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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Static response and Love numbers of Schwarzschild black holes

We derive the quadratic action for the physical degrees of freedom of massless spin-0, spin-1, and spin-2 perturbations on a Schwarzschild-(A)dS background in arbitrary dimensions. Here, we then use these results to compute the static response of asymptotically flat Schwarzschild black holes to external fields. Our analysis reproduces known facts about black hole Love numbers — in particular that they vanish for all types of perturbation in four spacetime dimensions — but also leads to new results. For instance, we find that neutral Schwarzschild black holes polarize in the presence of an electromagnetic background in any number of spacetime dimensions except four. Moreover, we calculate for the first time black hole Love numbers for vector-type gravitational perturbations in higher dimensions and find that they generically do not vanish. Along the way, we shed some light on an apparent discrepancy between previous results in the literature, and clarify some aspects of the matching between perturbative calculations of static response on a Schwarzschild background and the point-particle effective theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Geometry and dynamics of lipid membranes: The Scriven-Love number

The equations governing lipid membrane dynamics in planar, spherical, and cylindrical geometries are presented here. Unperturbed and first-order perturbed equations are determined and nondimensionalized. In membrane systems with a nonzero base flow, perturbed in-plane and out-of-plane quantities are found to vary over different length scales. Here, a new dimensionless number, named the Scriven-Love number, and the well-known Föppl–von Kármán number result from a scaling analysis. The Scriven-Love number compares out-of-plane forces arising from the in-plane, intramembrane viscous stresses to the familiar elastic bending forces, while the Föppl–von Kármán number compares tension to bending forces. Both numbers are calculated in past experimental works, and span a wide range of values in various biological processes across different geometries. In situations with large Scriven-Love and Föppl–von Kármán numbers, the dynamical response of a perturbed membrane is dominated by out-of-plane viscous and surface tension forces—with bending forces playing a negligible role. Calculations of non-negligible Scriven-Love numbers in various biological processes and in vitro experiments show in-plane intramembrane viscous flows cannot generally be ignored when analyzing lipid membrane behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Tidal Love numbers of analog black holes

Tidal Love numbers quantify the conservative static response of compact objects to external tidal fields, and are found to vanish exactly for asymptotically flat black holes in four-dimensional general relativity. Many aspects of the physics of black holes have an analog in the theory of supersonic acoustic flows, including the existence of an event horizon and associated phenomena, such as quasinormal modes and superradiance. In this paper, we investigate the tidal Love numbers of acoustic black holes in different number of dimensions. We find that they exhibit a number of similar properties as higher-dimensional general relativistic black holes, such as logarithmic running with radial distance, and vanishing tidal response for special multipole moments. As a result, we show that the latter is a consequence of ladder symmetries, analogous to those identified for black holes.

Classical black holes↗
NASA NTRS1994

Determination of tidal h Love number parameters in the diurnal band using an extensive VLBI data set

We use over a decade of geodetic Very Long Baseline Interferometry (VLBI) data to estimate parameters in a resonance expansion of the frequency dependence of the tidal h(sub 2) Love number within the diurnal band. The resonance is associated with the retrograde free core nutation (RFCN). We obtain a value for the real part of the resonance strength of (-0.27 +/- 0.03) x 10(exp -3); a value of -0.19 x 10(exp -3) is predicted theoretically. Uncertainties in the VLBI estimates of the body tide radial displacement amplitudes are approximately 0.5 mm (1.1 mm for the K1 frequency), but they do not yield sufficiently small Love number uncertainties for placing useful constraints on the frequency of the RFCN, given the much smaller uncertainties obtained from independent analyses using nutation or gravimetric data. We also consider the imaginary part of the tidal h(sub 2) Love number. The estimated imaginary part of the resonance strength is (0.00 +/- 0.02) x 10(exp -3). The estimated imaginary part of the nonresonant component of the Love number implies a phase angle in the diurnal tidal response of the Earth of 0.7 deg +/- 0.5 deg (lag).

Mitrovica, J. X.↗
NASA NTRS2003

Estimating the k2 Tidal Gravity Love Number of Mars

Analysis of the orbits of spacecraft can be used to infer global tidal parameters. For Mars, the Mars Global Surveyor (MGS) spacecraft has been used to estimate the second degree Love number, k2 from the tracking DSN tracking Doppler and range data by several authors. Unfortunately, neither of the spacecraft presently in orbit are ideally suited to tidal recovery because they are in sun-synchronous orbits that vary only slightly in local time; and, further, the sub-solar location only varies by about 25 degrees in latitude. Never-the less respectable estimates of the k2 tide have been made by several authors. We present an updated solution of the degree 2 zonal Love number, compare with previous dues, and analyze the sensitivity of the solution to orbital parameters, spacecraft maneuvers, and solution methodology. Estimating the k2 Tidal Gravity Love Number of Mars.

