Gravitational Modes Research Articles

Polar modes and isospectrality of Ellis-Bronnikov wormholes

We consider polar perturbations of static Ellis-Bronnikov wormholes and derive the coupled set of perturbation equations for the gravitational and the scalar field. For massless wormholes the perturbations decouple, and we obtain two identical master equations for the scalar and gravitational modes, which moreover agree with the master equation for the axial modes. Consequently there is isospectrality with threefold degenerate modes. For a finite mass of the background wormhole solutions, the equations are coupled. We then obtain two distinct branches of polar quasinormal modes for a given multipole number l, associated with the presence of the two types of fields. We calculate the quasi-normal mode frequencies and decay rates for the branches with l=2, 3 and 4. For a given l the real frequencies of the two branchesget the closer, the higher the multipole number gets.

Impact of thermal misbalance on acoustic-gravity waves in the solar atmosphere

ABSTRACT The joint effect of gravity and thermal misbalance on the dynamics of acoustic-gravity waves (AGW) in the solar atmosphere is considered. It is shown that the heating and cooling taken in the form of power functions lead to the linear dependence of stationary temperature profile. Estimates of the ratio of the characteristic length associated with thermal processes to the gravitational height show a predominant influence of thermal processes in the temperature range up to 2 MK and a comparable influence on the dynamics of AGW in the range from 2 to 10 MK. A study of the dispersion properties of AGW in an isothermal atmosphere showed that in regimes with an overwhelming influence of thermal processes, the acoustic cut-off frequency decreases up to $\sqrt{\gamma }$ times. At the same time, the maximum frequency of the gravitational mode (analogue of the Brunt–Väisälä frequency in the medium without non-adiabatic heating and cooling) decreases with increasing power of thermal processes, and then the gravitational mode can become purely oscillatory.

Polarization of Gravitational Waves in Modified Gravity

An investigation has been carried out on a reconfigured form of the Einstein-Hilbert action, denoted by f(R,Tϕ), where Tϕ represents the energy-momentum tensor trace of the scalar field under consideration. The study has focused on how the structural behavior of the scalar field changes based on the potential’s shape, which has led to the development of a new set of Friedmann equations. In the context of modified theories, researchers have extensively explored the range of gravitational wave polarization modes associated with relevant fields. In addition to the two transverse-traceless tensor modes that are typically observed in general relativity, two additional scalar modes have been identified: a massive longitudinal mode and a massless transverse mode, also known as the breathing mode.

Numerical relativity higher order gravitational waveforms of eccentric, spinning, nonprecessing binary black hole mergers

We use the open source, community-driven, numerical relativity software, the Einstein Toolkit to study the physics of eccentric, spinning, nonprecessing binary black hole mergers with mass-ratios $q=\{2, 4, 6\}$, individual dimensionless spin parameters $\chi_{1z}=\pm0.6$, $\chi_{2z}=\pm0.3$, that include higher order gravitational wave modes $\ell\leq4$, except for memory modes. Assuming stellar mass binary black hole mergers that may be detectable by the advanced LIGO detectors, we find that including modes up to $\ell=4$ increases the signal-to-noise of compact binaries between $3.5\%$ to $35\%$, compared to signals that only include the $\ell=|m|=2$ mode. We use two waveform models, TEOBResumS and SEOBNRE, which incorporate spin and eccentricity corrections in the waveform dynamics, to quantify the orbital eccentricity of our numerical relativity catalog in a gauge-invariant manner through fitting factor calculations. Our findings indicate that the inclusion of higher order wave modes has a measurable effect in the recovery of moderately and highly eccentric black hole mergers, and thus it is essential to develop waveform models and signal processing tools that accurately describe the physics of these astrophysical sources.

