Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, we expect its introduction to simplify the often highly technical analytical exploration of nonlinear gravitational dynamics.
We consider the quantum dynamics of a harmonic oscillator in noncommutative space under the influence of linearized gravitational waves (GW) in the long wave-length and low-velocity limit. Following the prescription in \cite{ncgw1} we quantize the system. The Hamiltonian of the system is solved by using standard algebraic iterative methods. The solution shows signatures of the coordinate noncommutativity via alterations in the oscillation frequency of the harmonic oscillator system from its commutative counterpart. Moreover, it is found that the response of the harmonic oscillator to periodic …
We present a quantum harmonic oscillator model of a collapsed star trapped in the potential well of its gravitational field. The model incorporates quantum matter (quantum fields) as a source to classical gravitational field. We describe the gravitationally collapsed star as a quantum harmonic oscillator in an analogy with an electron trapped in a potential well. The subtle point we raise in this paper is whether a standard black hole scenario is a correct description for a gravitational collapse in a semi-classical framework.
The "Bargmann framework" allows us to prove the equivalence of the Pais-Uhlenbeck oscillator with a spin-zero particle in a circularly polarized periodic gravitational wave. Pushing forward the symmetries (which include Carroll symmetry) of the latter, we derive conserved charges for the Pais-Uhlenbeck oscillator.
It is shown that the rate of corrections to the hydrogen atom and harmonic oscillator due to profound quantum-gravitational effect of space-time dimension running/reduction coincides well with those obtained by means of the minimum-length deformed quantum mechanics. The rate of corrections are pretty much the same within the accuracy by which we can judge the quantum-gravitational corrections at all. Such a convergence of results makes the concept of space-time dimension running more appreciable. As a remarkable distinction, the energy shift due to dimension reduction has the opposite sign as …
Newton's gravitational constant G, which determines the strength of gravitational interactions both in Newton's theory and in Einstein's General Relativity, is the least well known of all the fundamental constants. Given its importance, and with recent disparities between experimental measurements, a new approach is suggested. It is based on a purely gravitational oscillator without any non-gravitational restoring forces. The suggested technique is based on the oscillation period of a test mass oscillating through a hole bored in a solid sphere in free space, or, equivalently, in orbit. The pe…
In this paper, we derive the master equations for gravitational perturbations of vector and scalar type for static vacuum Lovelock black holes. Together with our previous work on the tensor type perturbation, we now provide the full set of master equations that governs all types of gravitational perturbations of static vacuum Lovelock black holes in any dimensions.
Gravitational perturbations of anti-deSitter spacetime play important roles in AdS/CFT correspondence and the brane world scenario. In this paper, we develop a gauge-invariant formalism of gravitational perturbations of maximally symmetric spacetimes including anti-deSitter spacetime. Existence of scalar-type master variables is shown and the corresponding master equations are derived.
A longstanding conjecture by Belinskii, Khalatnikov, and Lifshitz that the singularity in generic gravitational collapse is spacelike, local, and oscillatory is explored analytically and numerically in spatially inhomogeneous cosmological spacetimes. With a convenient choice of variables, it can be seen analytically how nonlinear terms in Einstein's equations control the approach to the singularity and cause oscillatory behavior. The analytic picture requires the drastic assumption that each spatial point evolves toward the singularity as an independent spatially homogeneous universe. In every…
This paper studies the perturbations of the continuously self-similar critical solution of the gravitational collapse of a massless scalar field (Roberts solution). The perturbation equations are derived and solved exactly. The perturbation spectrum is found to be not discrete, but occupying continuous region of the complex plane. The renormalization group calculation gives the value of the mass-scaling exponent equal to 1.
The general theory of time-dependent frequency and time-dependent mass ('effective mass') is described.The general theory for time-dependent harmonic- oscillator is applied in the present research for studying certain quantum effects in the interferometers for detecting gravitational waves.When an astronomical binary system approaches its point of coalescence the gravitational wave intensity and frequency are increasing and this can lead to strong deviations from the simple description of harmonic-oscillations for the interferometric masses on which the mirrors are placed.It is shown that unde…
We present a detailed analysis of the orbital stability of the Pais-Uhlenbeck oscillator, using Lie-Deprit series and Hamiltonian normal form theories. In particular, we explicitly describe the reduced phase space for this Hamiltonian system and give a proof for the existence of stable orbits for a certain class of self-interaction, found numerically in previous works, by using singular symplectic reduction.
This article presents the calculation of gravitational and electromagnetic radiation emitted from a classical simple harmonic oscillator (SHO). Here we show only the selected formulae and apply them to a toy problem without rigorous derivation. First, we calculate the explicit expressions for the gravitational waves polarizations and then obtain the power radiated away in gravitational waves using Brans-Dicke theory (BD). We also calculate the electromagnetic dipole and quadrupole power emitted by the SHO and compare them with their gravitational counterparts.
