Gravity Perturbations Research Articles

Horndeski-like gravity perturbation induced by large-magnitude earthquake

We hypothesis that large earthquakes generate Horndeski-like Gravitational Wave (GW). We find that such a Horndeski-like GW propagates with the speed of sound. The sound waves generated by an earthquake make a local and temporal change to the Earth’s diagravitational medium; therefore, they modify the GW speed in a standard, Alternative-Theory-of-Gravity (ATG) sense. The quantum of the Horndeski-like GW is a massless scalar quasiparticle and cannot exist outside of the propagation region of the P-field. The Horndeski-like GW may be detectable by future GW detectors with a sensitivity of 10–15 Hz-1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Hz}^{{-1/2}}$$\\end{document} in the region of 0.1–1 Hz.

Model for cosmological perturbations in affine gravity

Model for cosmological perturbations in affine gravity

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

Metric perturbations in noncommutative gravity

We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.

Cosmological higher-curvature gravities

We examine higher-curvature gravities whose Friedmann–Lemaître–Robertson–Walker configurations are specified by equations of motion which are of second order in derivatives, just like in Einstein gravity. We name these theories Cosmological Gravities and initiate a systematic exploration in dimensions D⩾3 . First, we derive an instance of Cosmological Gravity to all curvature orders and dimensions D⩾3 . Second, we study Cosmological Gravities admitting non-hairy generalizations of the Schwarzschild solution characterized by a single function whose equation of motion is, at most, of second order in derivatives. We present explicit instances of such theories for all curvature orders and dimensions D⩾4 . Finally, we investigate the equations of motion for cosmological perturbations in the context of generic Cosmological Gravities. Remarkably, we find that the linearized equations of motion for scalar cosmological perturbations in any Cosmological Gravity in D⩾3 contain no more than two time derivatives. We explicitly corroborate this aspect by presenting the equations for the scalar perturbations in some four-dimensional Cosmological Gravities up to fifth order in the curvature.

Subregion independence in gravity

In gravity, spacelike separated regions can be dependent on each other due to the constraint equations. In this paper, we give a natural definition of subsystem independence and gravitational dressing of perturbations in classical gravity. We find that extremal surfaces, non-perturbative lumps of matter, and generic trapped surfaces are structures that enable dressing and subregion independence. This leads to a simple intuitive picture for why extremal surfaces tend to separate independent subsystems. The underlying reason is that localized perturbations on one side of an extremal surface contribute negatively to the mass on the other side, making the gravitational constraints behave as if there exist both negative and positive charges. Our results support the consistency of islands in massless gravity, shed light on the Python’s lunch, and provide hints on the nature of the split property in perturbatively quantized general relativity. We also prove a theorem bounding the area of certain surfaces in spherically symmetric asymptotically de Sitter spacetimes from above and below in terms of the horizon areas of de Sitter and Nariai. This theorem implies that it is impossible to deform a single static patch without also deforming the opposite patch, provided we assume spherical symmetry and an energy condition.

Gauge-invariant cosmological perturbations in general teleparallel gravity

We study linear cosmological perturbations in the most general teleparallel gravity setting, where gravity is mediated by the torsion and nonmetricity of a flat connection alongside the metric. For a general linear perturbation of this geometry around a homogeneous and isotropic background geometry, we derive the irreducible decomposition of the perturbation variables, as well as their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms generated by a vector field. In addition, we also study these properties for the most general set of matter variables and gravitational field equations. We then make use of these result to construct gauge-invariant perturbation variables, using a general approach based on gauge conditions. We further calculate these quantities also in the metric and symmetric teleparallel geometries, where nonmetricity or torsion is imposed to vanish. To illustrate our results, we derive the energy-momentum–hypermomentum conservation equations for both the cosmological background and the linear perturbations. As another example, we study the propagation of tensor perturbations in the f(G), f(T) and f(Q) class of theories.