New total transmission modes of the Kerr geometry with Schwarzschild limit frequencies at complex infinity

In addition to the well-known quasinormal modes, the gravitational modes of the Kerr geometry also include sets of total-transmission modes. Each mode can be considered as an element of a sequence of modes parameterized by the angular momentum of the black hole. One family of gravitational total-transmission modes of Kerr have been known for some time. Modes in this family connect to a Schwarzschild limit where the mode frequency is finite and purely imaginary. Recently, what was thought to be an additional branch of this original family of modes was discovered. However, this new branch is actually a part of one of two entirely new families of total-transmission modes. Modes in these new families, surprisingly, connect to a Schwarzschild limit where the mode frequencies exist at complex infinity. We have numerically constructed full sets of sequences of gravitational total-transmission modes for harmonic indices $\ell=[2,8]$. Using these numerical sequences, we have been able to construct analytic asymptotic expansions for the mode frequencies and their associated separation constants. The asymptotic expansion for the separation constant used in constructing the total-transmission modes seems to be valid for general complex values of the oblateness parameter.

Gregory-Laflamme encounters Superradiance

We investigate the effect of superradiant scattering of gravitational perturbations on the stability of rotating black strings, focusing on the six dimensional equal-spinning Myers-Perry black string. We find that rapidly rotating black strings are unstable to gravitational superradiant modes within a bounded range of string lengths. The instability occurs because momentum along the string direction creates a potential barrier that allows for the confinement of superradiant modes. Yet, five dimensional Myers-Perry black holes do not have stable particle orbits so, unlike other known superradiant systems, these black strings remain stable to perturbations with sufficiently high azimuthal mode number — this is a ‘finite-m’ superradiant instability. For some parameters, this instability competes with the Gregory-Laflamme instability, but otherwise exists independently. The onset of this instability is degenerate and branches to multiple steady-state solutions. This paper is the first of a trilogy: in the next two, we construct two distinct families of rotating strings emerging from the superradiant onset (the ‘black resonator strings’ and ‘helical black strings’). We argue that similar physics is present in 5-dimensional Kerr black strings, but not in D > 6 equal-spinning Myers-Perry black strings.

Calculating quasinormal modes of Schwarzschild anti–de Sitter black holes using the continued fraction method

We investigate the scalar, gravitational, and electromagnetic quasinormal mode spectra of Schwarzschild anti-de Sitter black holes using the numerical continued fraction method. The spectra have similar, almost linear structures. With a few exceptions, the low overtone quasinormal modes are consistent with previously obtained results in the literature that use other numerical techniques. The intermediate and high overtone quasinormal modes, in comparison to the Schwarzschild case, converge very quickly to the asymptotic formulas previously obtained by analytic monodromy techniques. In addition, we find a connection between the analytic asymptotic formulas and the purely imaginary modes. In particular, these formulas can be used to predict the bifurcation of the lowest damped electromagnetic modes. Finally, we find no high overtone quasinormal modes with high oscillation frequency and low damping, which had been previously predicted.

The gravitational energy-momentum pseudo-tensor in higher-order theories of gravity

The problem of non-localizability and the non-uniqueness of gravitational energy in general relativity has been considered by many authors. Several gravitational pseudo-tensor prescriptions have been proposed by physicists, such as Einstein, Tolman, Landau, Lifshitz, Papapetrou, Moller, andWeinberg. We examine here the energy-momentum complex in higher-order theories of gravity applying the Noether theorem for the invariance of gravitational action under rigid translations. This, in general, is not a tensor quantity because it is not a covariant object but only an affine tensor, that is, a pseudo-tensor. Therefore we propose a possible prescription of gravitational energy and momentum density for ?k gravity governed by the gravitational Lagrangian L1 = (R + a0R2 + Pp k=1 akR?kR) ??g and generally for n-order gravity described by the gravitational Lagrangian L = L (g??, g??,i1, 1??,i1i2, g??,i1i2i3 ,..., g??,i1i2i3...in). The extended pseudo-tensor reduces to the one introduced by Einstein in the limit of general relativity where corrections vanish. Then, we explicitly show a useful calculation, i.e., the power per unit solid angle ? emitted by a massive system and carried by a gravitational wave in the direction ? x for a fixed wave number k. We fix a suitable gauge, by means of the average value of the pseudo-tensor over a spacetime domain and we verify that the local pseudo-tensor conservation holds. The gravitational energy-momentum pseudo-tensor may be a useful tool to search for possible further gravitational modes beyond the two standard ones of general relativity. Their finding could be a possible observable signatures for alternative theories of gravity.

