Gravitational Modes Research Articles

Linearized field equations and extra force in f(R,T(n)) extended gravity

We consider an extended theory of gravity with Lagrangian [Formula: see text], with [Formula: see text] being a [Formula: see text]th-order invariant made of contractions of the energy–momentum tensor. When [Formula: see text], this theory reduces to [Formula: see text] gravity, where [Formula: see text] accounts for the trace of the energy–momentum tensor. We study the gravitational wave polarization modes, from which it results that when the matter Lagrangian contains dynamical scalar fields minimally coupled to the geometry, further polarization modes arise with respect to General Relativity. Finally, we show that the motion for test particles is nongeodesic and we explicitly obtain the extra force.

Polarization modes of gravitational waves in Palatini-Horndeski theory

In this paper, the polarization modes of gravitational waves in Horndeski gravity are studied under the Palatini formalism. After obtaining the linearized equation of perturbations in Minkowski background, we find that the polarization modes of gravitational waves depend on the selection of the theoretical parameters. The polarization modes can be divided into quite rich cases by parameters. In all cases of parameter selection, there are $+$ and $\times$ modes propagating at the speed of light but no vector modes. The only difference from general relativity is scalar modes, especially the scalar degrees of freedom can be 0, 1 or 2 in different cases. The appropriate parameter cases can be expected to be selected in the detection of gravitational wave polarization modes by Lisa, Taiji and TianQin in the future.

Sensitivity of third-generation interferometers to extra polarizations in the stochastic gravitational wave background

When modified theories of gravity are considered, at most six gravitational wave polarization modes are allowed and classified in tensor modes, the only ones predicted by General Relativity (GR), along with additional vector and scalar modes. Therefore, gravitational waves represent a powerful tool to test alternative theories of gravitation. In this paper, we forecast the sensitivity of third-generation ground-based interferometers, Einstein Telescope and Cosmic Explorer, to non-GR polarization modes focusing on the stochastic gravitational wave background. We consider the latest technical specifications of the two independent detectors and the full network in order to estimate both the optimal signal-to-noise ratio and the detectable energy density limits relative to all polarization modes in the stochastic background for several locations on Earth and orientations of the two observatories. By considering optimal detector configurations, we find that in 5 years of observation the detection limit for tensor and extra polarization modes could reach $h_0^2\Omega^{T,V,S}_{GW} \approx 10^{-12}-10^{-11}$, depending on the network configuration and the stochastic background (i.e., if only one among vector and scalar modes exists or both are present). This means that the network sensitivity to different polarization modes can be approximately improved by a factor $10^3$ with respect to second-generation interferometers. We finally discuss the possibility of breaking the scalar modes degeneracy by considering both detectors angular responses to sufficiently high gravitational wave frequencies.

Detectable universes inside regular black holes

While spacetime in the vicinity outside astrophysical black holes is believed to be well understood, the event horizon and the interior remain elusive. Here, we discover a degenerate infinite spectrum of novel general relativity solutions with the same mass-energy and entropy that describe a dark energy universe inside an astrophysical black hole. This regular cosmological black hole is stabilized by a finite tangential pressure applied on the dual cosmological-black hole event horizon, localized up to a quantum indeterminacy. We recover the Bekenstein–Hawking entropy formula from the classical fluid entropy, calculated at a Tolman temperature equal to the cosmological horizon temperature. We further calculate its gravitational quasi-normal modes. We find that cosmological black holes are detectable by gravitational-wave experiments operating within the mu mathrm{Hz}–mathrm{Hz} range, like LISA space-interferometer.

Effective-one-body multipolar waveforms for eccentric binary black holes with nonprecessing spins

