The motion of a gyroscope freely falling into a Schwarzschild black hole (original) (raw)
Gyroscopic precession in the vicinity of a static blackhole’s event horizon
General Relativity and Gravitation, 2023
In this article, we investigate gyroscopic precession in the vicinity of a spherically symmetric static event horizon. Our goal is to address whether the gyroscopic precession frequency diverges when approaching an event horizon. To do so, we employ the Frenet–Serret formalism of gyroscopic precession, which provides a complete covariant formalism, and extend it to include arbitrary timelike curves. We analyze the precession frequency near the Schwarzschild and Schwarzschild-anti-de-Sitter black holes, using horizon-penetrating Kerr–Schild coordinates to eliminate coordinate singularities near the horizon. Our study shows that a diverging gyroscopic precession frequency is not a universal feature for a trajectory crossing an event horizon. As a counter-example, we construct a timelike curve passing through the event horizon along which the gyroscopic precession frequency remains finite at the horizon.
Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole
Physical Review D
The precession of a test gyroscope along unbound equatorial plane geodesic orbits around a Kerr black hole is analyzed with respect to a static reference frame whose axes point towards the "fixed stars." The accumulated precession angle after a complete scattering process is evaluated and compared with the corresponding change in the orbital angle. Limiting results for the non-rotating Schwarzschild black hole case are also discussed.
Spinning gyroscope in an acoustic black hole: precession effects and observational aspects
The European Physical Journal C
The exact precession frequency of a freelyprecessing test gyroscope is derived for a 2 + 1 dimensional rotating acoustic black hole analogue spacetime, without making the somewhat unrealistic assumption that the gyroscope is static. We show that, as a consequence, the gyroscope crosses the acoustic ergosphere of the black hole with a finite precession frequency, provided its angular velocity lies within a particular range determined by the stipulation that the Killing vector is timelike over the ergoregion. Specializing to the 'Draining Sink' acoustic black hole, the precession frequency is shown to diverge near the acoustic horizon, instead of the vicinity of the ergosphere. In the limit of an infinitesimally small rotation of the acoustic black hole, the gyroscope still precesses with a finite frequency, thus confirming a behaviour analogous to geodetic precession in a physical non-rotating spacetime like a Schwarzschild black hole. Possible experimental approaches to detect acoustic spin precession and measure the consequent precession frequency, are discussed.
The European Physical Journal C, 2020
The advanced state of cosmological observations constantly tests the alternative theories of gravity that originate from Einstein’s theory. However, this is not restricted to modifications to general relativity. In this sense, we work in the context of Weyl’s theory, more specifically, on a particular black hole solution for a charged massive source, which is confronted with the classical test of the geodetic precession, to obtain information about the parameters associated with this theory. To fully assess this spacetime, the complete geodesic structure for massive test particles is presented.
On the influence of gravitational radiation on a gyroscope
Classical and Quantum Gravity, 2000
We calculate the precession of a gyroscope at rest in a Bondi spacetime. It is shown that, far from the source, the leading term in the rate of precession of the gyroscope is simply expressed through the news function of the system, and vanishes if and only if there is no news. Rough estimates are presented, illustrating the order of magnitude of the expected effect for different scenarios. It is also shown from the next order term ( 1 r 2 ) that non-radiative (but time dependent) spacetimes will produce a gyroscope precession of that order, providing thereby "observational" evidence for the violation of the Huygens's principle.
Geodesics of the hyperbolically symmetric black hole
Physical review, 2020
We carry out a systematic study on the motion of test particles in the region inner to the horizon of a hyperbolically symmetric black hole. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the spherically symmetric case. It is found that test particles experience a repulsive force within the horizon, which prevents them to reach the center. These results are obtained for radially moving particles as well as for particles moving in the θ − R subspace. To complement our study we calculate the precession of a gyroscope moving along a circular path (non-geodesic) within the horizon. We obtain that the precession of the gyroscope is retrograde in the rotating frame, unlike the precession close to the horizon (R = 2m + ǫ) in the Schwarzschild spacetime, which is forward.
Gyroscope precession and general relativity
American Journal of Physics, 2001
Precession of a gyroscope in the presence of a gravitational field is of considerable interest, on account of the soon to be launched satellite test and because of its connection to Mach's principle. Nevertheless, this topic is not generally covered in the curriculum because of the mathematical sophistication required. We examine some of the simple physics involved and argue that by examining simple graviton-elementary particle couplings one can easily understand this phenomenon.
