Frame-dragging Research Articles

The LARES 2 satellite, general relativity and fundamental physics

LARES 2, successfully launched on July 13, 2022, is a new generation laser-ranged satellite. LARES is an acronym for LAser RElativity Satellite. The first LARES satellite was successfully launched on February 13, 2012 with the ESA-ASI-AVIO launch vehicle VEGA. LARES 2 was injected with extremely high precision onto a high-altitude orbit at about 5900 km altitude with the new ESA-ASI-AVIO launch vehicle VEGA C. Laser-ranged satellites have many applications, including to test Einstein’s theory of general relativity. The main general relativistic phenomenon that LARES 2 will test with high accuracy is the dragging of inertial frames, or frame-dragging. It will also test other aspects and principles of fundamental physics and general relativity, such as the weak equivalence principle at the foundation of viable gravitational theories. Frame-dragging is the name Einstein himself gave in 1913 to an intriguing phenomenon of general relativity which implies that a current of mass-energy, such as the rotation of a body, will generate spacetime curvature. Frame-dragging has a key role in high energy astrophysics, e.g., in the generation of gravitational waves by the collision of two black holes to form a rotating black hole. Frame-dragging by the rotating Earth was measured to a few percent accuracy by combining the data of the satellites LARES, LAGEOS and LAGEOS 2 (Ciufolini et al. in Eur Phys J C 79:872, 2019). LARES 2, thanks to its extremely high injection precision, is projected to improve the test of frame-dragging by at least an order of magnitude. LARES 2 has also relevant applications in space geodesy and geodynamics, e.g., in the study of the shape of the Earth and in the determination of the International Terrestrial Reference Frame (ITRF) by improving the determination of the Earth center of mass and by contributing to a better determination of its rotation axis.

Observational Signatures of Frame Dragging in Strong Gravity

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 rotation as it is being accreted. In total intensity images, infalling streams exhibit “S”-shaped features due to the switch in the tangential velocity. In linear polarization, a flip in the handedness of spatially resolved polarization ticks as a function of radius encodes a transition in the magnetic field geometry that occurs due to magnetic flux freezing in the dragged plasma. Using a network of telescopes around the world, the Event Horizon Telescope collaboration has demonstrated that it is now possible to directly image black holes on event horizon scales. We show that the phenomena described in this work would be accessible to the next-generation Event Horizon Telescope and extensions of the array into space, which would produce spatially resolved images on event horizon scales with higher spatial resolution and dynamic range.

H-AMR: A New GPU-accelerated GRMHD Code for Exascale Computing with 3D Adaptive Mesh Refinement and Local Adaptive Time Stepping

General relativistic magnetohydrodynamic (GRMHD) simulations have revolutionized our understanding of black hole accretion. Here, we present a GPU-accelerated GRMHD code H-AMR with multifaceted optimizations that, collectively, accelerate computation by 2–5 orders of magnitude for a wide range of applications. First, it introduces a spherical grid with 3D adaptive mesh refinement that operates in each of the three dimensions independently. This allows us to circumvent the Courant condition near the polar singularity, which otherwise cripples high-resolution computational performance. Second, we demonstrate that local adaptive time stepping on a logarithmic spherical-polar grid accelerates computation by a factor of ≲10 compared to traditional hierarchical time-stepping approaches. Jointly, these unique features lead to an effective speed of ∼109 zone cycles per second per node on 5400 NVIDIA V100 GPUs (i.e., 900 nodes of the OLCF Summit supercomputer). We illustrate H-AMR's computational performance by presenting the first GRMHD simulation of a tilted thin accretion disk threaded by a toroidal magnetic field around a rapidly spinning black hole. With an effective resolution of 13,440 × 4608 × 8092 cells and a total of ≲22 billion cells and ∼0.65 × 108 time steps, it is among the largest astrophysical simulations ever performed. We find that frame dragging by the black hole tears up the disk into two independently precessing subdisks. The innermost subdisk rotation axis intermittently aligns with the black hole spin, demonstrating for the first time that such long-sought alignment is possible in the absence of large-scale poloidal magnetic fields.

