Nonminimal spin-gravity interaction through unit gravimagnetic moment leads to modified Mathisson-Papapetrou-Tulczyjew-Dixon equations with improved behavior in the ultrarelativistic limit. We present exact Hamiltonian of the resulting theory and compute an effective $\frac{1}{c^2}$\,-Hamiltonian and leading post-Newtonian corrections to the trajectory and spin. Gravimagnetic moment causes the same precession of spin ${\bf S}$ as a fictitious rotation of the central body with angular momentum ${\bf J}=\frac{M}{m}{\bf S}$. So the modified equations imply a number of qualitatively new effects, that could be used to test experimentally, whether a rotating body in general relativity has null or unit gravimagnetic moment.
We compute exact Hamiltonian (and corresponding Dirac brackets) for spinning particle with gravimagnetic moment $κ$ in an arbitrary gravitational background. $κ=0$ corresponds to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations. $κ=1$ leads to modified MPTD equations with reasonable behavior in the ultrarelativistic limit. So we study the modified equations in the leading post-Newtonian approximation. Rotating body with unit gravimagnetic moment has qualitatively different behavior as compared with MPTD body: A) If a number of gyroscopes with various rotation axes are freely traveling…
We review the recent results on development of vector models of spin and apply them to study the influence of spin-field interaction on the trajectory and precession of a spinning particle in external gravitational and electromagnetic fields. The formalism is developed starting from the Lagrangian variational problem, which implies both equations of motion and constraints which should be presented in a model of spinning particle. We present a detailed analysis of the resulting theory and show that it has reasonable properties on both classical and quantum level. We describe a number of applica…
In this paper, we first investigate some aspects of frame dragging in strong gravity. The computations are carried out for the Kerr black hole and for the rotating Janis-Newman-Winicour solution, that is known to have a naked singularity on a surface at a finite radius. For the Kerr metric, a few interesting possibilities of gyroscope precession frequency, as measured by a Copernican observer outside the ergoregion, are pointed out. It is shown that for certain angular velocities of a stationary observer, this frequency might vanish exactly, close to the ergoregion. Similar computations are re…
In the present paper, we have considered the three parameters: mass, charge and rotation to discuss their combined effect on frame dragging for a charged rotating body. If we consider the ray of light which is emitted radially outward from a rotating body then the frame dragging shows a periodic nature with respect to coordinate $ϕ$ (azimuthal angle). It has been found that the value of frame dragging obtains a maximum at, $ ϕ=\fracπ{2}$ and a minimum at $ ϕ=\frac{3 π}{2}$.
We consider stationary, axially symmetric toroids rotating around spinless black holes, assuming the general-relativistic Keplerian rotation law, in the first post-Newtonian approximation. Numerical investigation shows that the angular momentum accumulates almost exclusively within toroids. It appears that various types of dragging (anti-dragging) effects are positively correlated with the ratio $M_\mathrm{D}/m$ ($M_\mathrm{D}$ is the mass of a toroid and $m$ is the mass of the black hole) - moreover, their maxima are proportional to $M_\mathrm{D}/m$. The horizontal sizes of investigated toroi…
In this paper, we review and analyze four specific general-relativistic problems in which gravitomagnetism plays an important role: the dragging of magnetic fields around rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, compared with the dragging by rotating gravitational waves. We demonstrate how the quantum detection of inertial frame dragging can be accomplished by using the Unruh-DeWitt detectors. Finally, we shall briefly show how ``instantaneous Machian gauges'' can be useful in the cosmological perturbation theory.
Magnetars are highly magnetized neutron stars. For a slowly rotating magnetar, the strong magnetic field deforms the star, making it axisymmetric with respect to the magnetic axis (the body symmetry axis). In magnetars, the rotation axis is tilted to the magnetic axis, and we have an oblique rotator. General relativistic treatment of the obliquely rotating magnetar gives rise to frame-dragging velocities both in the azimuthal and polar direction. Solving the Einstein equation up to first-order perturbation in rotation and second-order perturbation in the magnetic field, we calculate the geodes…
We compute the equation of state for an ensemble of degenerate fermions by using the curved spacetime of a slowly rotating axially symmetric star. We show that the equation of state computed in such curved spacetime depends on the gravitational time dilation as well as on the dragging of inertial frames, unlike an equation of state computed in a globally flat spacetime. The effect of gravitational time dilation leads to a significant enhancement of the maximum mass limit of a degenerate neutron star. However, such an enhancement due to the frame-dragging effect is extremely small. Nevertheless…
马赫原理和相对性原理已由H. I. Hartman和C. Nissim-Sabat在这篇文章中。据说有几种现象违反了应用于旋转运动的相对性原理。这些说法最近受到质疑。然而，在这两篇文章中，都没有援引惯性拖曳的广义相对论现象，双方也没有提供任何计算来证实他们的说法。在这里，我讨论了相对性原理在广义相对论的范围内对旋转运动的可能有效性，并指出惯性拖曳在这方面的意义。虽然我的主要观点是定性的，但我也提供了必要的计算来证明这些观点是如何作为广义相对论的结果出现的。
A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton's theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by mass-energy currents. These effects have recently been confirmed by classical observations. Here we show, for the first time, that they can be observed by a quantum detector. We study the response function of Unruh De-Witt detectors placed in a slowly rotating shell. We show that the response function picks up the presence of rotation even though the spacetime insi…
