scholarly journals Multipole expansion of gravitational waves: from harmonic to Bondi coordinates

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Luc Blanchet ◽  
Geoffrey Compère ◽  
Guillaume Faye ◽  
Roberto Oliveri ◽  
Ali Seraj
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Multipole Expansion ◽  
Multipole Moments ◽  
Exterior Region ◽  
Residual Symmetry ◽  
Mass Quadrupole ◽  
Quadratic Order

Abstract We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a functional of the mass and current multipole moments of the source, valid all-over the exterior region of the source. Imposing appropriate boundary conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual symmetry group. To quadratic order, in the case of the mass-quadrupole interaction, we determine the contributions of gravitational-wave tails in the NU metric, and prove that the expansion of the metric in terms of the radius is regular to all orders. The mass and angular momentum aspects, as well as the Bondi shear, are read off from the metric. They are given by the radiative quadrupole moment including the tail terms.

scholarly journals Radiation Driven Instability of Rapidly Rotating Relativistic Stars: Criterion and Evolution Equations Via Multipolar Expansion of Gravitational Waves

2017 ◽  
Vol 34 ◽  
Author(s):  
A. I. Chugunov
Keyword(s):  
Angular Momentum ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Evolution Equations ◽  
Leading Order ◽  
Relativistic Stars ◽  
Effective Spin ◽  
Wave Emission ◽  
Rotation Energy ◽  
Multipolar Expansion

AbstractI suggest a novel approach for deriving evolution equations for rapidly rotating relativistic stars affected by radiation-driven Chandrasekhar–Friedman–Schutz instability. This approach is based on the multipolar expansion of gravitational wave emission and appeals to the global physical properties of the star (energy, angular momentum, and thermal state), but not to canonical energy and angular momentum, which is traditional. It leads to simple derivation of the Chandrasekhar–Friedman–Schutz instability criterion for normal modes and the evolution equations for a star, affected by this instability. The approach also gives a precise form to simple explanation of the Chandrasekhar–Friedman–Schutz instability; it occurs when two conditions are met: (a) gravitational wave emission removes angular momentum from the rotating star (thus releasing the rotation energy) and (b) gravitational waves carry less energy, than the released amount of the rotation energy. To illustrate the results, I take the r-mode instability in slowly rotating Newtonian stellar models as an example. It leads to evolution equations, where the emission of gravitational waves directly affects the spin frequency, being in apparent contradiction with widely accepted equations. According to the latter, effective spin frequency decrease is coupled with dissipation of unstable mode, but not with the instability as it is. This problem is shown to be superficial, and arises as a result of specific definition of the effective spin frequency applied previously. Namely, it is shown, that if this definition is taken into account properly, the evolution equations coincide with obtained here in the leading order in mode amplitude. I also argue that the next-to-leading order terms in evolution equations were not yet derived accurately and thus it would be more self-consistent to omit them.

scholarly journals Gravitational waves from dynamical tides in white dwarf binaries

2019 ◽  
Author(s):  
L O McNeill ◽  
R A Mardling ◽  
B Müller
Keyword(s):  
Angular Momentum ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Frequency Band ◽  
White Dwarf ◽  
White Dwarfs ◽  
Momentum Exchange ◽  
Tidal Dissipation ◽  
Tidal Forcing ◽  
Tidal Torques

Abstract We study the effect of tidal forcing on gravitational wave signals from tidally relaxed white dwarf pairs in the LISA, DECIGO and BBO frequency band (0.1 − 100 mHz). We show that for stars not in hydrostatic equilibrium (in their own rotating frames), tidal forcing will result in energy and angular momentum exchange between the orbit and the stars, thereby deforming the orbit and producing gravitational wave power in harmonics not excited in perfectly circular synchronous binaries. This effect is not present in the usual orbit-averaged treatment of the equilibrium tide, and is analogous to transit timing variations in multiplanet systems. It should be present for all LISA white dwarf pairs since gravitational waves carry away angular momentum faster than tidal torques can act to synchronize the spins, and when mass transfer occurs as it does for at least eight LISA verification binaries. With the strain amplitudes of the excited harmonics depending directly on the density profiles of the stars, gravitational wave astronomy offers the possibility of studying the internal structure of white dwarfs, complimenting information obtained from asteroseismology of pulsating white dwarfs. Since the vast majority of white-dwarf pairs in this frequency band are expected to be in the quasi-circular state, we focus here on these binaries, providing general analytic expressions for the dependence of the induced eccentricity and strain amplitudes on the stellar apsidal motion constants and their radius and mass ratios. Tidal dissipation and gravitation wave damping will affect the results presented here and will be considered elsewhere.