Nonanalytic behavior of the relativistic r -modes in slowly rotating neutron stars

An inconsistency between the theoretical analysis and numerical calculations of the relativistic $r$-modes puzzles the neutron star community since the Kojima's finding of the continuous part in the $r$-mode oscillation spectrum in 1997. In this paper, after a brief review of the Newtonian $r$-mode theory and of the literature devoted to the continuous spectrum of $r$-modes, we apply our original approach to the study of relativistic oscillation equations. Working within the Cowling approximation, we derive the general equations, governing the dynamics of discrete relativistic $r$-modes for both barotropic (isentropic) and nonbarotropic stars. A detailed analysis of the obtained equations in the limit of extremely slow stellar rotation rate reveals that, because of the effect of inertial reference frame-dragging, the relativistic $r$-mode eigenfunctions and eigenfrequencies become {\it non-analytic} functions of the stellar angular velocity, $\Omega$. We also derive the explicit expressions for the $r$-mode eigenfunctions and eigenfrequencies for very small values of $\Omega$. These expressions explain the asymptotic behavior of the numerically calculated eigenfrequencies and eigenfunctions in the limit $\Omega\to 0$. All the obtained $r$-mode eigenfrequencies take discrete values in the frequency range, usually associated with the continuous part of the spectrum. No indications of the continuous spectrum, at least in the vicinity of the Newtonian $l=m=2$ $r$-mode frequency $\sigma=-4/3 \ \Omega$, are found.

Constraints on ultralight axions, vector gauge bosons, and unparticles from geodetic and frame-dragging measurements

The geodetic and frame-dragging effects are the direct consequences of the spacetime curvature near Earth which can be probed from the Gravity probe B (GP-B) satellite. The satellite result matches quite well with Einstein’s general relativistic result. The gyroscope of the satellite which measures the spacetime curvature near Earth contains lots of electrons and nucleons. Ultralight axions, vector gauge bosons, and unparticles can interact with these electrons and nucleons through different spin-dependent and spin-independent operators and change the drift rate of the gyroscope. Some of these ultralight particles can either behave as a long range force between some dark sector or Earth and the gyroscope or they can behave as a background oscillating dark matter fields or both. These ultralight particles can contribute an additional precession of the gyroscopes, limited to be no larger than the uncertainty in the GP-B measurements. Compared with the experimental results, we obtain bounds on different operator couplings.

Bayesian Accretion Modeling: Axisymmetric Equatorial Emission in the Kerr Spacetime

The Event Horizon Telescope (EHT) has produced images of two supermassive black holes, Messier 87* (M 87*) and Sagittarius A* (Sgr A*). The EHT collaboration used these images to indirectly constrain black hole parameters by calibrating measurements of the sky-plane emission morphology to images of general relativistic magnetohydrodynamic (GRMHD) simulations. Here, we develop a model for directly constraining the black hole mass, spin, and inclination through signatures of lensing, redshift, and frame dragging, while simultaneously marginalizing over the unknown accretion and emission properties. By assuming optically thin, axisymmetric, equatorial emission near the black hole, our model gains orders of magnitude in speed over similar approaches that require radiative transfer. Using 2017 EHT M 87* baseline coverage, we use fits of the model to itself to show that the data are insufficient to demonstrate existence of the photon ring. We then survey time-averaged GRMHD simulations fitting EHT-like data, and find that our model is best-suited to fitting magnetically arrested disks, which are the favored class of simulations for both M 87* and Sgr A*. For these simulations, the best-fit model parameters are within ∼10% of the true mass and within ∼10° for inclination. With 2017 EHT coverage and 1% fractional uncertainty on amplitudes, spin is unconstrained. Accurate inference of spin axis position angle depends strongly on spin and electron temperature. Our results show the promise of directly constraining black hole spacetimes with interferometric data, but they also show that nearly identical images permit large differences in black hole properties, highlighting degeneracies between the plasma properties, spacetime, and, most crucially, the unknown emission geometry when studying lensed accretion flow images at a single frequency.

Atom interferometers and a small-scale test of general relativity

Since the first appearance of general relativity in 1916, various experiments have been conducted to test the theory. Due to the weakness of the interactions involved, all of the documented tests were carried out in a gravitational field generated by objects of an astronomical scale. We propose an idea for an experiment that could detect purely general-relativistic effects in a lab-generated gravitational field. It is shown that a set of dense rapidly-revolving cylinders produce a frame-dragging effect substantial enough to be two orders of magnitude away from the observable range of the next generation of atomic interferometers. The metric tensor due to a uniform rotating axisymmetric body in the weak-field limit is calculated and the phase shift formula for the interferometer is derived. This article is meant to demonstrate feasibility of the concept and stimulate further research into the field of low-scale experiments in general relativity. It is by no means a fully developed experiment proposal.