We construct an inspiral-merger-ringdown eccentric gravitational-wave (GW) model for binary black holes with non-precessing spins within the effective-one-body formalism. This waveform model, SEOBNRv4EHM, extends the accurate quasi-circular SEOBNRv4HM model to eccentric binaries by including recently computed eccentric corrections up to 2PN order in the gravitational waveform modes, notably the $(l,|m|)=(2,2),(2,1),(3,3),(4,4),(5,5)$ multipoles. The waveform model reproduces the zero eccentricity limit with an accuracy comparable to the underlying quasi-circular model, with the unfaithfulness of $\lesssim1\%$ against quasi-circular numerical-relativity (NR) simulations. When compared against 28 public eccentric NR simulations from the Simulating eXtreme Spacetimes catalog with initial orbital eccentricities up to $e\simeq0.3$ and dimensionless spin magnitudes up to $+0.7$, the model provides unfaithfulness $<1\%$, showing that both the $(2,|2|)$-modes and the higher-order modes are reliably described without calibration to NR datasets in the eccentric sector. The waveform model SEOBNRv4EHM is able to qualitatively reproduce the phenomenology of dynamical captures, and can be extended to include spin-precession effects. It can be employed for upcoming observing runs with the LIGO-Virgo-KAGRA detectors and used to re-analyze existing GW catalogs to infer the eccentricity parameters for binaries with $e\lesssim0.3$ (at 20 Hz or lower) and spins up to $\lesssim 0.9-0.95$. The latter is a promising region of the parameter space where some astrophysical formation scenarios of binaries predict mild eccentricity in the ground-based detectors' bandwidth. Assessing the accuracy and robustness of the eccentric waveform model SEOBNRv4EHM for larger eccentricities and spins will require comparisons with, and, likely, calibration to eccentric NR waveforms in a larger region of the parameter space.

Barnich–Troessaert bracket as a Dirac bracket on the covariant phase space

The Barnich–Troessaert bracket is a proposal for a modified Poisson bracket on the covariant phase space for general relativity. The new bracket allows us to compute charges, which are otherwise not integrable. Yet there is a catch. There is a clear prescription for how to evaluate the new bracket for any such charge, but little is known how to extend the bracket to the entire phase space. This is a problem, because not every gravitational observable is also a charge. In this paper, we propose such an extension. The basic idea is to remove the radiative data from the covariant phase space. This requires second-class constraints. Given a few basic assumptions, we show that the resulting Dirac bracket on the constraint surface is nothing but the BT bracket. A heuristic argument is given to show that the resulting constraint surface can only contain gravitational edge modes.

Excitation of gravitational wave modes by a center-of-mass velocity of the source

Most gravitational wave (GW) sources are moving relative to us. This motion is often closely related to the environment of the source and can thus provide crucial information about the formation of the source and its host. Recently, LIGO and Virgo detected for the first time the subdominant modes of GWs. We show that a motion of the center of mass of the source can affect these modes, where the effect is proportional to the velocity of the source. The effect on the GW modes in turn affects the overall frequency of the GW, thus leading to a phase shift. We study the impact of this effect on LIGO/Virgo detections and show that it is detectable for sources with high mass ratios and inclinations. This effect breaks the degeneracy between the mass and Doppler shift in GW observations and opens a new possibility of detecting the motion of a GW source even for constant velocities.

The Role of Longitudinal Polarizations in Horndeski and Macroscopic Gravity: Introducing Gravitational Plasmas

We discuss some general and relevant features of longitudinal gravitational modes in Horndeski gravity and their interaction with matter media. Adopting a gauge-invariant formulation, we clarify how massive scalar and vector fields can induce additional transverse and longitudinal excitations, resulting in breathing, vector, and longitudinal polarizations. We review, then, the interaction of standard gravitational waves with a molecular medium, outlining the emergence of effective massive gravitons, induced by the net quadrupole moment due to molecule deformation. Finally, we investigate the interaction of the massive mode in Horndeski gravity with a noncollisional medium, showing that Landau damping phenomenon can occur in the gravitational sector as well. That allows us to introduce the concept of “gravitational plasma”, where inertial forces associated with the background field play the role of cold ions in electromagnetic plasma.

Finding the Ultralight Boson from a Black Hole’s Ringdown

Solving the problem of dark matter remains one of the greatest unsolved mystery of fundamental physics. One possible dark matter candidate is the scalar ultralight boson, with mass « 1eV. If they exist, ultralight bosons will form clouds of significant total mass about rotating black holes, affecting the spacetime around the black hole. After the inspiral phase of a binary merger, the bosonic cloud can affect the perturbations to the black hole, resulting in deviations in the quasinormal mode frequencies of the ringdown signal of a binary merger. Here, we compute these shifts in the gravitational quasinormal mode frequencies for such a system, and conduct an injection campaign with supermassive black holes detected by the Laser Interferometer Space Antenna. We find that detections of the ringdown phase of supermassive black holes can rule out or confirm the existence of cloud-forming ultralight bosons of mass ∼ 10−18eV at redshift z > 1 if cloud dissipation effects during the inspiral can be neglected.