scholarly journals Gravitational waves from mountains in newly born millisecond magnetars

2021 ◽  
Vol 502 (4) ◽  
pp. 4680-4688
Author(s):  
Ankan Sur ◽  
Brynmor Haskell
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Massive Star ◽  
Gamma Ray ◽  
Dipole Radiation ◽  
X Ray ◽  
Binary Neutron Star ◽  
Spin Period ◽  
Lower Maximum ◽  
Wave Emission

ABSTRACT In this paper, we study the spin-evolution and gravitational-wave luminosity of a newly born millisecond magnetar, formed either after the collapse of a massive star or after the merger of two neutron stars. In both cases, we consider the effect of fallback accretion; and consider the evolution of the system due to the different torques acting on the star, namely the spin-up torque due to accretion and spin-down torques due to magnetic dipole radiation, neutrino emission, and gravitational-wave emission linked to the formation of a ‘mountain’ on the accretion poles. Initially, the spin period is mostly affected by the dipole radiation, but at later times, accretion spin the star up rapidly. We find that a magnetar formed after the collapse of a massive star can accrete up to 1 M⊙, and survive on the order of 50 s before collapsing to a black hole. The gravitational-wave strain, for an object located at 1 Mpc, is hc ∼ 10−23 at kHz frequencies, making this a potential target for next-generation ground-based detectors. A magnetar formed after a binary neutron star merger, on the other hand, accretes at the most 0.2 M⊙ and emits gravitational waves with a lower maximum strain of the order of hc ∼ 10−24, but also survives for much longer times, and may possibly be associated with the X-ray plateau observed in the light curve of a number of short gamma-ray burst.

scholarly journals Gravitational wave–gauge field dynamics

2017 ◽  
Vol 26 (12) ◽  
pp. 1742005 ◽  
Author(s):  
R. R. Caldwell ◽  
C. Devulder ◽  
N. A. Maksimova
Keyword(s):  
Quantum Gravity ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Gauge Field ◽  
Linear Combination ◽  
Effective Mass ◽  
Normal Modes ◽  
New Approaches ◽  
Insight Into

The dynamics of a gravitational wave propagating through a cosmic gauge field are dramatically different than in vacuum. We show that a gravitational wave acquires an effective mass, is birefringent, and its normal modes are a linear combination of gravitational waves and gauge field excitations, leading to the phenomenon of gravitational wave–gauge field oscillations. These surprising results provide an insight into gravitational phenomena and may suggest new approaches to a theory of quantum gravity.

Tidal deformation of quantum black holes

2021 ◽  
pp. 2142011
Author(s):  
Ram Brustein ◽  
Yotam Sherf
Keyword(s):  
Black Holes ◽  
Perturbation Theory ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Excited Level ◽  
Love Number ◽  
Standard Time ◽  
Love Numbers ◽  
Classical Black Holes ◽  
Quantum Perturbation Theory

The response of a gravitating object to an external tidal field is encoded in its Love numbers, which identically vanish for classical black holes (BHs). Here we show, using standard time-independent quantum perturbation theory, that for a quantum BH, generically, the Love numbers are nonvanishing and negative. We calculate the quadrupolar electric quantum Love number of slowly rotating BHs and show that it depends most strongly on the first excited level of the quantum BH. Finally, we discuss the detectability of the quadrupolar quantum Love number in future precision gravitational-wave observations and show that, under favourable circumstances, its magnitude is large enough to imprint an observable signature on the gravitational waves emitted during the inspiral. Phase of two moderately spinning BHs.