Generalized Amit-Roginsky model from perturbations of 3D quantum gravity

Generalized Amit-Roginsky model from perturbations of 3D quantum gravity

Effective field theory of black hole perturbations in vector-tensor gravity

We formulate the effective field theory (EFT) of vector-tensor gravity for perturbations around an arbitrary background with a timelike vector profile, which can be applied to study black hole perturbations. The vector profile spontaneously breaks both the time diffeomorphism and the U(1) symmetry, leaving their combination and the spatial diffeomorphism as the residual symmetries in the unitary gauge. We derive two sets of consistency relations which guarantee the residual symmetries of the EFT. Also, we provide the dictionary between our EFT coefficients and those of generalized Proca (GP) theories, which enables us to identify a simple subclass of the EFT that includes the GP theories as a special case. For this subclass, we consider the stealth Schwarzschild(-de Sitter) background solution with a constant temporal component of the vector field and study the decoupling limit of the longitudinal mode of the vector field, explicitly showing that the strong coupling problem arises due to vanishing sound speeds. This is in sharp contrast to the case of gauged ghost condensate, in which perturbations are weakly coupled thanks to certain higher-derivative terms, i.e., the scordatura terms. This implies that, in order to consistently describe this type of stealth solutions within the EFT, the scordatura terms must necessarily be taken into account in addition to those already included in the simple subclass.

Design and implementation of a seismic Newtonian noise cancellation system for the Virgo gravitational-wave detector

Terrestrial gravity perturbations caused by seismic fields produce the so-called Newtonian noise in gravitational-wave detectors, which is predicted to limit their sensitivity in the upcoming observing runs. In the past, this noise was seen as an infrastructural limitation, i.e., something that cannot be overcome without major investments to improve a detector’s infrastructure. However, it is possible to have at least an indirect estimate of this noise by using the data from a large number of seismometers deployed around a detector’s suspended test masses. The noise estimate can be subtracted from the gravitational-wave data, a process called Newtonian noise cancellation (NNC). In this article, we present the design and implementation of the first NNC system at the Virgo detector as part of its AdV+ upgrade. It uses data from 110 vertical geophones deployed inside the Virgo buildings in optimized array configurations. We use a separate tiltmeter channel to test the pipeline in a proof-of-principle. The system has been running with good performance over months.

Gauge fixing in cosmological perturbations of Unimodular Gravity

With focus on the cosmological evolution of linear perturbations of matter and geometry, we calculate the equivalent expressions to that of the Newtonian and Synchronous gauges within the framework of Unimodular Gravity, being these two gauges commonly used and implemented in Boltzmann codes. An important aspect of our analysis is the inclusion of the energy-momentum current violation, as well as its perturbations. Moreover, for the first time we demonstrate that it is possible to fix both gauges consistently, although as it has been already noticed in previous literature, neither of them is recovered in the sense of the dynamics given in General Relativity for matter and metric fluctuations. Specifically, we show that since the unimodular constraint at the level of linear perturbations lead to only one degree of freedom of scalar modes of metric fluctuations, the dynamics in Unimodular Gravity forces to keep the anisotropic stress in the Newtonian gauge, whereas the cold dark matter comoving frame can not be set in the Synchronous gauge. The physical implications on the density contrast of cold dark matter is reviewed, and the Sachs-Wolfe effect is obtained and compared with previous results in the literature of cosmological perturbations in Unimodular Gravity.