Scattering amplitudes for binary systems beyond GR

Amplitude methods have proven to be a promising technique to perform Post-Minkowskian calculations used as inputs to construct gravitational waveforms. In this paper, we show how these methods can be extended beyond the standard calculations in General Relativity with a minimal coupling to matter. As proof of principle, we consider spinless particles conformally coupled to a gravitational helicity-0 mode. We clarify the subtleties in the matching procedure that lead to the potential for conformally coupled matter. We show that in the probe particle limit, we can reproduce well known results for the field profile. With the scattering amplitudes at hand, we compute the conservative potential and scattering angle for the binary system. We find that the result is a non trivial expansion that involves not only the coupling strengths, but also a non trivial dependence on the energy/momentum of the scattered particles.

Detectability of gravitational higher order modes in the third-generation era

Detection of higher order modes of gravitational waves in third-generation (3G) ground-based detectors such as Cosmic Explorer and Einstein Telescope is explored. Using the astrophysical population of binary black holes based on events reported in the second gravitational wave catalog by Laser Interferometer Gravitational Wave Observatory (LIGO) and Virgo (GWTC-2), in conjunction with the Madau-Dickinson model for redshift evolution of the binary black hole mergers, we assess the detectability of these higher order modes using a network consisting of three 3G detectors. We find that the two subleading modes [(3,3) and (4,4)] can be detected in approximately 30% of the population with a network signal-to-noise ratio of 3 or more, and for nearly 10% of the sources, the five leading modes will be detectable. Besides, a study concerning the effect of binary's mass ratio and its orbital inclination with the observer's line-of-sight in detecting various modes is presented. For a few selected events of the LIGO-Virgo catalog, we identify the modes that would have been detected if a 3G detector was operational when these events were recorded. We also compute the detectability of higher modes by Voyager and find that only $\ensuremath{\sim}6$ and 2% of the detectable population will have an associated detection of (3,3) and (4.4) modes, respectively. Observing these higher order modes in the 3G era would have a huge impact on the science possible with these detectors ranging from astrophysics and cosmology to testing strong-field gravity.

EHT tests of the strong-field regime of general relativity

Following up on a recent analysis by Psaltis et al (2020 Phys. Rev. Lett. 125 141104), we show that the observed shadow size of M87* can be used to unambiguously and robustly constrain the black hole geometry in the vicinity of the circular photon orbit. Constraints on the post-Newtonian weak-field expansion of the black hole’s metric are instead more subtle to obtain and interpret, as they rely on combining the shadow-size measurement with suitable theoretical priors. We provide examples showing that post-Newtonian constraints resulting from shadow-size measurements should be handled with extreme care. We also discuss the similarities and complementarity between the EHT shadow measurements and black-hole gravitational quasi-normal modes.

Thermal effects and scalar modes in the cosmological propagation of gravitational waves

We consider thermal effects in the propagation of gravitational waves on a cosmological background. In particular, we consider scalar field cosmologies and study gravitational modes near cosmological singularities. We point out that the contribution of thermal radiation can heavily affect the dynamics of gravitational waves giving enhancement or dissipation effects both at quantum and classical level. These effects are considered both in General Relativity and in modified theories like F ( R ) gravity which can be easily reduced to scalar&#x2013;tensor cosmology. The possible detection and disentanglement of standard and scalar gravitational modes on the stochastic background are also discussed.

Intrinsic Gravitational Modes Sustained by Black Hole Collapsing Binaries

Intrinsic Gravitational Modes Sustained by Black Hole Collapsing Binaries

Gravitational waves in non-local gravity

We derive gravitational waves in a theory with non-local curvature corrections to the Hilbert–Einstein Lagrangian. In addition to the standard two massless tensor modes, with plus and cross polarizations, helicity 2 and angular frequency ω 1, we obtain a further scalar massive mode with helicity 0 and angular frequency ω 2, whose polarization is transverse. It is a breathing mode, which, at the lowest order of an effective parameter γ, presents a speed difference between nearly null and null plane waves. Finally, the quasi-Lorentz E(2)-invariant class for the non-local gravity is type N 3, according to the Petrov classification. This means that the presence (or absence) of gravitational wave modes is observer-independent.