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

One of the most promising strategies to test gravity in the strong-field, large curvature regime is gravitational spectroscopy: the measurement of black hole quasi-normal modes from the ringdown signal emitted in the aftermath of a compact binary coalescence, searching for deviations from the predictions of general relativity. This strategy is only effective if we know how quasi-normal modes of black holes are affected by modifications of general relativity; and if we know this for rotating black holes, since binary coalescences typically lead to black holes with spins $J/M^2\sim 0.7$. In this article, we compute for the first time the gravitational quasi-normal modes of rotating black holes up to second order in the spin in a modified gravity theory. We consider Einstein-dilaton Gauss-Bonnet gravity, one of the simplest theories which modifies the large-curvature regime of gravity and which can be tested with black hole observations. To enhance the domain of validity of the spin expansion, we perform a Pad\'e resummation of the quasi-normal modes. We find that when the second order in spin is not included, the effect of gravity modifications may be seriously underestimated. A comparison with the general relativistic case suggests that this approach should be accurate up to spins $\sim 0.7$; therefore, our results can be used in the data analysis of ringdown signals.

Island on codimension-two branes in AdS/dCFT

The previous studies of the island and double holography mainly focus on codimension-one branes. This paper explores the island on the codimension-two brane in AdS/dCFT. The codimension-two brane is closely related to conical singularity, which is very different from the codimension-one brane. We analyze the mass spectrum of gravitons on the codimension-two brane and find that the larger the brane tension is, the smaller the gravitational mass is. The massless mode is forbidden by either the boundary or normalization conditions. We prove that the first massive gravitational mode is located on the codimension-two brane; the larger the tension, the better the localization. It is similar to the case of codimension-one brane and builds an excellent physical foundation for the study of black hole evolution on codimension-two branes. We find that the Page curve of eternal black holes can be recovered due to the island ending on the codimension-two brane. The new feature is that the extremal surface passing the horizon cannot be defined after some finite time in the no-island phase. Fortunately, this unusual situation does not affect the Page curve since it happens after Page time.

Pulsar and cosmic variances of pulsar timing-array correlation measurements of the stochastic gravitational wave background

Pulsar timing-array correlation measurements offer an exciting opportunity to test the nature of gravity in the cosmologically novel nanohertz gravitational wave regime. The stochastic gravitational wave background is assumed Gaussian and random, while there are limited pulsar pairs in the sky. This brings theoretical uncertainties to the correlation measurements, namely the pulsar variance due to pulsar samplings and the cosmic variance due to Gaussian signals. We demonstrate a straightforward calculation of the mean and the variances on the Hellings-Downs correlation relying on a power spectrum formalism. We keep arbitrary pulsar distances and consider gravitational wave modes beyond Einstein gravity as well as off the light cone throughout, thereby presenting the most general and, most importantly, numerically efficient calculation of the variances.

AI and extreme scale computing to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non-precessing black hole mergers

We use artificial intelligence (AI) to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non precessing binary black hole mergers. We trained AI models using 14 million waveforms, produced with the surrogate model NRHybSur3dq8, that include modes up to ℓ≤4 and (5,5), except for (4,0) and (4,1), that describe binaries with mass-ratios q≤8, individual spins s{1,2}z∈[−0.8,0.8], and inclination angle θ∈[0,π]. Our probabilistic AI surrogates can accurately constrain the mass-ratio, individual spins, effective spin, and inclination angle of numerical relativity waveforms that describe such signal manifold. We compared the predictions of our AI models with Gaussian process regression, random forest, k-nearest neighbors, and linear regression, and with traditional Bayesian inference methods through the PyCBC Inference toolkit, finding that AI outperforms all these approaches in terms of accuracy, and are between three to four orders of magnitude faster than traditional Bayesian inference methods. Our AI surrogates were trained within 3.4 hours using distributed training on 1,536 NVIDIA V100 GPUs in the Summit supercomputer.

