Spinning Object Research Articles

Horizon replicas in black hole shadows

Recently, new exploratory channels have opened up for the physics of highly compact objects, such as gravitational waves and black hole shadows. Moreover, more precise analysis and observations are now possible in the physics of accretion around compact objects. These advancements provide in particular an unprecedented insight into the physics near the horizons of a black hole. In this work we focus on the shadow boundary of a Kerr black hole, introducing observables related to special null orbits, called horizons replicas, solutions of the shadow edge equations which are related to particular photon orbits, defined by constraints on their impact parameter, carrying information about the angular momentum of the central spinning object. These orbits are related to particular regions on the shadow boundary and might be used to determine the spin of the black hole. The results provide the conditions by which horizon replicas are imprinted in the black hole shadow profile, in dependence on the black hole dimensionless spin and observational angle, providing eventually new templates for the future observations.

Analytic solutions for drag and Magnus forces

When a spinning object moves in air, it is affected by three forces: the gravitational force, the drag force, and the Magnus force. The equations of motion for such an object are nonlinear, making it difficult to find analytic solutions. Hence, numerical solutions using computers are often preferred. This paper provides two examples of analytic solutions of the equations of motion with the drag and Magnus forces: nearly vertical motion and motion of a light object. In these two cases, we find analytic solutions for the velocity and the position of the object, avoiding mathematical difficulties. It is suitable for university students studying physics.

Active Resonance Fitting Energy Harvesting from Spinning Objects

Abstract Energy harvesting is an emerging topic in the recent energy global problem. Energy can be harvested from different resources such as sea waves, wind, solar, etc. In this research, energy harvesting from spinning objects using vibrations will be addressed in addition to how to conduct active fitting procedures to allow the vibrating elements at all time work under resonance condition. Any spinning object has a centrifugal force that affects the vibrating element and cause more stiffness to its normal condition, which helps increasing the vibrating element natural frequency keeping with the increasing driving/spinning frequency until a certain limit. Thus, a new methodology by actively customizing the vibrating element beam length is proposed to manipulate its natural frequency according the spinning frequency.

Rotating metrics and new multipole moments from scattering amplitudes in arbitrary dimensions

We compute the vacuum metric generated by a generic rotating object in arbitrary dimensions up to third post-Minkowskian order by computing the classical contribution of scattering amplitudes describing the graviton emission by massive spin-1 particles up to two loops. The solution depends on the mass, angular momenta, and on up to two parameters related to generic quadrupole moments. In D=4 spacetime dimensions, we recover the vacuum Hartle-Thorne solution describing a generic spinning object to second order in the angular momentum, of which the Kerr metric is a particular case obtained for a specific mass quadrupole moment dictated by the uniqueness theorem. At the level of the effective action, the case of minimal couplings corresponds to the Kerr black hole, while any other mass quadrupole moment requires nonminimal couplings. In D>4, the absence of black-hole uniqueness theorems implies that there are multiple spinning black hole solutions with different topology. Using scattering amplitudes, we find a generic solution depending on the mass, angular momenta, the mass quadrupole moment, and a new stress quadrupole moment which does not exist in D=4. As special cases, we recover the Myers-Perry and the single-angular-momentum black ring solutions, to third and first post-Minkowksian order, respectively. Interestingly, at variance with the four-dimensional case, none of these solutions corresponds to the minimal coupling in the effective action. This shows that, from the point of view of scattering amplitudes, black holes are the “simplest” general relativity vacuum solutions only in D=4. Published by the American Physical Society 2024

Charged spinning fermionic configurations and a mass gap

We consider a self-consistent axially symmetric system supported by a classical nonlinear spinor field minimally coupled to electric and magnetic Maxwell fields. The presence of the nonlinearity of the spinor field ensures the existence of a minimum positive energy of the system (a mass gap), of a minimum charge (a charge gap), and of a minimum magnetic moment. In turn, the presence of the electric charge results in qualitative changes in the behavior of physical characteristics of the systems under consideration as compared with the case of an electrically neutral spinor field. It is shown that, with a suitable choice of free system parameters, there exists a regular finite-energy particlelike solution describing a localized spinning object whose physical parameters correspond to the main characteristics of an electron/positron (including the spin equal to 1/2), but with the characteristic size comparable to the corresponding Compton wavelength. Also, we show that four local Dirac equations are equivalent to two nonlocal equations.