Radiation-reaction force and multipolar waveforms for eccentric, spin-aligned binaries in the effective-one-body formalism

While most binary inspirals are expected to have circularized before they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models used to detect those binaries, infer their properties, and shed light on their astrophysical environment. We develop a multipolar effective-one-body (EOB) eccentric waveform model for compact binaries whose components have spins aligned or antialigned with the orbital angular momentum. The waveform model contains eccentricity effects in the radiation-reaction force and gravitational modes through second post-Newtonian (PN) order, including tail effects, and spin-orbit and spin-spin couplings. We recast the PN-expanded, eccentric radiation-reaction force and modes in factorized form so that the newly derived terms can be directly included in the state-of-the-art, quasi-circular--orbit EOB model currently used in LIGO/Virgo analyses (i.e., the SEOBNRv4HM model).

Loop quantum gravity boundary dynamics and gauge theory

In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3 + 1 space-time dimensions, the boundary theory lives on the 2 + 1-dimensional time-like boundary and is supposed to describe the time evolution of gravitational boundary modes—‘edge modes’—living on the two-dimensional boundary of space, i.e. the space-time corner. We do not analyse the boundary structures of general relativity and their quantization, and focus instead on investigating which boundary theories can be supported by the standard loop quantum gravity formalism and spin network states. Focussing on ‘electric’ excitations—quanta of area—living on the corner, we formulate their dynamics in terms of classical spinor variables and we show that the coupling constants of a polynomial Hamiltonian can be understood as the components of a background metric on the 2 + 1-dimensional time-like boundary. This leads to a conjecture of a deeper correspondence between boundary Hamiltonian and boundary metric states. We further show that one can reformulate the quanta of area data in terms of a connection, transporting the spinors on the boundary surface and whose SU(2) component would define ‘magnetic’ excitations (tangential Ashtekar–Barbero connection), thereby opening the door to writing the loop quantum gravity boundary dynamics as a 2 + 1-dimensional gauge theory.

Quasinormal modes of rotating black holes in Einstein-dilaton Gauss-Bonnet gravity: The first order in rotation

Gravitational spectroscopy---the measurement of the quasi-normal modes of a black hole from the ringdown signal of a binary black hole coalescence---is one of the most promising tools to test gravity in the strong-field, large-curvature regime, but without the knowledge of the black hole quasinormal modes in specific cases of modified gravity theories, only null tests of general relativity are possible. More specifically, we need to know the modes of rotating black holes, because typical compact binary mergers lead to black holes with large spins. In this article we compute, for the first time, the gravitational quasinormal modes of rotating black holes in a modified gravity theory, up to first order in the spin. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest modifications of general relativity in the large-curvature regime. We find that the shifts in the mode frequencies and damping times due to general relativity modifications are significantly magnified by rotation.

Analytic study of dark photon and gravitational wave production from axion

Axion-like fields heavier than about 10−27 eV are expected to oscillate in the radiation dominated epoch when the Hubble parameter drops below their mass. Considering the Chern-Simons coupling with a dark gauge boson, large amount of dark photons are produced during a short time interval through tachyonic resonance instability. The produced dark photons then source gravitational tensor modes leading to chiral gravitational waves. Through this process, one can indirectly probe a large parameter space of coupled axion-dark photon models. In this work we first find an analytic expression for the number density of the dark photons produced during the tachyonic resonance regime. Second, by using the saddle point approximation we find an analytic expression for the gravitational wave spectrum in terms of the mass, coupling and misalignment angle. Our analytic results can be used for the observational analysis of these types of scenarios.

Spin angular momentum of gravitational wave interference

Spin angular momentum (SAM) is an important feature for wave systems, prominent in various properties like spin-momentum locking of wave propagations. Here, we study the SAM of gravitational waves in general relativity based on the Noether theorem in classical field theory. We demonstrate gravitational wave spin in various interference cases and evanescent waves, which is manifested as locally rotating metric perturbations, driving particles on geodesic spheroid locally deformed in elliptical trajectories. For non-polarized gravitational wave modes of zero SAM, their superpositions can induce nonzero density of SAM with interfered patterns. The evanescent gravitational wave shows clear SAM, which is also a consequence of wave interference between propagating and transverse evanescent components. The spin-momentum locking relations are clearly present for all different interference cases of wave modes and components based on general relativity.