Quantum corrections to frame-dragging in scattering amplitudes

Frame-dragging effect manifests itself as polarization direction rotation when linearly polarized electromagnetic/gravitational wave scatters from a spinning point source through gravitational interactions, an effect also known as the gravitational Faraday rotation. Treating general relativity as an effective field theory, the Faraday rotation angle and its quantum corrections are computed using scattering amplitudes. While the classical rotation angle is universal as expected from the equivalence principle, the quantum corrections are found to be different between electromagnetic and gravitational waves, supporting earlier studies that some formulations of the equivalence principle may need reformulation in the quantum regime.

Equation of states in the curved spacetime of slowly rotating degenerate stars

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, in general relativity the frame-dragging effect is crucial for computing angular momentum of the star which is also shown to be enhanced significantly due to the usage of curved spacetime in computing the equation of state.

Gravitational Faraday Rotation of gravitational waves by a Kerr black hole

Gravitational Faraday Rotation (GFR) is a frame-dragging effect induced by rotating massive objects, which is one of the important, yet studied characteristics of lensed gravitational waves (GWs). In this work, we calculate the GFR angle χ g of GWs in the weak deflection limit, assuming it is lensed by a Kerr black hole (BH). We find that the GFR effect changes the initial polarization state of the lensed GW. Compared with the Einstein deflection angle, the dominant term of the rotation angle χ g is a second-order correction to the polarization angle, which depends on the light-of-sight component of BH angular momentum. Such a rotation is tiny and degenerates with the initial polarization angle. In some critical cases, the GFR angle is close to the detection capability of the third-generation GW detector network, although the degeneracy has to be broken.

Propagation time delay and frame dragging effects of lightlike geodesics in the timing of a pulsar orbiting SgrA*

ABSTRACTTiming a pulsar in a close orbit around the supermassive black hole SgrA* at the centre of the Milky Way would open the window for an accurate determination of the black hole parameters and for new tests of general relativity and alternative modified gravity theories. An important relativistic effect which has to be taken into account in the timing model is the propagation delay of the pulses in the gravitational field of the black hole. Due to the extreme mass ratio of the pulsar and the supermassive back hole we use the test particle limit to derive an exact analytical formula for the propagation delay of lightlike geodesics in a Kerr space–time, and deduce a relativistic formula for the corresponding frame dragging effect on the arrival time. As an illustration, we treat an edge-on orbit in which the frame dragging effect on the emitted lightlike geodesics is expected to be maximal. We compare our formula for the propagation time delay with Post-Newtonian approaches, and in particular with the frame dragging terms derived in previous works by Wex & Kopeikin and Rafikov & Lai. Our approach correctly identifies the asymmetry of the frame dragging delay with respect to superior conjunction, avoids singularities in the time delay, and indicates that in the Post-Newtonian approach frame dragging effects on the lightlike pulses are generally slightly overestimated.

Ultra-High-Energy Particles at the Border of Kerr Black Holes Triggered by Magnetocentrifugal Winds

The source, origin, and acceleration mechanisms of ultra-high-energy cosmic rays (UHECR) (E>1020 eV, beyond the GZK limit) remain uncertain and unclear. The main explanations are associated with particular mechanisms, such as the Fermi mechanism, in which charged particles could be accelerated by clouds of magnetized gas moving within our Galaxy, or by the magnetic reconnection of field lines at, e.g., the core of high-energy astrophysical sources, where the topology of the magnetic field is rearranged and magnetic energy is converted into kinetic energy. However, the recent observation of extragalactic neutrinos may suggest that the source of UHECRs is likely an extragalactic supermassive black hole. In the present work, we propose that charged particles can be accelerated to ultrahigh energies in marginally bound orbits near extreme rotating black holes and could be triggered by collisions of magnetocentrifugal winds; the accretion disk surrounding the black hole would provide such winds. The ultra-high-energy process is governed by the frame-dragging effects of the black hole spacetime.