We use the vector model of spinning particle to analyze the influence of spin-field coupling on the particle's trajectory in ultra-relativistic regime. The Lagrangian with minimal spin-gravity interaction yields the equations equivalent to the Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations of a rotating body. We show that they have unsatisfactory behavior in the ultra-relativistic limit. In particular, three-dimensional acceleration of the particle increases with velocity and becomes infinite in the ultra-relativistic limit. The reason is that in the equation for trajectory emerges the …
Kochi University（高知大学）；Indian Institute of Science（印度科学学院）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所交叉理论数学科学中心（iTHEMS））；University of Tübingen（蒂宾根大学）
Radio pulsars in short-period eccentric binary orbits can be used to study both gravitational dynamics and binary evolution. The binary system containing PSR J1141$-$6545 includes a massive white dwarf (WD) companion that formed before the gravitationally bound young radio pulsar. We observe a temporal evolution of the orbital inclination of this pulsar that we infer is caused by a combination of a Newtonian quadrupole moment and Lense-Thirring precession of the orbit resulting from rapid rotation of the WD. Lense-Thirring precession, an effect of relativistic frame-dragging, is a prediction o…
Originally introduced in connection with general relativistic Coriolis forces, the term $\textit{frame-dragging}$ is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two a…
We report an incipient exploration of the Lense-Thirring precession effect in a rotating \textit{acoustic analogue black hole} spacetime. An exact formula is deduced for the precession frequency of a gyroscope due to inertial frame dragging, close to the ergosphere of a `Draining Bathtub' acoustic spacetime which has been studied extensively for acoustic Hawking radiation of phonons and also for `superresonance'. The formula is verified by embedding the two dimensional spatial (acoustic) geometry into a three dimensional one where the similarity with standard Lense-Thirring precession results …
Objects orbiting in the presence of a rotating massive body experience a gravitomagnetic frame-dragging effect, known as the Lense-Thirring effect, that has been experimentally confirmed in the weak-field limit. In the strong-field limit, near the horizon of a rotating black hole, frame dragging becomes so extreme that all objects must co-rotate with the black hole's angular momentum. In this work, we perform general relativistic numerical simulations to identify observable signatures of frame dragging in the strong-field limit that appear when infalling gas is forced to flip its direction of …
We study analytically the asymptotic late-time evolution of realistic rotating collapse. This is done by considering the asymptotic late-time solutions of Teukolsky's master equation, which governs the evolution of gravitational, electromagnetic, neutrino and scalar perturbations fields on Kerr spacetimes. In accordance with the no-hair conjecture for rotating black-holes we show that the asymptotic solutions develop inverse power-law tails at the asymptotic regions of timelike infinity, null infinity and along the black-hole outer horizon (where the power-law behaviour is multiplied by an osc…
In this work, we elaborate on the development of a general relativistic formalism that allows one to analytically express the mass and spin parameters of the Kerr black hole in terms of observational data: the total redshift and blueshift of photons emitted by geodesic massive particles revolving the black hole and their orbital parameters. Thus, we present concise closed formulas for the mass and spin parameters of the Kerr black hole in terms of few directly observed quantities in the case of equatorial circular orbits either when the black hole is static or is moving with respect to a dista…
We show that a primeval seed magnetic field arises due to spin-degeneracy breaking of fermions caused by the dragging of inertial frames in the curved spacetime of rotating astrophysical bodies. This seed magnetic field would arise even due to electrically neutral fermions such as neutrons. As an example, we show that an ideal neutron star rotating at $500$ revolutions per second, having mass $0.83$ M$_{\odot}$ and described by an ensemble of degenerate neutrons, would have $0.12$ Gauss seed magnetic field at its center arising through the breaking of spin-degeneracy.
The existence of quintessential dark energy around a black hole has considerable consequences on its spacetime geometry. Hence, in this article, we explore its effect on horizons and the silhouette generated by a Kerr-Newman black hole in quintessential dark energy. Moreover, to analyze the deflection angle of light, we utilize the Gauss-Bonnet theorem. The obtained result demonstrates that, due to the dragging effect, the black hole spin elongates its shadow in the direction of the rotational axis, while increases the deflection angle. On the other hand, the black hole charge diminishing its …
In axistationary asymptotically flat spacetimes zero angular momentum observers (ZAMOs) define an absolute standard of non--rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein's equations for an approximate thin shell model where we keep a degree of freedom by relaxing the natural assumption of vanishing rotation at asymptotic infinity at the outset of the analysis. The solution reveals tha…
We investigate the Hong-Ou-Mandel (HOM) effect $-$ a two-photon quantum-interference effect $-$ in the space-time of a rotating spherical mass. In particular, we analyze a common-path HOM setup restricted to the surface of the earth and show that, in principle, general-relativistic frame-dragging induces observable shifts in the HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time-dilation effects in HOM interference, for a dual-arm configuration. The formalism thus presented establishes a basis for encoding general-relativis…
We comment on a recent study reporting evidence for the general relativistic Lense-Thirring secular precession of the inclination $I$ of the orbital plane to the plane of the sky of the tight binary system PSR J1141-6545 made of a white dwarf and an emitting radiopulsar of comparable masses. The quadrupole mass moment $Q_2^\mathrm{c}$ and the angular momentum ${\boldsymbol S}^\mathrm{c}$ of the white dwarf cause the detectable effects on $I$ with respect to the present-day accuracy in the pulsar's timing. The history-dependent and model-dependent assumptions to be made on $Q_2^\mathrm{c}$ and …