Seismic prompt gravity strain signals in a layered spherical Earth

Seismic waves generated by an earthquake can produce dynamic perturbations in the Earth’s gravity field before the direct arrival of P-waves. Observations of these so-called prompt elasto-gravity signals by ground-based gravimeters and broadband seismometers have been reported for some large events, such as the 2011 MW9.1 Tohoku earthquake. Recent studies have introduced prompt gravity strain signals (PGSSs) as a new type of observable seismic gravity perturbation that can be used to measure the spatial gradient of the perturbed gravity field. Theoretically, these types of signals can be recorded by in-development instruments termed gravity strainmeters, although no successful detection has been reported as yet. Herein, we propose an efficient approach for PGSSs based on a multilayered spherical Earth model. We compared the simulated waveforms with analytical solutions obtained from a homogeneous half-space model, which has been used in earlier studies. This comparison indicates that the effect of the Earth’s structural stratification is significant. With the help of the new simulation approach, we also demonstrated how the PGSSs depend on the magnitude of the seismic source. We further conducted synthetic tests estimating earthquake magnitude using gravity strain signals to demonstrate the potential application of this type of signal in earthquake early warning systems. These results provide essential information for future studies on the synthesis and application of earthquake-induced gravity strain signals.

Spectral-infinite-element simulations of seismic wave propagation in self-gravitating, rotating 3-D Earth models

SUMMARY Although observation of gravity perturbations induced by earthquakes is possible, simulation of seismic wave propagation in a self-gravitating, rotating Earth model with 3-D heterogeneity is challenging due to the numerical complexities associated with the unbounded Poisson/Laplace equation that governs gravity perturbations. Therefore, gravity perturbations are generally omitted, and only the background gravity is taken into account using the so-called Cowling approximation. However, gravity perturbations may be significant for large earthquakes (Mw ≥ 6.0) and long-period responses. In this study, we develop a time-domain solver based on the spectral-infinite-element approach, which combines the spectral element method inside the Earth domain with a mapped-infinite-element method in the infinite space outside. This combination allows us to solve the complete, coupled momentum-gravitational equations in a fully discretized domain while accommodating complex 3-D Earth models. We compute displacement and gravity perturbations considering various Earth models, including Preliminary Reference Earth Model and S40RTS and conduct comprehensive benchmarks of our method against the spherical harmonics normal-mode approach and the direct radial integration method. Our 3-D simulations accommodate topography, bathymetry, rotation, ellipticity and oceans. Results show that our technique is accurate and stable for long simulations. Our method provides a new scope for incorporating earthquake-induced gravity perturbations into source and adjoint tomographic inversions.

On the ghost problem of conformal gravity

We study the metric perturbations around the de Sitter and Minkowski backgrounds in Conformal Gravity. We confirm the presence of ghosts in both cases. In the de Sitter case, by applying the Maldacena boundary conditions — the Neumann boundary condition and the positive-frequency mode condition — to the metric, we show that one cannot recover a general solution for the perturbations. In turn, alongside the Neumann boundary condition, we derive an additional condition with which the perturbations of conformal gravity and dS perturbations of Einstein gravity with cosmological constant coincide. We further show that the Neumann boundary condition does not lead to a general solution in Minkowski space. Conversely, we derive the alternative boundary conditions, with which we attain an agreement between the perturbations of conformal and Einstein gravity in full generality, thus removing the ghost of conformal gravity.

Universal Teukolsky equations and black hole perturbations in higher-derivative gravity

Universal Teukolsky equations and black hole perturbations in higher-derivative gravity

Using Cosmological Perturbation Theory to Distinguish between GR and Unimodular Gravity

Unimodular gravity is one of the oldest geometric gravity theories and alternatives to general relativity. Essentially, it is based on the Einstein–Hilbert Lagrangian with an additional constraint on the determinant of the metric. It can be explicitly shown that unimodular gravity can be recast as general relativity in the presence of a cosmological constant. This fact has led to many discussions on the equivalence of both theories at the classical and quantum levels. Here, we present an analysis focused on the classical scalar perturbations around a cosmological background. We focus on the unusual situation in which the typical conservation laws are not adopted. The discussion is extended to the case where a non-minimal coupled scalar field is introduced. We also present a gauge-invariant analysis showing that perturbations in unimodular gravity display instabilities. Our results reinforce that the equivalence is not verified completely at a cosmological perturbative level.