About 300 days Optical Quasi-periodic Oscillations in the Long-term Light Curves of the Blazar PKS 2155-304

Based on the long-term light curves collected from the Catalina Sky Survey (CSS) (from 2005 to 2013) and the All-Sky Automated Survey for Supernovae (ASAS-SN) (from 2014 to 2018), optical quasi-periodic oscillations (QPOs) about 300 days can be well determined in the well-known blazar PKS 2155-304 through four different methods: the generalized Lomb-Scargle periodogram (GLSP) method, the weighted wavelet Z-transform technique, the epoch-folded method and the redfit method. The GLSP determined significance level for the periodicity is higher than 99.9999% based on a false alarm probability. The redfit provided confidence level for the periodicity is higher than 99% in the ASAS-SN light curve, after considering the effects of red noise. Based on continuous autoregressive process created artificial light curves, the probability of detecting fake QPOs is lower than 0.8%. The determined optical periodicity of 300 days from the CSS and ASAS-SN light curves is well consistent with the reported optical periodicity in the literature. Moreover, three possible models are discussed to explain the optical QPOs in PKS 2155-304: the relativistic frame-dragging effect, the binary black hole model and the jet precession model.

Covariant Evolution of Gravitoelectromagnetism

The long-range gravitational terms associated with tidal forces, frame-dragging effects, and gravitational waves are described by the Weyl conformal tensor, the traceless part of the Riemann curvature that is not locally affected by the matter field. The Ricci and Bianchi identities provide a set of dynamical and kinematic equations governing the matter coupling and evolution of the electric and magnetic parts of the Weyl tensor, so-called gravitoelectric and gravitomagnetic fields. A detailed analysis of the Weyl gravitoelectromagnetic fields can be conducted using a number of algebraic and differential identities prescribed by the 1+3 covariant formalism. In this review, we consider the dynamical constraints and propagation equations of the gravitoelectric/-magnetic fields and covariantly debate their analytic properties. We discuss the special conditions under which gravitational waves can propagate, the inconsistency of a Newtonian-like model without gravitomagnetism, the nonlinear generalization to multi-fluid models with different matter species, as well as observational effects caused by the Weyl fields via the kinematic quantities. The 1+3 tetrad and 1+1+2 semi-covariant methods, which can equally be used for gravitoelectromagnetism, are briefly explained, along with their correspondence with the covariant formulations.

Towards a full general relativistic approach to galaxies

We analyse the dynamics of a single disk galaxy from a general relativistic viewpoint. We investigate dark matter (DM) effects in terms of a known family of stationary axially-symmetric solutions of Einstein equations coupled to a rotating dust. These effects are generated by the non-Newtonian features of such solutions and are ascribed to the essential role of frame dragging. Indeed, in such models, the off-diagonal elements of the metric are, in general, of the same order of magnitude of the diagonal ones. We generalize the results of Balasin and Grumiller (BG) to the physical case of differentially rotating dust. In particular, we find that for differential rotation the amount of energy density required to account for the flat rotation curves of disk galaxies is reduced with respect to the BG rigid rotation case. This stresses the discrepancy between Newtonian gravity and general relativity (GR), even at low velocities and low energy densities.

ВЛИЯНИЕ ЗАРЯДА В ЧЕРНОЙ ДЫРЕ БАРДИНА НА ЗАДЕРЖКУ ВРЕМЕНИ ПРИБЫТИЯ СИГНАЛОВ

In this paper we consider an impact of Bardeen black hole charge on times of arrival of signals on the time delay caused by frame-dragging effect. This effect can arise in astrophysical systems, where one of the companions of the binary system emits a variable electromagnetic signal. A variable signal travels on both sides of a rotating object in the equatorial plane. We consider a spherically symmetric regular black hole by Bardeen as a rotating object, which has a deviation parameter g besides mass M and spin a. This parameter is related to the described nonlinear electrodynamics, and the Bardeen metric reduces to the Kerr metric when g = 0. We investigate times of arrival of signals effect in a realistic final lens system in a Bardeen black hole compared to a Kerr–Newman black hole. It is noteworthy that an influence of electric charge on the time delay in the Kerr–Newman black hole appears in the second and third orders, and an influence of the charge in the Bardeen black hole only in the third order. The contribution of the leading-order time delay with the capabilities of modern equipment is fundamentally measurable, however, the influence of the charge manifests itself only in the third, therefore, this study is more of academic interest than practical. For the binary system pulsar – black hole Cygnus X-1, numerical values were tabulated.

