Frame-dragging Research Articles

Mesoscopic interference for metric and curvature & gravitational wave detection

A compact detector for space-time metric and curvature is highly desirable. Here we show that quantum spatial superpositions of mesoscopic objects could be exploited to create such a detector. We propose a specific form for such a detector and analyse how asymmetries in its design allow it to directly couple to the curvature. Moreover, we also find that its non-symmetric construction and the large mass of the interfered objects, enable the detection gravitational waves (GWs). Finally, we discuss how the construction of such a detector is in principle possible with a combination of state of the art techniques while taking into account the known sources of decoherence and noise. To this end, we use Stern–Gerlach interferometry with masses ∼10−17 kg, where the interferometric signal is extracted by measuring spins and show that accelerations as low as 5 × 10−15 ms−2 Hz−1/2, as well as the frame dragging effects caused by the Earth, could be sensed. The GW sensitivity scales differently from the stray acceleration sensitivity, a unique feature of the proposed interferometer. We identify mitigation mechanisms for the known sources of noise, namely gravity gradient noise, uncertainty principle and electro-magnetic forces and show that it could potentially lead to a metre sized, orientable and vibrational noise (thermal/seismic) resilient detector of mid (ground based) and low (space based) frequency GWs from massive binaries (the predicted regimes are similar to those targeted by atom interferometers and LISA).

Gravitational fields of the magnetic-type

Local conformal symmetry introduces the conformal curvature (Weyl tensor) that gets split into its (gravito-) electric and magnetic (tensor) parts. Newtonian tidal forces are expected from the gravitoelectric field, whereas general-relativistic frame-dragging effects emerge from the gravitomagnetic field. The symmetric, traceless gravitoelectric and gravitomagnetic tensor fields can be visualized by their eigenvectors and eigenvalues. In this paper, we depict the gravitoelectric and gravitomagnetic fields around a slowly rotating black hole. This suggests that the phenomenon of ultra-fast outflows observed at the centers of active galaxies may give evidence for the gravitomagnetic fields of spinning supermassive black holes. We also question whether the current issues in our contemporary observations might be resolved by the inclusion of gravitomagnetism on large scales in a perturbed FLRW model.

EFEK SERETAN KERANGKA INERSIAL DI DALAM MEDAN BINTANG NEUTRON YANG BEROTASI DAN STASIONER

The inertial frame dragging effect of rotating neutron star has been studied. Inertial frame dragging effect, also well known as Lense Thirring effect, has been predicted using general theory of relativity in 1918. When the neutron star rotates very quickly, the space time around it will be dragged to the direction of the rotation. The Lense Thirring effect is small enough for small objects so it will be clearly seen for massive objects like compact stars, especially neutron star. Later, we derive the equation of frame dragging rate () inside the rotating neutron star, which is axisymmetrik and stationary. Frame dragging rate is decreasing from the center to the surface of stars. It is also noted that is proportional to the angular velocity of star.

Weak-lensing observables in relativistic N-body simulations

ABSTRACT We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first order in the vector part, frame dragging. Integrating the photon geodesics backwards from the observer to the emitters, we solve the Sachs optical equations and study in detail the weak-lensing convergence, ellipticity and rotation. For the first time, we apply such an analysis to a high-resolution relativistic N-body simulation, which consistently includes the leading-order corrections due to general relativity on both large and small scales. These are related to the question of gauge choice and to post-Newtonian corrections, respectively. We present the angular power spectra and one-point probability distribution functions for the weak-lensing variables, which we find are broadly in agreement with comparable Newtonian simulations. Our geometric approach, however, is more robust and flexible, and can therefore be applied consistently to non-standard cosmologies and modified theories of gravity.

