effects included. We also show that future space-based and multiband gravitational-wave observations have the potential to go beyond existing bounds on the theory. The bounds presented here are comparable to those found in via the inspiral-merger-ringdown consistency tests.
The extreme-gravity collisions between black holes allow us to probe the underlying theory of gravity. We apply the theory-agnostic inspiral-merger-ringdown consistency test to an example theory beyond general relativity for the first time. Here we f
ocus on the string-inspired Einstein-dilaton Gauss-Bonnet gravity and modify the inspiral, ringdown, and remnant black hole properties of the gravitational waveform. We found that future multiband observations allow us to constrain the theory stronger than current observations by an order of magnitude. The formalism developed here can easily be applied to other theories.
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 equatio
ns of state, that 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 $sim 3%$ 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.
Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations in
stead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2+2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well studied physical system: the metric perturbations of a static black hole. The $2+2$ formalism we present can be generalized to $m+n$ dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of $m+n$ formalism for vacuum spacetime splittings.
Two low mass neutron stars, J0737-3039B and the companion to J1756-2251, show strong evidence of being formed from the collapse of an ONeMg core in an electron capture supernova (ECSN) or in an ultra-stripped iron core collapse supernova (FeCCSN). Us
ing three different systematically generated sets of equations of state we explore the relationship between the moment of inertia of J0737-3039A and the binding energy of the two low mass neutron stars. We find this relationship, a less strict variant of the recently discovered I-Love-Q relations, is nevertheless more robust than a previously explored correlation between the binding energy and the slope of the nuclear symmetry energy L. We find that, if either J0737-3039B or the J1756-2251 companion were formed in an ECSN, no more than 0.06 solar masses could have been lost from the progenitor core, more than four times the mass loss predicted by current supernova modeling. A measurement of the moment of inertia of J0737-3039A to within 10% accuracy from pulsar timing, possible within a decade, can discriminate between formation scenarios such as ECSN or ultra-stripped FeCCSN and, given current constraints on the predicted core mass loss, potentially rule them out. Using the I-Love-Q relations we find that an Advanced LIGO can potentially measure the neutron star tidal polarizability to equivalent accuracy in a neutron star-neutron star merger at a distance of 200 Mpc, thus obtaining similar constraints on the formation scenarios. Such information on the occurrence of ECSNe is important for population synthesis calculations, especially for estimating the rate of binary neutron star mergers and resulting electromagnetic and gravitational wave signals. Further progress needs to be made modeling the core collapse process that leads to low-mass neutron stars, particularly in making robust predictions for the mass loss from the progenitor core.