The timbre of Hawking gravitons: an effective description of energy transport from holography

Planar black holes in AdS, which are holographically dual to compressible relativistic fluids, have a long-lived phonon mode that captures the physics of attenuated sound propagation and transports energy in the plasma. We describe the open effective field theory of this fluctuating phonon degree of freedom. The dynamics of the phonon is encoded in a single scalar field whose gravitational coupling has non-trivial spatial momentum dependence. This description fits neatly into the paradigm of classifying gravitational modes by their Markovianity index, depending on whether they are long-lived. The sound scalar is a non-Markovian field with index 3 − d for a d-dimensional fluid. We reproduce (and extend) the dispersion relation of the holographic sound mode to quartic order in derivatives, constructing in the process the effective field theory governing its attenuated dynamics and associated stochastic fluctuations. We also remark on the presence of additional spatially homogeneous zero modes in the gravitational problem, which remain disconnected from the phonon Goldstone mode.

AdS/BCFT and Island for curvature-squared gravity

In this paper, we investigate AdS/BCFT for curvature-squared gravity. To warm up, we start with Gauss-Bonnet gravity. We derive the one point function of stress tensor and show that the central charge related to the norm of displacement operator is positive for the couplings obeying causality constraints. Furthermore, by imposing the null energy condition on the end-of-the-world brane, we prove the holographic g-theorem for Gauss-Bonnet gravity. This corrects a wrong point of view in the literature, which claims that the holographic g-theorem is violated for Gauss-Bonnet gravity. As a by-product, we obtain the boundary entropy and A-type boundary central charges in general dimensions. We also study AdS/BCFT for general curvature-squared gravity. We find that it is too restrictive for the shape of the brane and the dual BCFT is trivial if one imposes Neumann boundary conditions for all of the gravitational modes. Instead, we propose to impose Dirichlet boundary condition for the massive graviton, while imposing Neumann boundary condition for the massless graviton. In this way, we obtain non-trivial shape dependence of stress tensor and well-defined central charges. In particular, the holographic g-theorem is satisfied by general curvature-squared gravity. Finally, we discuss the island and show that the Page curve can be recovered for Gauss-Bonnet gravity. Interestingly, there are zeroth-order phase transitions for the Page curve within one range of couplings obeying causality constraints. Generalizing the discussions to holographic entanglement entropy and holographic complexity in AdS/CFT, we get new constraints for the Gauss-Bonnet coupling, which is stronger than the causality constraint.

Gravitational wave modes in matter

A general linear gauge-invariant equation for dispersive gravitational waves (GWs) propagating in matter is derived. This equation describes, on the same footing, both the usual tensor modes and the gravitational modes strongly coupled with matter. It is shown that the effect of matter on the former is comparable to diffraction and therefore negligible within the geometrical-optics approximation. However, this approximation is applicable to modes strongly coupled with matter due to their large refractive index. GWs in ideal gas are studied using the kinetic average-Lagrangian approach and the gravitational polarizability of matter that we have introduced earlier. In particular, we show that this formulation subsumes the kinetic Jeans instability as a collective GW mode with a peculiar polarization, which is derived from the dispersion matrix rather than assumed a priori. This forms a foundation for systematically extending GW theory to GW interactions with plasmas, where symmetry considerations alone are insufficient to predict the wave polarization.