Dragging of inertial frames in the composed black-hole-particle system and the weak cosmic censorship conjecture

We analyze a gedanken experiment in which a spinning particle that also possesses an extrinsic orbital angular momentum is captured by a spinning Kerr black hole. The gravitational spin-orbit interaction decreases the energy of the particle, thus allowing one to test the validity of the Penrose weak cosmic censorship conjecture in extreme situations that have not been analyzed thus far. It is explicitly shown that, to leading order in the black-hole-particle interactions, the linearized test particle can over-spin the black hole, thus exposing its inner spacetime singularity to external observers. However, we prove that the general relativistic effect of dragging of inertial frames by the orbiting particle contributes to the energy budget of the system a non-linear black-hole-particle interaction term that ultimately ensures the validity of the Penrose cosmic censorship conjecture in this type of gedanken experiments.

Observational appearance of rapidly rotating neutron stars

Neutron stars (NSs) in low-mass X-ray binaries rotate at frequencies high enough to significantly deviate from sphericity (ν*∼ 200–600 Hz). First, we investigate the effects of rapid rotation on the observational appearance of a NS. We propose analytical formulae relating gravitational mass and equatorial radius of the rapidly rotating NS to the massMand radiusRof a non-rotating NS of the same baryonic mass using accurate fully relativistic computations. We assume that the NS surface emission is described by the Planck function with two different emission patterns: the isotropic intensity and that corresponding to the electron-scattering dominated atmosphere. For these two cases we compute spectra from an oblate rotating NS observed at different inclination angles using the modified oblate Schwarzschild approximation, where light bending is computed in Schwarzschild metric, but frame dragging and quadrupole moment of a NS are approximately accounted for in the photon redshift calculations. In particular, we determine the solid angle at which a rotating NS is seen by a distant observer, the observed colour temperature and the blackbody normalization. Then, we investigate how rapid rotation affects the results of NS radius determination using the cooling tail method applied to the X-ray burst spectral evolution. We approximate the local spectra from the NS surface by a diluted blackbody with the luminosity-dependent dilution factor using previously computed NS atmosphere models. We then generalize the cooling tail method to the case of a rapidly rotating NS to obtain the most probable values ofMandRof the corresponding non-rotating NS with the same baryonic mass. We show that the NS radius could be overestimated by 3–3.5 km for face-on stars ofR ≈ 11 km rotating atν*= 700 Hz if the version of the cooling tail method for a non-rotating NS is used. We apply the method to an X-ray burst observed from the NS rotating atν* ≈ 532 Hz in SAX J1810.8−2609. The resulting radius of the non-rotating NS (assumingM = 1.5M⊙) becomes 11.8 ± 0.5 km if it is viewed at inclinationi = 60° andR = 11.2 ± 0.5 km for a face-on view, which are smaller by 0.6 and 1.2 km than the radius obtained using standard cooling tail method ignoring rotation. The corresponding equatorial radii of these rapidly rotating NSs are 12.3 ± 0.6 km (fori = 60°) and 11.6 ± 0.6 km (fori = 0°).

The Bardeen–Petterson effect in accreting supermassive black hole binaries: a systematic approach

ABSTRACT Disc-driven migration is a key evolutionary stage of supermassive black hole binaries hosted in gas-rich galaxies. Besides promoting the inspiral, viscous interactions tend to align the spins of the black holes with the orbital angular momentum of the disc. We present a critical and systematic investigation of this problem, also known as the Bardeen–Petterson effect. We design a new iterative scheme to solve the non-linear dynamics of warped accretion discs under the influence of both relativistic frame dragging and binary companion. We characterize the impact of the disc ‘critical obliquity’, which marks regions of the parameter space where stationary solutions do not exist. We find that black hole spins reach either complete alignment or a critical configuration. Reaching the critical obliquity might imply that the disc breaks as observed in hydrodynamical simulations. Our findings are important to predict the spin configurations with which supermassive black hole binaries enter their gravitational-wave driven regime and become detectable by LISA.