Behavior of a test gyroscope moving towards a rotating traversable wormhole
Journal of Cosmology and Astroparticle Physics, 2017
The geodesic structure of the Teo wormhole is briefly discussed and some observables are derived that promise to be of use in detecting a rotating traversable wormhole indirectly, if it does exist. We also deduce the exact Lense-Thirring (LT) precession frequency of a test gyroscope moving toward a rotating traversable Teo wormhole. The precession frequency diverges on the ergoregion, a behavior intimately related to and governed by the geometry of the ergoregion, analogous to the situation in a Kerr spacetime. Interestingly, it turns out that here the LT precession is inversely proportional to the angular momentum (a) of the wormhole along the pole and around it in the strong gravity regime, a behavior contrasting with its direct variation with a in the case of other compact objects. In fact, divergence of LT precession inside the ergoregion can also be avoided if the gyro moves with a non-zero angular velocity in a certain range. As a result, the spin precession frequency of the gyro can be made finite throughout its whole path, even very close to the throat, during its travel to the wormhole. Furthermore, it is evident from our formulation that this spin precession not only arises due to curvature or rotation of the spacetime but also due to the non-zero angular velocity of the spin when it does not move along a geodesic in the strong gravity regime. If in the future, interstellar travel indeed becomes possible through a wormhole or at least in its vicinity, our results would prove useful in determining the behavior of a test gyroscope which is known to serve as a fundamental navigation device.
Gödel spacetime: Planar geodesics and gyroscope precession
Physical Review D
We study elliptic-like geodesic motion on hyperplanes orthogonal to the cylindrical symmetry axes of the Gödel spacetime by using an eccentricity-semi-latus rectum parametrization which is familiar from the Newtonian description of a two-body system. We compute several quantities which summarize the main features of the motion, namely the coordinate time and proper time periods of the radial motion, the frequency of the azimuthal motion, the full variation of the azimuthal angle over a period, etc. Exact as well as approximate (i.e., Taylor-expanded in the limit of small eccentricity) analytic expressions of all these quantities are obtained. Finally, we consider their application to the gyroscope precession frequency along these orbits, generalizing the existing results for the circular case.
Orbital Motion of a test particle around a Schwarzschild's Black Hole in STVG gravity
Cornell University - arXiv, 2022
In this article, we have examined the existence of a static spherically symmetric solution in the Scalar Tensor Vector Gravity (STVG) and investigated its horizon distances to develop boundary limitations for our test particle. We have computed the Kretschmann invariant of the metric to study the singularities and verify that it reduces to general relativity's Kretschmann invariant as α → 0. Further, we investigated the orbital motion of a time-like and light-like test particle around the static solution by developing an effective potential and the radius of the innermost stable circular orbit(ISCO).
Radially Falling Reference Frames in Gravity
none, 2019
We find a singularity-free coordinate system describing the Schwarzchild solution by transforming to the reference frame which is everywhere in free fall, which is of course a non-rigid frame of reference. To develop some intuition for such a reference frame we first make the transformation for the non-relativistic case and find that it is identical to the relativistic solution in this frame. Singularity free descriptions of the Schwarzchild solution have been found before, but the coordinates used had obscure physical while our coordinates have simple and direct meanings. In the course of our investigation, we discover the principle that relativistic gravity is essentially non-static, and the natural tendency to study statics before dynamics should be forsworn in favor of finding singularity-free solutions. (Of course, singularities at points where the assumed energy-momentum tensor is singular are permitted.)
Geodetic Motion Around Rotating Black Hole in Nonlocal Gravity
arXiv: General Relativity and Quantum Cosmology, 2019
Recently the non-local gravity theory has come out to be a good candidate for an effective field theory of quantum gravity and also it can provide rich phenomenology to understand late-time accelerating expansion of the universe. For any valid theory of gravity, it has to surmount solar system tests as well as strong field tests. Having motivations to prepare the framework for the strong field test of the modified gravity using Extreme Mass Ratio Inspirals(EMRIs), here we try to obtain the metric for Kerr-like blackhole for a non-local gravity model known as RR model and calculate the shift in orbital frequencies of a test particle moving around the blackhole. We also derive the metric for a rotating object in the weak gravity regime for the same model.