Quasinormal modes of slowly-rotating black holes in dynamical Chern-Simons gravity

The detection of gravitational waves from compact binary mergers by the LIGO/Virgo Collaboration has, for the first time, allowed us to test relativistic gravity in its strong, dynamical, and nonlinear regime, thus opening a new arena to confront general relativity (and modifications thereof) against observations. We consider a theory which modifies general relativity by introducing a scalar field coupled to a parity-violating curvature term known as dynamical Chern-Simons gravity. In this theory, spinning black holes are different from their general relativistic counterparts and can thus serve as probes to this theory. We study linear gravito-scalar perturbations of black holes in dynamical Chern-Simons gravity at leading order in spin and (i) obtain the perturbed field equations describing the evolution of the perturbed gravitational and scalar fields, (ii) numerically solve these equations by direct integration to calculate the quasinormal mode frequencies for the dominant and higher multipoles and tabulate them, (iii) find strong evidence that these rotating black holes are linearly stable, and (iv) present general fitting functions for different multipoles for gravitational and scalar quasinormal mode frequencies in terms of spin and Chern-Simons coupling parameter. Our results can be used to validate the ringdown of small-spin remnants of numerical relativity simulations of black hole binaries in dynamical Chern-Simons gravity and pave the way towards future tests of this theory with gravitational wave ringdown observations.

Ellis drainhole solution in Einstein-Æther gravity and the axial gravitational quasinormal modes

In this work, the Ellis drainhole solution is derived in Einstein-Æther gravity, and subsequently, the axial quasinormal modes of the resulting drainhole are investigated. Owing to the presence of a minimally coupled scalar field with antiorthodox coupling polarity, the resultant metric solution is featured by a throat instead of a horizon, for which static æther solution becomes feasible. Moreover, the derived master equations for the axial gravitational perturbations consist of two coupled vector degrees of freedom. By utilizing the finite difference method, the temporal profiles of the quasinormal oscillations are evaluated, and, subsequently, the complex frequencies are extracted and compared against the specific values obtained by the WKB method when the coupling is turned off. Besides, the effect of the coupling on the low-lying quasinormal spectrum is explored, and its possible physical relevance is discussed.

Chirality of gravitational waves in Chern-Simons f(R) gravity cosmology

In this paper we shall consider an axionic Chern-Simons-corrected $f(R)$ gravity theoretical framework, and we shall study the chirality of the generated primordial gravitational waves. Particularly, we shall consider two main axion models, the canonical misalignment axion model and the kinetic axion model, both of which provide an interesting particle phenomenology, in the presence of ${R}^{2}$ terms in the inflationary Lagrangian. The axion does not affect significantly the background evolution during the inflationary era, which is solely controlled by ${R}^{2}$ gravity. However, due to the presence of the Chern-Simons term, the tensor perturbations are directly affected, and our aim is to reveal the extent of the effects of the Chern-Simons term on the gravitational wave modes, for both the axion models. We aim to produce analytical descriptions of the primordial tensor mode behavior, and thus we solve analytically the evolution equations of the tensor modes, for a nearly de Sitter primordial evolution controlled by the ${R}^{2}$ gravity. We focus the analytical study on superhorizon and subhorizon modes. For the misalignment model, we were able to produce analytic solutions for both the subhorizon and superhorizon modes, in which case we find the behavior of the circular polarization function. Our results indicate that the produced tensor spectrum is strongly chiral. For the kinetic axion model though, analytic solutions are obtained only for the superhorizon modes. In order to have a grasp of the behavior of the chirality of the tensor modes, we studied the chirality of the superhorizon modes, however, a more complete study is needed, which is impossible to do analytically though.

Gravitational quasinormal modes for Lifshitz black branes

We study the scalar and vector channels of gravitational quasinormal modes for Lifshitz black branes emerging in Einstein-Maxwell-Dilaton and Einstein-Proca theories in four and five dimensions, finding significant differences between the two models. In particular, rather surprisingly, in the Einstein-Maxwell-Dilaton model the dispersion relations for the shear and sound modes are given by ωshear ∼ −i k4 and ωsound ∼ −i k2, while in the Einstein-Proca model they take the more conventional form ωshear ∼ −i k2 and ωsound ∼ k —the proportionality constants depend on the dynamical exponent and the appropriate factors of temperature. Through the holographic duality, this calculation provides information about the relaxation of the momentum and energy flux operators in a putative dual Lifshitz field theory. Comparing with the dispersion relations obtained directly by considering Lifshitz hydrodynamics suggest that the mass density of the equilibrium state in the Einstein-Maxwell-Dilaton model is infinite.

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.