Lense–Thirring effect on accretion flow from counter-rotating tori

ABSTRACT We study the accretion flow from a counter-rotating torus orbiting a central Kerr black hole (BH). We characterize the flow properties at the turning point of the accreting matter flow from the orbiting torus, defined by the condition uϕ = 0 on the flow toroidal velocity. The counter-rotating accretion flow and jet-like flow turning point location along BH rotational axis is given. Some properties of the counter-rotating flow thickness and counter-rotating tori energetics are studied. The maximum amount of matter swallowed by the BH from the counter-rotating tori is determined by the background properties. The fast spinning BH energetics depends mostly on BH spin rather than on the properties of the counter-rotating fluids or the tori masses. The turning point is located in a narrow orbital corona (spherical shell), for photons and matter flow constituents, surrounding the BH stationary limit (outer ergosurface), depending on the BH spin–mass ratio and the fluid initial momentum only. The turning corona for jet-like flow has larger thickness, it is separated from the torus flow turning corona and it is closer to the BH stationary limit. Turning points of matter accreting from torus and from jets are independent explicitly of the details of the accretion and tori model. The turning corona could be observable due to an increase of flow luminosity and temperature. The corona is larger on the BH equatorial plane, where it is the farthest from the central attractor, and narrower on the BH poles.

Spin Precession in the Gravity Wave Analogue Black Hole Spacetime

It was predicted that the spin precession frequency of a stationary gyroscope shows various anomalies in the strong gravity regime if its orbit shrinks, and eventually, its precession frequency becomes arbitrarily high very close to the horizon of a rotating black hole. Considering the gravity waves of a flowing fluid with a vortex in a shallow basin, which acts as a rotating analogue black hole, one can observe the predicted strong gravity effect on the spin precession in the laboratory. Attaching a thread with the buoyant particles and anchoring it to the bottom of the fluid container with a short-length miniature chain, one can construct a simple local test gyroscope to measure the spin precession frequency in the vicinity of the gravity wave analogue black hole. The thread acts as the axis of the gyroscope. By regulating the orbital frequency of the test gyroscope, one can also measure the strong gravity Lense–Thirring effect and geodetic/de-Sitter effect with this experimental set-up as the special cases. For example, to measure the Lense–Thirring effect, the length of the miniature chain can be set to zero, so that the gyroscope becomes static. One can also measure the geodetic precession with this system by orbiting the test gyroscope in the so-called Keplerian frequency around the non-rotating analogue black hole that can be constructed by making the rotation of the fluid/vortex negligible compared to its radial velocity.

How to Interpret Gravitational Events in the Gravity Probe B Mission? (Gravitational Phonons and Gravitational Deformation Potential)

The Gravity Probe B Mission (GPB) collected valuable experimental data in the years 2004-2005. The geodetic drift in the orbit plane was interpreted as the curvature precession through the space-time curved by the Earth´s mass. The frame-dragging effect was interpreted using the Lense-Thirring-Schiff model based on the dragging of the orbit plane of a satellite around the rotating Earth. Both these effects were visible in the CORRECTED data. The gist of this contribution is to describe these gravitational events as the result of the joint effects of the gravitational deformation potential and the gravitational phonons in the gyroscope rotors. The gravitational phonon velocity is “hidden” in the formula discovered by Albert Einstein in his last Prague´s paper in 1912. Gravitational phonons and the gravitational deformation potential acting on the gyroscope rotors deform slightly the gyroscope rotor geometry and form both observed longitudinal and transverse precessions. This new interpretation of subtle gravitational precessions was tested on the RAW experimental data published by the GPB Team. The observed gravitational events occur in the classical 3D space in this scenario. We propose to re-analyze all GPB data according this classical model without additional corrections. The new Gravity Probe C + D missions might deliver more illustrative data comparing this model with the predictions of the general theory of relativity.

Energy Extraction via Magnetic Reconnection in the Ergosphere of a Rotating Non-Kerr Black Hole

Abstract Magnetic reconnection in the ergosphere is investigated for a relativistic plasma around a rotating non-Kerr black hole. For a rotating non-Kerr black hole immersed in a magnetic field generated by an externally material, antiparallel magnetic field line could form in the ergosphere due to frame dragging. Therefore, magnetic reconnection could occur in the ergosphere. This magnetic reconnection may generate negative energy at infinity by redistributing the angular momentum during the process. The results show that, taking into account the effect of the deformed parameter, extraction of energy from a rotating non-Kerr black hole by magnetic reconnection could be enhanced in the presence of a positive deformed parameter.