Rotating gravitational lenses: a kinematic approach
This paper uses the Kerr geodesic equations for massless particles to derive an acceleration vector in both Boyer-Lindquist and Cartesian coordinates. As a special case, the Schwarzschild acceleration due to a non-rotating mass has a particularly simple and elegant form in Cartesian coordinates. Using forward integration, these equations are used to plot the caustic pattern due to a system consisting of a rotating point mass with a smaller non-rotating planet. Additionally, first and second order approximations to the paths are identified, which allows for fast approximations of paths, deflection angles and travel-time delays.
Gyroscope precession in cylindrically symmetric spacetimes
Classical and Quantum Gravity, 2000
We present calculations of gyroscope precession in spacetimes described by Levi-Civita and Lewis metrics, under different circumstances. By doing so we are able to establish a link between the parameters of the metrics and observable quantities, providing thereby a physical interpretation for those parameters, without specifying the source of the field.
Determination of the angular momentum of the Kerr black hole from equatorial geodesic motion
Journal of Cosmology and Astroparticle Physics
We present a method to determine the angular momentum of a black hole based on observations of the trajectories of the bodies in the Kerr spacetime. We use the Hamilton equations to describe the dynamics of a particle and present results for equatorial trajectories, obtaining an algebraic equation for the magnitude of the black hole's angular momentum with coefficients given by observable quantities. We tailor a numerical code to solve the dynamical equations and use it to generate synthetic data. We apply the method in some representative examples, obtaining the parameters of the trajectories as well as the black hole's angular momentum in good agreement with the input data.
Since the advent of the General Theory of Relativity by Albert Einstein by 1915, the concepts of singularity and the concept of infinite curvature as a black hole has become a widely discussed concept. For many years, astronomers and astrophysicists have discussed the possibility of such objects existing and both theoretical work as well as observational work has been conducted on the subject. In fact, many eminent scientists such as Schwarzchild, Kerr, Penrose, Hawking have explored the concept of black holes and all that it pertains. Even with the scientific and observational capabilities of the 21st century, the concept of black holes still remains a mystery to some extent. An object with highly strong gravitational field such that even light cannot escape from its surface and with a singularity at its centre is termed as a black hole. Here we discuss the different aspects related to these black holes, the theoretical developments on the subject, nature of the space-time around black holes as predicted by the mathematical theory of black holes, and also, the observational advancements in this field to date. Black holes have been seen gaining ever more attention since the recent discoveries of black holes at the centre of galaxies like our own. Now it is widely starting to be believed that the supermassive black holes in galactic centers are the central engines for any galaxy formation. Black holes have finally started to enjoy the attention that they long deserved. They are no more the hidden monsters feeding away stellar companions, but on the contrary, they are now the objects closely related to the origin of galaxies and to the large scale structure formation in the universe. In case of stellar black holes, we know that it is the result of a gravitational collapse of a star (with mass M>3 M_sun) at the end of its evolution. Such a continuous gravitational collapse leads to an implosion and subsequent formation of a subspace called the event horizon of the black hole. A limiting radius r_g= 2GM⁄c^2 , called the gravitational radius or the event horizon, for a black hole of mass M exists such that the escape velocity of any particle leaving its boundary is equal to the speed of light. Thus no signal or particles can ever leave the boundary of the black hole. This makes it a challenge to identify a black hole in space, since it does not reflect or produce any signals to detect its presence. Einstein’s theory of Gravitation has successfully provided a framework to study the nature of space-time around black holes. We would intend to have a close look at the physical characteristics of space-time in the vicinity of stellar black holes and calculate the spacecraft trajectories in such extremely curved spacetimes. We conduct a numerical and computational study of the geodesics in strongly curved spacetime using the appropriate mathematical equations describing motion in these spacetimes as elaborated in the black hole theory.
Acceleration of particles by rotating black holes: Near-horizon geometry and kinematics
Gravitation and Cosmology, 2012
Nowadays, the effect of infinite energy in the centre of mass frame due to nearhorizon collisions attracts much attention.We show generality of the effect combining two seemingly completely different approaches based on properties of a particle with respect to its local light cone and calculating its velocity in the locally nonrotaing frame directly. In doing so, we do not assume that particles move along geodesics.
Radial Free Fall into Schwarzschild Black Holes Using the Generalized Metric
The problem of radial free fall one of the most interesting problems in black holes physics. Using the Generalized Metricusing the velocity and acceleration equations of radial free falling massive particle has been formulated. Applying weak field approximation of generalized equations of velocity and acceleration,the same GR equations for acceleration and velocity obtained