Simultaneous measurement of spin and precession based on light's orbital angular momentum.

The rotational Doppler effect of the vortex beam is a recently emerged promising application of the optical vortex with orbital angular momentum. In this paper, we combine the method of the micro-Doppler effect of the traditional radar and the rotational Doppler effect of the vortex beam and propose an approach of rotational micro-Doppler effect, realizing the simultaneous measurement of spin and precession. We firstly analyze the rotational micro-Doppler characteristic introduced by precession under the illuminating of vortex beam and calculate the rotational micro-Doppler parameters related to the spin and precession. Then we conduct an experiment of using the vortex beam to detect a spinning object with precession and the rotational micro-Doppler frequency is successfully observed. By extracting the rotational micro-Doppler parameters, the simultaneous and independent measurement of spin and precession is realized. Both the theoretical analysis and experimental results indicate that the rotational micro-Doppler effect is an effective extension of the rotational Doppler effect and is also a feasible application of the vortex beam detection.

Change in momentum proportional to the change in angular momentum of the particle

Recently, Ahn et al. created dumbbell-shaped silica nanoparticles, then optically levitated in vacuum, capable of spinning at 300 billion revolutions per minute, driven only by the force and torque of laser. This is by far the fastest spinning object in the world. We show that in this system, there is an additional change in momentum (or extra force) that is proportional to the change in the angular momentum of the particle (or torque). We suggest that this effect also applies to microscopic particles. In the experiment of Ahn et al., although the angular momentum of the particle itself L is large, the rate of change of the angular momentum [Formula: see text] may not be large. Therefore, experimentally, the physical effects associated with changes in angular momentum can be verified either by applying very strong force and torque to the particle, or by allowing the axis of rotation of the particle to find a way to change very quickly.

Detection of a spinning object using a superimposed optical vortex array.

The optical vortex (OV) carries unique orbital angular momentum (OAM) and experiences a Doppler frequency shift when backscattered from a spinning object. This rotational Doppler effect (RDE) has provided a solution for the non-contact detection of rotating motion. The reported RDE researches mainly use a single OV that generates frequency shifts proportional to its topological charge and has low robustness to light incidence. Here, we show the distinctive RDE of superimposed optical vortex array (SOVA). We analyze the holistic OAM of SOVA which is represented in terms of a superposition of azimuthal harmonics and displays a unique modal gathering effect. In the experiment of RDE, the frequency shift signals of SOVA show a precise mapping to the OAM modes and the modal gathering effect contributes to enhance the amplitude of signals, which has the potential to enhance robustness against non-coaxial incidence. This finding provides a new aspect of RDE and a pioneered example for introducing various SOVAs into rotation detection.

Theory of gyroscopic effects for rotating objects

Scientists began to study gyroscopic effects at the time of the Industrial Revolution. Famous mathematician L. Euler described only one gyroscopic effect, which is the precession torque that does not explain other ones. Since those times, scientists could not explain the physics of gyroscopic effects, Recent studies and the method of causal investigatory dependency demonstrated, that the nature of gyroscopic effects turned out that be more sophisticated than contemplated by researchers. The external torque acting on the spinning objects generates the system of the eight inertial torques and their interrelated motions around axes presented in the 3D coordinate system. The interrelated torques and motions of the spinning disc were described by mathematical models, and validated by practical tests that explain the physics of the gyroscopic effects based on the kinetic energy conservation law. The inertial torques generated by the centrifugal, and Coriolis forces, the change in the angular momentum, and the dependent motions of the spinning object around axes constitute the fundamental principles of the gyroscope theory. The derived gyroscopic theory opened a new chapter in the dynamics of rotating objects of classical mechanics that should be presented in all word encyclopedias.

