Gyroscopic precession in the vicinity of a static blackhole’s event horizon (original) (raw)
Related papers
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 motion of a gyroscope freely falling into a Schwarzschild black hole
General Relativity and Gravitation, 1991
In this note we investigate the motion of the axis of a gyroscope freely falling along the radial geodesic in Schwarzschild space-time. It is shown that the gyroscope's axis rotates to the radial direction in the orthonormal frame as it falls into the black hole.
Spin precession in a black hole and naked singularity spacetimes
Physical Review D, 2017
We propose here a specific criterion to address the existence or otherwise of Kerr naked singularities, in terms of the precession of the spin of a test gyroscope due to the frame dragging by the central spinning body. We show that there is indeed an important characteristic difference in the behavior of gyro spin precession frequency in the limit of approach to these compact objects, and this can be used, in principle, to differentiate the naked singularity from black hole. Specifically, if gyroscopes are fixed all along the polar axis upto the horizon of a Kerr black hole, the precession frequency becomes arbitrarily high, blowing up as the event horizon is approached. On the other hand, in the case of naked singularity, this frequency remains always finite and well-behaved. Interestingly, this behavior is intimately related to and is governed by the geometry of the ergoregion in each of these cases which we analyze here. One intriguing behavior that emerges is, in the Kerr naked singularity case, the Lense-Thirring precession frequency (ΩLT) of the gyroscope due to frame-dragging effect decreases as (ΩLT ∝ r) after reaching a maximum, in the limit of r = 0, as opposed to r −3 dependence in all other known astrophysical cases.
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.
On gravitomagnetic precession around black holes
Monthly Notices of the Royal Astronomical Society, 1999
We compute exactly the frequency of Lense-Thirring precession for point masses in the Kerr metric, for arbitrary black hole mass and specific angular momentum. We show that this frequency, for point masses at or close to the innermost stable orbit, and for holes with moderate to extreme rotation, is less than, but comparable to the rotation frequency. Thus, if the quasi-periodic oscillations observed in the modulation of the Xray flux from some black holes candidates, BHCs, are due to Lense-Thirring precession of orbiting material, we predict that a separate, distinct QPO ought to be observed in each object.
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.
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.
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.
A Thought Experiment to Distinguish the Kerr Black Hole and Over-spinning Singularities
2016
We propose a thought experiment here to distinguish an over-spinning Kerr singularity from a Kerr black hole, using the gyroscopic precession due to the frame-dragging effect. We show that there is an important characteristic difference in behavior of the gyroscope precession frequency for these objects, which can be used to distinguish one from the other. Specifically, if we lower the gyroscope along the pole of the Kerr black hole, the precession frequency becomes arbitrarily high, blowing up as the event horizon is approached. However, in the case of an over-spinning Kerr singularity, this frequency always remains finite and is fully well-behaved. It turns out that this behavior is intimately related to and governed by the nature of ergoregions in each of these cases. Interestingly, it turns out that in the over-spinning singularity case, the precession frequency (ΩLT) of the gyro decreases as (ΩLT ∝ r) after reaching a maximum, in the limit of approach to the singularity. In principle, such a behavior can be used to tell apart the black hole from a naked singularity.