Research on Dynamic Simulation of AUV Launching a Towed Navigation Buoyage

2013 ◽  
Vol 433-435 ◽  
pp. 1170-1174
Author(s):  
Guang Pan ◽  
Zhi Dong Yang ◽  
Xiao Xu Du
Keyword(s):  
Angular Momentum ◽  
Boundary Conditions ◽  
Dynamic Simulation ◽  
Numerical Scheme ◽  
Mathematic Model ◽  
Dynamic Equations ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
Towed Cable ◽  
Undersea Vehicle

A mathematic model was established to simulate the process of AUV (autonomous undersea vehicle) launching a towed buoyage. Based on the lumped mass method and moment theorem and angular momentum theorem, dynamic equations of the cable and the buoyage were developed, respectively. Then the boundary conditions and the numerical scheme to deal with the cable with non-fixed length were presented. Moreover, the process of AUV launching a towed cable was simulated. By using the model, the results show the trajectory of buoyage and shape of towed cable can be well predicted.

Boundary conditions for Maxwell fields in Kerr-AdS spacetimes

2016 ◽  
Vol 25 (09) ◽  
pp. 1641011 ◽  
Author(s):  
Mengjie Wang
Keyword(s):  
Black Holes ◽  
Angular Momentum ◽  
Boundary Conditions ◽  
Energy Flux ◽  
Momentum Flux ◽  
De Sitter ◽  
Perturbative Methods ◽  
Flux Boundary Conditions ◽  
Maxwell Fields ◽  
New Type

Perturbative methods are useful to study the interaction between black holes and test fields. The equation for a perturbation itself, however, is not complete to study such a composed system if we do not assign physically relevant boundary conditions. Recently we have proposed a new type of boundary conditions for Maxwell fields in Kerr-anti-de Sitter (Kerr-AdS) spacetimes, from the viewpoint that the AdS boundary may be regarded as a perfectly reflecting mirror, in the sense that energy flux vanishes asymptotically. In this paper, we prove explicitly that a vanishing energy flux leads to a vanishing angular momentum flux. Thus, these boundary conditions may be dubbed as vanishing flux boundary conditions.

scholarly journals An Analysis of Gravitational waves

2021 ◽  
Author(s):  
Vaibhav Kalvakota
Keyword(s):  
Gravitational Wave ◽  
Gravitational Waves ◽  
Mathematical Structure ◽  
Gauge Condition ◽  
Field Tensor ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Minkowski Metric ◽  
Wave Detector ◽  
The Masses

The September 14, 2015 gravitational wave observations showed the inspiral of two black holes observed from Hanford and Livingston LIGO observatories. This detection was significant for two reasons: firstly, it coupled the result and avoided the possibility of a false alarm by 5σ , meaning that the detected “noise” was indeed from an astronomical source of gravitational waves. We will discuss the primary landscape of gravitational waves, their mathematical structure and how they can be used to predict the masses of the merger system. We will also discuss gravitational wave detector optimisations, and then we will consider the results from the detected merger GW150914. We will consider a straight-forward mathematical approach, and we will primarily be interested in the mathematical modelling of gravitational waves from General Relativity (Section 1). We will first consider a “perturbed” Minkowski metric, and then we will discuss the properties of the perturbation addition tensor. We will then discuss on the gravitational field tensor, and how it arises from the perturbation tensor. We will then talk about the gauge condition, essentially the gauge “freedom” , and then we will talk about the curvature tensor, leading eventually to the effect of gravitational waves on a ring of particles. We will consider the polarisation tensor, which maps the amplitude and polarisation details. The polarisation splits into plus polarised and cross polarised waves, which is technically the effect of a propagating gravitational wave through a ring of particles. We will then talk about the linearized Einstein Field Equations, and how the physical system of merger is encoded into the mathematical structural unity of the metric. We will then talk about the detection of these gravitational waves and how the detector can be optimised, or how the detector can be set so that any “noise” detected can fall in the error margins, and how the detector can prevent the interferometric “photon-noise” from being detected (Section 2.2). Then, we will discuss data results from the source GW150914 detection by LIGO (Section 3).

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