On-chip generation of Bessel–Gaussian beam via concentrically distributed grating arrays for long-range sensing

Bessel beam featured with self-healing is essential to the optical sensing applications in the obstacle scattering environment. Integrated on-chip generation of the Bessel beam outperforms the conventional structure by small size, robustness, and alignment-free scheme. However, the maximum propagation distance (Zmax) provided by the existing approaches cannot support long-range sensing, and thus, it restricts its potential applications. In this work, we propose an integrated silicon photonic chip with unique structures featured with concentrically distributed grating arrays to generate the Bessel–Gaussian beam with a long propagation distance. The spot with the Bessel function profile is measured at 10.24 m without optical lenses, and the photonic chip’s operation wavelength can be continuously performed from 1500 to 1630 nm. To demonstrate the functionality of the generated Bessel–Gaussian beam, we also experimentally measure the rotation speeds of a spinning object via the rotational Doppler Effect and the distance through the phase laser ranging principle. The maximum error of the rotation speed in this experiment is measured to be 0.05%, indicating the minimum error in the current reports. By the compact size, low cost, and mass production potential of the integrated process, our approach is promising to readily enable the Bessel–Gaussian beam in widespread optical communication and micro-manipulation applications.

Publisher's Note: “Observation of the rotational Doppler shift of a spinning object based on an acoustic vortex with a Fresnel-spiral zone plate” [J. Appl. Phys. 133, 114502 (2023)

First Page

Observation of the rotational Doppler shift of a spinning object based on an acoustic vortex with a Fresnel-spiral zone plate

It has been demonstrated that sound waves carrying orbital angular momentum undergo frequency modulation after being reflected by a rotating object. In this paper, we, observed the rotational Doppler shift phenomenon of the acoustic vortex in an underwater environment by using a Fresnel-spiral zone plate for the construction of the focused acoustic vortex with controllable topological charge. The positive and negative rotation speeds of the spinning object are precisely determined with the rotational frequency shift and the acoustic vortex's topological charge. The rotational Doppler effect of acoustic vortex provides a possibility to improve the detection and recognition accuracy of Autonomous Underwater Vehicles with propellers.

Computational Ghost Rotational Doppler Metrology

We present a scheme for measuring a rotational Doppler frequency shift with only a single-shot measurement. Our protocol benefits from the combination of computational temporal ghost imaging and heterodyne detection of the rotational Doppler effect. Specifically, by multiplexing a series of elaborately designed ring-shaped spatial patterns, we map the temporal rotational Doppler signal into the spatial domain and thus can collect the Doppler signal with a camera in a single-shot exposure. Then, by calculating intensity correlations between the resulting elaborate spatial patterns and the image captured by the camera, we reconstruct the temporal Doppler signal. In our experiments, we succeed in demonstrating fairly good performance for measuring the angular velocity of a real spinning object with a rough surface. Our scheme could find potential applications in remote sensing and could also inspire more attempts to develop protocols for temporal detection and processing on the basis of space-time duality.

Free-space remote detection of a spinning object using the combined vortex beam.

The rotational Doppler effect (RDE) associated with orbital angular momentum (OAM) has been used for remote sensing of a spinning object. However, one of the challenges of long-range detection stems from the low echo signal power. In this paper, we propose a new detection scheme that uses the combined vortex beam (CVB) generated by coherent beam combining (CBC) technology as the probe beam to enhance the echo signal power. Furthermore, we establish a rotational speed remote sensing model based on RDE, the emitted power and emission diameter of the probe beam are investigated in detail. The results show that, compared with the superposition vortex beam (SVB) generated by a single laser beam, the CVB detection scheme can significantly enhance the echo signal intensity and detection distance. The measuring range and accuracy of rotational speed are also studied in detail. And finally, we present the first experimental demonstration of the RDE arising directly from the interaction of the CVB with a rotating rough surface. The scheme proposed in our paper offers a good reference for practical application of the remote detection based on RDE.

Flexible online planning based residual space object de-spinning for dual-arm space-borne maintenance

De-spinning a Residual Space Object is an important premise for space-borne maintenance, especially when the relative pose between a chaser and a spinning object is inaccurate due to measurement errors. In this paper, an online trajectory planning strategy for Residual Space Object de-spinning mission under the dual-arm space robotic set-up is proposed. A novel method named Soft Recurrent Actor-Critic is formulated to plan a flexible dual-arm approaching strategy, wherein the minimum requirement of sensors are only two on-board cameras. The Recurrent Neural Network is introduced to cope with the measurement errors. Moreover, the collision limitation and the minimal joints torque variant constraint are taken into account in reward function design for safety concerns. The effectiveness of the proposed method is demonstrated in two simulations, results show that nearly 30 percent performance improvement over the two state-of-the-art methods was achieved.