General relativistic manifestations of orbital angular and intrinsic hyperbolic momentum in electromagnetic radiation

General relativistic effects in the weak field approximation are calculated for electromagnetic Laguerre–Gaussian beams. The current work is an extension of previous work on the precession of a spinning neutral particle in the weak gravitational field of an optical vortex. In the current work, the metric perturbation is extended to all coordinate configurations and includes gravitational effects from circular polarization and intrinsic hyperbolic momentum. The final metric reveals frame-dragging effects due to intrinsic spin angular momentum (SAM), orbital angular momentum (OAM), and spin–orbit coupling. When investigating the acceleration of test particles in this metric, an unreported gravitational phenomenon was found. This effect is analogous to the motion of charged particles in the magnetic field produced by a current-carrying wire. It was found that the gravitational influence of SAM and OAM affects test-rays traveling perpendicular to the intense beam and from this a gravitational Aharonov–Bohm analog is pursued.

Times of arrival (TOA) of signals in the Kerr-MOG black hole

Modified gravity (MOG) theories are alternatives to general relativity (GR) that arose primarily from the need to explain the observed galactic flat rotation curves without invoking the elusive dark matter hypothesized by GR. A well known MOG is the Scalar–Tensor–Vector–Gravity developed by Moffat, who has also found a spinning solution called the Kerr-MOG black hole (BH) characterized by the spin a and MOG parameter $$\alpha $$, the latter determining the strength of the gravitational vector forces. We consider the static-MOG metric ($$a=0$$) to first understand how the nature of geometry drastically changes depending on different sectors of $$\alpha $$. Then we study the influence of $$\alpha $$ in each sector on a new astrophysical diagnostic caused by frame dragging, viz., the difference $$\varDelta t$$ in the times of arrival at the observer of signals emanating from a variable pulsar (PSR) passing behind a Kerr-MOG lens in a PSR-BH binary system. The study generalizes the zeroth order Laguna–Wolszczan formula up to third PPN order in $$\left( 1/r\right) $$ using thin-lens approximation, which reveals how $$\varDelta t$$ is influenced both by a and $$\alpha $$. The magnitude and sign of $$\alpha $$ indicate deviations from GR ($$\alpha =0$$) and future measurements may constrain $$\alpha $$ provided a suitable binary is identified.

Lense-Thirring frame dragging induced by a fast-rotating white dwarf in a binary pulsar system.

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 observed 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 (LT) precession of the orbit resulting from rapid rotation of the WD. LT precession, an effect of relativistic frame dragging, is a prediction of general relativity. This detection is consistent with an evolutionary scenario in which the WD accreted matter from the pulsar progenitor, spinning up the WD to a period of <200 seconds.

Pulsar timing detects frame dragging

Gravitation Frame dragging is a predicted phenomenon in general relativity, whereby a rotating mass drags the surrounding spacetime around with it. Venkatraman Krishnan et al. analyzed timing observations of PSR J1141-6545, a young pulsar in a binary orbit with a white dwarf. Modeling the arrival times of the radio pulses showed a long-term drift in the orbital parameters. After considering possible contributions to this drift, they concluded that it is dominated by frame dragging (the Lense-Thirring effect) of the rapidly spinning white dwarf. These observations verify a prediction of general relativity and provide constraints on the evolutionary history of the binary system. Science , this issue p. [577][1] [1]: /lookup/doi/10.1126/science.aax7007

The Polarization of X-Rays from Warped Black Hole Accretion Disks

Abstract It is commonly assumed that in black hole (BH) accretion disks the angular momenta of the disk and the BH are aligned. However, for a significant fraction of stellar-mass BHs and supermassive BHs, the momenta may not be aligned. In such systems, the interplay of disk viscosity and general relativistic frame dragging can cause the disk to warp or break into two (or more) distinct planes; this is called the Bardeen–Petterson effect. We have developed a general relativistic ray-tracing code to find the energy spectra and polarization of warped accretion disks, accounting for the emission from the disk and for photons reflecting one or multiple times off the warped accretion disk segments. We find that polarization angle can be used to give a lower limit on the misalignment angle when a previous measurement of the jet, which is thought be aligned with the BH angular momentum, can be spatially resolved.