A thought experiment is proposed to demonstrate the existence of a gravitational, vector Aharonov-Bohm effect. A connection is made between the gravitational, vector Aharonov-Bohm effect and the principle of local gauge invariance for nonrelativistic quantum matter interacting with weak gravitational fields. The compensating vector fields that are necessitated by this local gauge principle are shown to be incorporated by the DeWitt minimal coupling rule. The nonrelativistic Hamiltonian for weak, time-independent fields interacting with quantum matter is then extended to time-dependent fields, …
In this paper, we construct corrections to the raising and lowering (i.e. ladder) operators for a quantum harmonic oscillator subjected to a polynomial type perturbation of any degree and to any order in perturbation theory. We apply our formalism to a couple of examples, namely q and p 4 perturbations, and obtain the explicit form of those operators. We also compute the expectation values of position and momentum for the above perturbations. This construction is essential for defining coherent and squeezed states for the perturbed oscillator. Furthermore, this is the first time that correctio…
We calculate the quasinormal modes (QNMs) for gravitational perturbations of the Schwarzschild black hole in the five dimensional (5D) spacetime with a continued fraction method. For all the types of perturbations (scalar-gravitational, vector-gravitational, and tensor-gravitational perturbations), the QNMs associated with l=2, l=3, and l=4 are calculated. Our numerical results are summarized as follows: (i) The three types of gravitational perturbations associated with the same angular quantum number l have a different set of the quasinormal (QN) frequencies; (ii) There is no purely imaginary…
It is noted that the Niederer transformation can be used to find the explicit relation between time-dependent linear oscillators, including the most interesting case when one of them is harmonic. A geometric interpretation of this correspondence is provided by certain subclasses of pp-waves; in particular the ones strictly related to the proper conformal transformations. This observation allows us to show that the pulses of plane gravitational wave exhibiting the maximal conformal symmetry are analytically solvable. Particularly interesting is the circularly polarized family for which some asp…
Dynamics of small-amplitude perturbations in the global anti-de Sitter (AdS) spacetime is restricted by selection rules that forbid effective energy transfer between certain sets of normal modes. The selection rules arise algebraically because some integrals of products of AdS mode functions vanish. Here, we reveal the relation of these selection rules to AdS isometries. The formulation we discover through this systematic approach is both simpler and stronger than what has been reported previously. In addition to the selection rule considerations, we develop a number of useful representations …
Light undergoes perturbation as gravitational waves pass by. This is shown by solving Maxwell's equations in a spacetime with gravitational waves; a solution exhibits a perturbation due to gravitational waves. We determine the perturbation for a general case of both light and gravitational waves propagating in arbitrary directions. It is also shown that a perturbation of light due to gravitational waves leads to a delay of the photon transit time, which implies an equivalence between the perturbation analysis of Maxwell's equations and the null geodesic analysis for photon propagation. We pres…
In this paper, we study the perturbation problem of the scalar, electromagnetic, and gravitational waves under the traversable Lorentzian wormhole geometry. The unified form of the potential for the Schrödinger type one-dimensional wave equation is found.
We investigate the dynamics of two quantum mechanical oscillator system-bath toy models obtained by truncating to zero spatial dimensions linearized gravity coupled to a massive scalar field and scalar QED. The scalar-gravity toy model maps onto the phase damped oscillator, while the scalar QED toy model approximately maps onto an oscillator system subject to two-photon damping. The toy models provide potentially useful insights into solving for open system quantum dynamics relevant to the full scalar QED and weak gravitational field systems, in particular operational probes of the decoherence…
We present a hydrodynamic model that describes excitation of linear stellar oscillations by a stochastic background of gravitational waves (SBGW) of astrophysical and cosmological origin. We find that this excitation mechanism is capable of generating solar g-mode amplitudes close to or comparable with values expected from excitation by turbulent convection, which is considered to be the main driving force for solar-like oscillations. A method is presented that places direct upper bounds on the SBGW in a frequency range, in which the SBGW is expected to contain rich astrophysical information. …
A simplified form of a nonsymmetric metric is used to develop the coupling of the electrostatic and gravitational fields, which only occurs in dynamic solutions. The coupling results in a resonance in an object near the Schwarzschild radius. The resonator is unique in that the frequency decreases with radius, reaching a lower limit near 0.4 Hz at the gravitational limit. The limiting frequency does not depend on the mass or any other parameter. It is a constant of physics. Gravitational contraction supplies energy to the resonator, causing it to break into oscillation. The solution is in reaso…
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in 3 + 1 dimensions on which our study is focused) scalar wave equations, and then we show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known. These results show that the concept of polarization of a grav…
In this paper, the quasinormal modes of gravitational perturbation around some well-known regular black holes were evaluated by using the WKB approximation as well as the asymptotic iteration method. Through numerical calculation, we make a detailed analysis of the gravitational QNM frequencies by varying the characteristic parameters of the gravitational perturbation and the spacetime charge parameters of the regular black holes. It is found that the imaginary part of quasinormal modes as a function of the charge parameter has different monotonic behaviors for different black hole spacetimes.…
Some previously published expressions for the perturbation of light by gravitational waves exhibit pathological behaviour in the limit of parallel propagation. We show that this is caused by similarly pathological initial or boundary data and can thus be remedied by implementing better-behaved initial conditions.