Comments on “horizontal gravity disturbance vector in atmospheric dynamics” by Peter C. Chu

In a recent paper [Chu (2023; Chu23)], the author formulated the equations governing atmospheric motion in a spheroidal coordinate system. Since the mass distribution of the Earth is not exactly spheroidal, the true gravity is not vertical in that coordinate system. Chu23 compared the magnitude of the static horizontal component of gravity in that system to those of the dynamically active forces and concluded that the horizontal components of gravity should not be neglected. In recent papers by the authors [Chang and Wolfe (2022; CW22) and Stewart and McWilliams (2022; CW22)], we explained that the actual interpretation of the approximation made in atmospheric and oceanic modeling is not neglecting the horizontal component of the true gravity, but is a geometrical approximation, approximating nearly spheroidal geopotential surfaces with bumps on which the true gravity is vertical by exactly spheroidal surfaces. We showed that under such an interpretation, the errors due to the geometrical approximation are small. Chu23 claimed that CW22 and SM22 erroneously neglected the gravity perturbations in their analyses. Here, we explain further the differences between these approaches, in the process showing that the criticisms of Chu23 on CW22 and SM22 are invalid, further supporting our conclusion that the horizontal component of the true gravity is not relevant in ocean and atmospheric dynamics. Physically, the reason why horizontal gravity is irrelevant in the coordinate system used by Chu23 is that it is balanced by a static horizontal pressure gradient force.

J2 섭동을 고려한 랑데부 및 도킹 시뮬레이션

In this paper, simulation analysis for close operation during rendezvous/docking considering perturbation was described. The technology to control satellites based on their relative motion is expected to be a very important core technology. Rendezvous/docking is a technology underlying on-orbit servicing technology and is an essential process for approaching a target satellite. Therefore, in this paper, we introduce a feedback control system for rendezvous/docking verification considering gravity perturbation and analyze the rendezvous/docking situation through the proper gain value.

On the Treatment of Exterior Domains for the Time-Harmonic Equations of Stellar Oscillations

In a recent article we started to analyze the time-harmonic equations of stellar oscillations. As a first step we considered bounded domains together with an essential boundary condition and established the well-posedness of the equation. In this article we consider the physical relevant case of the domain being $\mathbb{R}^3$. We discuss the treatment of the exterior domain, and show how to couple the two parts to obtain a well-posedness result. Further, for the Cowling approximation (which neglects the Eulerian perturbation of gravity) we derive a scalar equation in the atmosphere, couple it to the vectorial interior equation, and prove the well-posedness of the new system. This coupled system has the big advantages that it simplifies the construction of approximating transparent boundary conditions and leads to significant less degrees of freedom for discretizations.

Tidal Heating at Europa Using the Multifrequency Analysis of Tidal Heating Toolkit

We evaluate the thermal response of Europa’s ice shell to the gravity perturbation of Jupiter using a comprehensive toolkit (dubbed Multifrequency Analysis of Tidal Heating, MATH) that evaluates tidal heating and heat flow in planetary bodies. The tidal heating source is radially resolved and can capture the temperature-dependent pattern of heat production with depth. We use MATH to examine the steady-state thermal profiles through a conductive Europan ice shell, considering the tidal effects of long-term eccentricity variations, obliquity, libration, and nonsynchronous rotation (NSR). In each case, we vary the shell thickness, calculate the combination of tidal heating generated within the shell and heat flux into the shell base that would maintain that thickness, and track the resulting surface heat flux. We find that Europa’s ice shell should be, on average, no more than 12–17 km thick, due to long-term eccentricity variations, and could be even thinner if the basal heat flux is nonnegligible. These results are more consistent with inferences from Europa’s surface geology than previous tidal heating studies that used simplified interior models, a globally averaged tidal heating rate, and/or constant eccentricity. We also find that, for a given stable shell thickness, the surface heat flow remains fairly consistent even as other parameters are varied, perhaps providing an additional method for constraining ice shell thicknesses on ocean-bearing moons. Although Europa’s tidal heat budget and shell thickness seem relatively insensitive to constant obliquity, libration, and NSR, moons in closer-in orbits may be more sensitive to these other effects and should be further explored.