Smith, David E.↗
DOE OSTI2024

Ladder symmetries and Love numbers of Reissner-Nordström black holes

It is well known that asymptotically flat black holes in general relativity have vanishing tidal Love numbers. In the case of Schwarzschild and Kerr black holes, this property has been shown to be a consequence of a hidden structure of ladder symmetries for the perturbations. In this work, we extend the ladder symmetries to non-rotating charged black holes in general relativity. As opposed to previous works in this context, we adopt a more general definition of Love numbers, including quadratic operators that mix gravitational and electromagnetic perturbations in the point-particle effective field theory. We show that the calculation of a subset of those couplings in full general relativity is affected by an ambiguity in the split between source and response, which we resolve through an analytic continuation. As a result, we derive a novel master equation that unifies scalar, electromagnetic and gravitational perturbations around Reissner-Nordström black holes. The equation is hypergeometric and can be obtained from previous formulations via nontrivial field redefinitions, which allow to systematically remove some of the singularities and make the presence of the ladder symmetries more manifest.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Tidal Love numbers and Green’s functions in black hole spacetimes

Tidal interactions play a crucial role in deciphering gravitational wave signals emitted by the coalescence of binary systems. They are usually quantified by a set of complex coefficients which include tidal Love numbers, describing the conservative response to an external perturbation. In the static case, these are found to vanish exactly for asymptotically flat black holes in general relativity in four space-time dimensions, and recently they have been generalized to dynamical interactions. In the context of response theory, the retarded Green’s function provides the complete description of the behavior of dynamical systems. Here, in this work we investigate the relation between Love numbers and Green’s functions, and highlight the relevance of radiation reaction effects to their connection. As a special case, we discuss Banados-Teitelboim-Zanelli black holes, where the absence of radiative modes allows us to make a direct link between them.

classical black holes↗
DOE OSTI2023

Implications of the weak gravity conjecture for tidal Love numbers of black holes

The weak gravity conjecture indicates that extremal black holes in the low-energy effective field theory should be able to decay. This criterion gives rise to nontrivial constraints on the coefficients of higher-order derivative corrections to gravity. In this paper, we investigate the tidal deformability of neutral black holes due to higher-order derivative corrections. As a proof of concept, we consider a correction of cubic order in the Riemann curvature tensor. The tidal Love numbers of neutral black holes receive leading-order corrections from higher-order derivative terms, since black holes in pure General Relativity have vanishing tidal Love number. We conclude that the interplay between the tidal deformability of black holes and the weak gravity conjecture provides useful information about the effective field theory.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2002

Lunar Love Numbers and the Deep Lunar Interior

Observationally determined values of the Love number k2 are larger than existing models of the lunar interior predict. The region between the deep moonquakes and core may be a low velocity zone from a partial melt. Additional information is contained in the original extended abstract.

Williams, J. G.↗
DOE OSTI2022

Tidal Love numbers of novel and admixed celestial objects

A sub-fraction of dark matter or new particles trapped inside celestial objects can significantly alter their macroscopic properties. Here, we investigate the new physics imprint on celestial objects by using a generic framework to solve the Tolman-Oppenheimer-Volkoff (TOV) equations for up to two fluids. We test the impact of populations of new particles on celestial objects, including the sensitivity to self-interaction sizes, new particle mass, and net population mass. Applying our setup to neutron stars and boson stars, we find rich phenomenology for a range of these parameters, including the creation of extended atmospheres. These atmospheres are detectable by their impact on the tidal love number, which can be measured at upcoming gravitational wave experiments such as Advanced LIGO, the Einstein Telescope, and LISA. We release our calculation framework as a publicly available code at this URL, allowing the TOV equations to be generically solved for arbitrary new physics models in novel and admixed celestial objects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Ladder symmetries of black holes. Implications for love numbers and no-hair theorems

It is well known that asymptotically flat black holes in general relativity have a vanishing static, conservative tidal response. Here, we show that this is a result of linearly realized symmetries governing static (spin 0,1,2) perturbations around black holes. The symmetries have a geometric origin: in the scalar case, they arise from the (E)AdS isometries of a dimensionally reduced black hole spacetime. Underlying the symmetries is a ladder structure which can be used to construct the full tower of solutions, and derive their general properties: (1) solutions that decay with radius spontaneously break the symmetries, and must diverge at the horizon; (2) solutions regular at the horizon respect the symmetries, and take the form of a finite polynomial that grows with radius. Taken together, these two properties imply that static response coefficients — and in particular Love numbers — vanish. Moreover, property (1) is consistent with the absence of black holes with linear (perturbative) hair. We also discuss the manifestation of these symmetries in the effective point particle description of a black hole, showing explicitly that for scalar probes the worldline couplings associated with a non-trivial tidal response and scalar hair must vanish in order for the symmetries to be preserved.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Supergravity black holes, Love numbers, and harmonic coordinates