We consider the late-time evolution of {\it gravitational} and electromagnetic perturbations in realistic {\it rotating} Kerr spacetimes. We give a detailed analysis of the mode-coupling phenomena in rotating gravitational collapse. A consequence of this phenomena is that the late-time tail is dominated by modes which, in general, may have an angular distribution different from the original one. In addition, we show that different types of fields have {\it different} decaying rates. This result turns over the traditional belief (which has been widely accepted during the last three decades) tha…
We present integral estimates for the shift and induced metric in the maximal isothermal gauge, corresponding to linear axially symmetric gravitational perturbations over the Minkowski and extreme Kerr metric. These bounds are a step towards finding pointwise bounds for the perturbations. In particular the presented estimate for the shift includes the horizon for the extreme Kerr case.
In this paper, the gravitational wave generation by a slowly rotating thin-shell wormhole is considered. Since the rotating thin-shell wormhole is assumed to be an axisymmetric rigid body, the rotation axis coincides with the largest principal axis which means there is no precession motion. However, if there is a perturbation in the angular velocity, the rotating wormhole can move with precession by perturbation which make arise the gravitational waves. We derive the gravitational wave spectrum, energy loss rate, and angular momentum loss rate.
We study the stability of $D \geq 7$ asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.
The gravitational perturbation of the Morris-Thorne wormhole has been derived by using the Newman-Penrose formalism. We apply Teukolsky equation to the wormhole spacetime, compute the perturbed Weyl scalars, $Ψ_{4}^{(1)}$ and obtain its master equation, decomposed in spin weighted spherical harmonics with spin weight $-2$. For simplicity, we consider the perturbation provoked by a single gaussian pulse of pressureless dust matter.
A pair of wave equations is presented for the gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled and determines the propagation of the electromagnetic perturbation. The other is for the propagation of the shear of a principal null direction and has a source term given by the solution of the first equation. This result is expected to have important applications in astrophysical models.
We study the induced primordial gravitational waves (GW) coming from the effect of scalar perturbation on the tensor perturbation at the second order of cosmological perturbation theory. We use the evolution of the standard model degrees of freedom with respect to temperature in the early Universe to compute the induced gravitational waves bakcground. Our result shows that the spectrum of the induced GW is affected differently by the standard model degrees of freedom than the GW coming from first order tensor perturbation. This phenomenon is due to the presence of scalar perturbations as a sou…
Using second order black hole perturbation theory, we show that the difference between the ADM mass and the final black hole mass, computed to the lowest significant order, is equal, to the same order, to the total gravitational radiation energy, obtained applying the Landau and Lifschitz (pseudotensor) equation to the first order perturbation. This result may be considered as a consistency check for the theory.
The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum back-action noise. Several back-action evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homo…
Gravitational perturbations of neutron stars and black holes are well known sources of gravitational radiation. If the compact object is immersed in or endowed with a magnetic field, the gravitational perturbations would couple to electromagnetic perturbations and potentially trigger synergistic electromagnetic signatures. We present a detailed analytic calculation of the dynamics of coupled gravitational and electromagnetic perturbations for both neutron stars and black holes. We discuss the prospects for detecting the electromagnetic waves in these scenarios and the potential that these wave…
In this paper, the quasinormal modes of gravitational perturbation around a Schwarzschild black hole surrounded by quintessence were evaluated by using the third-order WKB approximation. Due to the presence of quintessence, the gravitational wave damps more slowly.
Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multidimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based…
A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as the gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in the nonlinear order. The tensor perturbations generated by the quadratic combination of linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an…
The back reaction of gravitational perturbations in a homogeneous background is determined by an effective energy-momentum tensor quadratic in the perturbations. We show that this nonlinear feedback effect is important in the case of long wavelength scalar perturbations in inflationary universe models. We also show how to solve an old problem concerning the gauge dependence of the effective energy-momentum tensor of perturbations.
Since the discovery of the large angular scale anisotropies in the microwave background radiation, the behaviour of cosmological perturbations (especially, density perturbations and gravitational waves) has been of great interest. In this study, after a detailed and rigorous treatment of the behaviour of gravitational waves in viscous cosmic media, we conclude that the damping of cosmological gravitational waves of long wavelengths is negligible for most cases of physical interest. A preliminary analysis suggests that similar results hold for density perturbations in the long wavelength limit.…