Landau levels in a gravitational field: the Levi-Civita and Kerr spacetimes case

We have recently found that the gravitational field of a static spherical mass removes the Landau degeneracy of the energy levels of a particle moving around the mass inside a magnetic field by splitting the energy of the Landau orbitals. In this paper we present the second part of our investigation of the effect of gravity on Landau levels. We examine the effect of the gravitational fields created by an infinitely long massive cylinder and a rotating spherical mass. In both cases, we show that the degeneracy is again removed thanks to the splitting of the particle's orbitals. The first case would constitute an experimental test - which is quantum mechanical in nature - of the gravitational field of a cylinder. The approach relies on the Newtonian approximation of the gravitational potential created by a cylinder but, in view of self-consistency and for future higher-order approximations, the formalism is based on the full Levi-Civita metric. The second case opens up the possibility for a novel quantum mechanical test of the well-known rotational frame-dragging effect of general relativity.

Spontaneous Wave Function Collapse with Frame Dragging and Induced Gravity

I impose the Newtonian criteria of inertial frames on the c.o.m.trajectories of massive objects undergoing spontaneous collapse of their wave function. The corresponding modification of the so far used stochastic Schrödinger equation eliminates the Brownian motion of the c.o.m., and restores the exact inertial motion for free masses. For the collapse of Schrödinger cat states the Born rule is satisfied invariably. The proposed machinery comes from the radical assumption that, in the vicinity of the spontaneously localized mass, the stochastic fluctuations of the c.o.m.—inevitable in the collapse process—would drag the physical inertial frame with themselves. The perspective of a general theory is presented where the spontaneous-collapse-caused breakdown of local energy-momentum conservation could be remedied by altering the metric, resulting in collapse-induced curvature of the space-time. My assumption of frame-drag by quantized masses is independent of the general relativistic frame-drag by classical masses.

On the frequency correlations of low-frequency QPOs with kilohertz QPOs in accreting millisecond X-ray pulsars

ABSTRACT We investigate frequency correlations of low frequency (LF, &amp;lt;80 Hz) and kHz quasi-periodic oscillations (QPOs) using the complete RXTE data sets on six accreting millisecond X-ray pulsars (AMXPs) and compare them to those of non-pulsating neutron star (NS) low-mass X-ray binaries with known spin. For the AMXPs SAX J1808.4−3658 and XTE J1807−294, we find frequency-correlation power-law indices that, surprisingly, are significantly lower than in the non-pulsars, and consistent with the relativistic precession model (RPM) prediction of 2.0 appropriate to test-particle orbital and Lense–Thirring precession frequencies. As previously reported, power-law normalizations are significantly higher in these AMXPs than in the non-pulsating sources, leading to requirements on the NS specific moment of inertia in this model that cannot be satisfied with realistic equations of state. At least two other AMXPs show frequency correlations inconsistent with those of SAX J1808.4−3658 and XTE J1807−294, and possibly similar to those of the non-pulsating sources; for two AMXPs no conclusions could be drawn. We discuss these results in the context of a model that has had success in black hole (BH) systems involving a torus-like hot inner flow precessing due to (prograde) frame dragging, and a scenario in which additional (retrograde) magnetic and classical precession torques not present in BH systems are also considered. We show that a combination of these interpretations may accommodate our results.

Gravitomagnetism and pulsar beam precession near a Kerr black hole

ABSTRACT A rotating black hole causes the spin axis of a nearby pulsar to precess due to geodetic and gravitomagnetic frame-dragging effects. The aim of our theoretical work here is to explore how this spin precession can modify the rate at which pulses are received on Earth. Towards this end, we obtain the complete evolution of the beam vectors of pulsars moving on equatorial circular orbits in the Kerr space–time, relative to asymptotic fixed observers. We proceed to establish that such spin precession effects can significantly modify observed pulse frequencies and, in specific, we find that the observed pulse frequency rises sharply as the orbit shrinks, potentially providing a new way to locate horizons of Kerr black holes, even if observed for a very short time period. We also discuss implications for detections of sub-millisecond pulsars, pulsar nulling, quasi-periodic oscillations, multiply peaked pulsar Fourier profiles, and how Kerr black holes can potentially be distinguished from naked singularities.