A problem which has now come to a head in general relativity, primarily as a result of the many recent detections of gravitational waves from the coalescence of compact binaries, is that there are very few viable theories against which to “test” it. To perform realistic tests of theories of gravity, we need to be able to look beyond general relativity and evaluate the consistency of a parametrized, physically acceptable, family of black hole metric alternatives with observational data from, especially, gravitational wave detections using, for example, an agnostic Bayesian approach. In this paper we further examine properties of one class of such metrics, which in fact arise as solutions of ungauged supergravity. In particular, we examine the massless, neutral, minimally coupled scalar wave equation in a general stationary, axisymmetric background metric such as that of a charged rotating black hole, when the scalar field is either time independent or in the low-frequency, near-zone limit, with a view to calculating the Love numbers of tidal perturbations, and of obtaining harmonic coordinates for the background metric. For a four-parameter family of charged asymptotically flat rotating black hole solutions of ungauged supergravity theory known as STU black holes, which includes Kaluza-Klein black holes and the Kerr-Sen black hole as special cases, we find that all time-independent solutions, and hence the harmonic coordinates of the metrics, are identical to those of the Kerr solution. In the low-frequency limit we find the scalar fields exhibit the same SL(2,R) symmetry as holds in the case of the Kerr solution. We point out extensions of our results to a wider class of metrics, which includes solutions of Einstein-Maxwell-dilaton theory.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1996

Venusian k(sub 2) Tidal Love Number from Magellan and PVO Tracking Data

The k(sub 2) potential ove number which scales the tidal deformation of Venus by the Sun has been estimated from Doppler tracking of Magellan and Pioneer Venus Orbiter (PVO) spacecraft data. The nominal range for k(sub 2) from theoretical models is 0.23(less than or equal to)k(sub 2)(less than or equal to)0.29 for a liquid iron core and about 0.17 if the iron core has solidified. Our best estimate of this parameter is k(sub 2) = 0.295 +/- 0.662 (2X formal {delta}) and supports the hypothesis that Venus core is solid.

orbiter pvo↗
DOE OSTI2021

High-Order Multipole and Binary Love Number Universal Relations

Using a data set of approximately 2 million phenomenological equations of state consistent with observational constraints, we construct new equation-of-state-insensitive universal relations that exist between the multipolar tidal deformability parameters of neutron stars, Λ l , for several high-order multipoles (l = 5,6,7,8), and we consider finite-size effects of these high-order multipoles in waveform modeling. We also confirm the existence of a universal relation between the radius of the 1.4M ⊙ NS, R 1.4 and the reduced tidal parameter of the binary, Λ˜, and the chirp mass. We extend this relation to a large number of chirp masses and to the radii of isolated NSs of different mass M, R M . We find that there is an optimal value of M for every M such that the uncertainty in the estimate of R M is minimized when using the relation. We discuss the utility and implications of these relations for the upcoming LIGO O4 run and third-generation detectors.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Constraints on short-term mantle rheology from the J2 observation and the dispersion of the 18.6 y tidal Love number

Information derived from data recently acquired from the LAGEOS satellite is used to place some constraints on the rheological parameters of short-term mantle rheology. The validity of Lambeck and Nakiboglu's (1983) rheological model is assessed by formally developing an expression for the transformed shear modulus using a truncated retardation spectrum. This analytical formula is used to show that the parameters of the above mentioned model are not consistent at all with the amount of anelastic dispersion expected in the Chandler wobble and with the attenuation of seismic normal modes. The feasibility of a standard linear solid (SLS) rheology operating over intermediate timescales between 1 and 100 yr is investigated to determine whether the tidal dispersion at 18.6 yr can be explained by this model. An attempt is made to place some constraints on the parameters of the SLS model and the nature of short-term mantle rheology for timescales of less than 100 yr is discussed.

Sabadini, R.↗
NASA NTRS1972

On the determination of the long period tidal perturbations in the elements of artificial earth satellites

The magnitude of the tidal effects depends upon the elastic properties of the earth as described by Love numbers. The Love numbers appear as the coefficients in the expansion of the exterior tidal potential in terms of spherical harmonics (in Maxwellian form). A single averaging process was performed only along the parallels of latitude. This process preserves additional long period tidal effects (with periods of a few days or more). It also eliminates the short period effects with periods of one day or less.

Musen, P.↗