Gravitational lensing, memory, and the Penrose limit

In this paper, we discuss the gravitational field of ultrarelativistic extended spinning objects. For this purpose, we use a solution of the linearized gravitational equations obtained in the frame where such an object is translationally at rest, and boost this solution close to the speed of light. In order to obtain a regular limiting metric for non-spinning matter, it is sufficient to keep the energy of the boosted body fixed. This process is known as the Penrose limit. We demonstrate that in the presence of rotation, an additional rescaling is required for the angular momentum density components in the directions orthogonal to the boost. As a result of the Lorentz contraction, the thickness of the body in the direction of the boost shrinks. The body takes the form of a pancake, and its gravitational field is localized in the null plane. We discuss light and particle scattering in this gravitational field, and calculate the scattering parameters associated with the gravitational memory effect. We also show that by taking the inverse of the Penrose transform, one can use the obtained scattering map to study the gravitational lensing effect in the rest frame of a massive spinning object.

Principles of Classical Mechanics Describe Gyroscopic Effects

The unexplainable motions of the simple spinning top toy, boomerang, and other spinning objects attracted people since the time of ancient civilizations. The intricated motions of the rotating objects and the action of the unknown forces were named gyroscopic effects. The physicists and mathematicians tried to solve them beginning from the Industrial Revolution until our time. One gyroscopic effect which is the side motion of the spinning disc was described by L. Euler and presented in the world encyclopaedias as the fundamental principle of gyroscope theory. The origin of gyroscopic effects is more sophisticated than in published and simplified theories. Analytical solutions to other gyroscopic effects were described only in our times. The system of the interrelated inertial torques generated by the rotating mass acts on the spinning object based on the principle of mechanical energy conservation. This system presents the fundamental principles of gyroscope theory.

Detection of a Spinning Object at Different Beam Sizes Based on the Optical Rotational Doppler Effect

The rotational Doppler effect (RDE), as a counterpart of the conventional well-known linear Doppler effect in the rotating frame, has attracted increasing attention in recent years for rotating object detection. However, the effect of the beam size on the RDE is still an open question. In this article, we investigated the influence of the size of the probe light; i.e., the size of the ring-shaped orbital angular momentum (OAM)-carrying optical vortex (OV), on the RDE. Both the light coaxial and noncoaxial incident conditions were considered in our work. We analyzed the mechanism of the influence on the RDE under the light coaxial, lateral misalignment, and oblique incidence conditions based on the small-scatterer model. A proof-of-concept experiment was performed to verify the theoretical predictions. It was shown that both the signal-to-noise ratio and the frequency spectrum width were related to the OV size. The larger the beam size, the stronger the RDE signal observed in the practical detection. Especially in the lateral misalignment condition, the large OV size effectively reduced the signal spreading and enhanced the signal strength. These findings may be useful for practical application of the optical RDE in remote sensing and metrology.

Four-dimensional regular black strings in bilocal gravity

In this paper, we obtain a static black string solution for a bilocal gravitational source in 3+1 dimensions. The solution is regular at the origin and tends asymptotically to the ordinary static uncharged black string solution of general relativity. It allows an event horizon and an internal horizon depending on the value of the mass density. A mass remnant associated with a vanishing Hawking temperature is also found. In order to stabilize the solution, a perfect cosmological fluid with state parameter ω>−1 should be present throughout space. However, energy conditions do not exclude an exotic substance nearby the black string. Finally, we find the stationary counterpart of the solution and analyze the behavior of the horizons according to the mass and angular momentum of the spinning object.

Detection of a spinning object with circular procession using an optical vortex beam.

The rotational Doppler effect (RDE) provides an efficient way to measure rotational frequency using an optical vortex beam. Crucially, most research based on the RDE just involves a spinning object or a spinning object coupled with a longitudinal velocity along the beam propagation. We analyze the interaction mechanism between optical orbital angular momentum and a spinning object with circular procession and experimentally demonstrate simultaneous measurements of two rotational frequencies. This technique broadens application of the RDE in optical metrology and remote detection of targets with micro-motions.