The flyby anomaly and the gravitational–magnetic field induced frame-dragging effect around the Earth

ABSTRACT The anomalous energy difference observed during the Earth flybys is modelled here as a dynamical effect resulting from the coupling of the gravitational and the magnetic fields of the Earth. The theoretical analysis shows that general relativistic frame-dragging can become modified under the Earth’s magnetic field by orders of magnitude. For 12 flyby cases, including the null results reported in some recent flybys, the predicted velocities correspond to the observed velocities within the observational error. The gravitomagnetic effect is also shown to account for the linear distance relation, time-variation of the anomalous energy, and the reduction in the anomalous velocity for high-altitude flybys near the Earth.

Black Hole Spin Signature in the Black Hole Shadow of M87 in the Flaring State

Abstract Imaging the immediate vicinity of supermassive black holes (SMBHs) and extracting a BH-spin signature is one of the grand challenges in astrophysics. M87 is known as one of the best targets for imaging the BH shadow and it can be partially thick against synchrotron self-absorption (SSA), particularly in a flaring state with a high mass accretion rate. However, little is known about influences of the SSA-thick region on BH shadow images. Here we investigate BH shadow images of M87 at 230 GHz properly taking into account the SSA-thick region. When the BH has a high spin value, the corresponding BH shadow image shows the positional offset between the center of the photon ring and that of the SSA-thick ring at the innermost stable circular orbit (ISCO) due to the frame-dragging effect in the Kerr spacetime. As a result, we find that a dark-crescent structure is generally produced between the photon ring and the SSA-thick ISCO ring in the BH shadow image. The scale size of the dark crescent increases with BH spin: its width reaches up to ∼2 gravitational radius when the BH spin is 99.8% of its maximum value. The dark crescent is regarded as a new signature of a highly spinning BH. This feature is expected to appear in flaring states with relatively high mass accretion rate rather than the quiescent states. We have simulated the image reconstruction of our theoretical image by assuming the current and future Event Horizon Telescope (EHT) array, and have found that the future EHT including space–very long baseline interferometry in 2020s can detect the dark crescent.

Introduction to Black Holes

In these lectures an introduction to black holes in general relativity is presented. First the Schwarzschild black hole and its properties are discussed by studying the geodesics of light and matter. Several coordinate systems are introduced, and the maximal analytic extension of the Schwarzschild solution is obtained, including a white hole, a second universe, and a non-traversable wormhole. Subsequently the properties of the rotating Kerr black hole are discussed. These include, in particular, the ring singularity, the horizons, frame dragging and the ergoregion. As an interesting astrophysical application the photon region and the black hole shadow are addressed.

A rapidly changing jet orientation in the stellar-mass black-hole system V404 Cygni.

Powerful relativistic jets are one of the main ways in which accreting black holes provide kinetic feedback to their surroundings. Jets launched from or redirected by the accretion flow that powers them are expected to be affected by the dynamics of the flow, which for accreting stellar-mass black holes has shown evidence for precession1 due to frame-dragging effects that occur when the black-hole spin axis is misaligned with the orbital plane of its companion star2. Recently, theoretical simulations have suggested that the jets can exert an additional torque on the accretion flow3, although the interplay between the dynamics of the accretion flow and the launching of the jets is not yet understood. Here we report a rapidly changing jet orientation-on a time scale of minutes to hours-in the black-hole X-ray binary V404 Cygni, detected with very-long-baseline interferometry during the peak of its 2015 outburst. We show that this changing jet orientation can be modelled as the Lense-Thirring precession of a vertically extended slim disk that arises from the super-Eddington accretion rate4. Our findings suggest that the dynamics of the precessing inner accretion disk could play a role in either directly launching or redirecting the jets within the inner few hundred gravitational radii. Similar dynamics should be expected in any strongly accreting black hole whose spin is misaligned with the inflowing gas, both affecting the observational characteristics of the jets and distributing the black-hole feedback more uniformly over the surrounding environment5,6.