Distinguishing Black Hole and Naked Singularity in MOG via Inertial Frame Dragging Effect (original) (raw)
Related papers
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.
Spin Precession in the Gravity Wave Analogue Black Hole Spacetime
Universe
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 ...
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.
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.
Mass and spin of a Kerr black hole in modified gravity and a test of the Kerr black hole hypothesis
In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular momentum, and the charge of the Kerr black hole solution in the scalar-tensor-vector gravity theory [known as the Kerr-MOG (modified gravity) black hole configuration]; we study in detail as well several properties of this solution such as the stationary limit surface, the event horizon, and the ergosphere, and conclude that the new deformation parameter α affects the geometry of the Kerr-MOG black hole significantly in addition to the ADM mass and spin parameters. Moreover, the ADM mass and black hole event horizon definitions allow us to set a novel upper bound on the deformation parameter and to reveal the correct upper bound on the black hole spin. We further find the geodesics of motion of stars and photons around the Kerr-MOG black hole. By using them we reveal the expressions for the mass and the rotation parameter of the Kerr-MOG black hole in terms of the red-and blueshifts of photons emitted by geodesic particles, i.e., by stars. These calculations supply a new and simple method to further test the general theory of relativity in its strong field limit: If the measured red-and blueshifts of photons exceed the bounds imposed by the general theory of relativity, then the black hole is not of Kerr type. It could also happen that the measurements are allowed by the Kerr-MOG metric, implying that the correct description of the dynamics of stars around a given black hole should be performed using MOG or another modified theory of gravity that correctly predicts the observations. In particular, this method can be applied to test the nature of the putative black hole hosted at the center of the Milky Way in the near future.
Mass and spin of a Kerr-MOG black hole and a test for the Kerr black hole hypothesis
2017
In this paper we compute the Arnowitt-Deser-Misner (ADM) mass, the angular momentum and the charge of the Kerr black hole solution in the scalar-tensor-vector gravity theory [known as the Kerr-MOG (modified-gravity) black hole configuration]; we study in detail as well several properties of this solution such as the stationary limit surface, the event horizon, and the ergosphere, and conclude that the new deformation parameter α affects the geometry of the Kerr-MOG black hole significantly in addition to the ADM mass and spin parameters. Moreover, the ADM mass and black hole event horizon definitions allow us to set a novel upper bound on the deformation parameter and to reveal the correct upper bound on the black hole spin. We further find the geodesics of motion of stars and photons around the Kerr-MOG black hole. By using them we reveal the expressions for the mass and the rotation parameter of the Kerr-MOG black hole in terms of the red-and blueshifts of photons emitted by geodesic particles, i.e., by stars. These calculations supply a new and simple method to further test the general theory of relativity in its strong field limit: If the measured redand blueshifts of photons exceed the bounds imposed by the general theory of relativity, then the black hole is not of Kerr type. It could also happen that the measurements are allowed by the Kerr-MOG metric, implying that the correct description of the dynamics of stars around a given black hole should be performed using MOG or another modified theory of gravity that correctly predicts the observations. In particular, this method can be applied to test the nature of the putative black hole hosted at the center of the Milky Way in the near future.
2022
In this work, we elaborate on the development of a general relativistic formalism that allows one to analytically express the mass and spin parameters of the Kerr black hole in terms of observational data: the total redshift and blueshift of photons emitted by geodesic massive particles revolving the black hole and their orbital parameters. Thus, we present concise closed formulas for the mass and spin parameters of the Kerr black hole in terms of few directly observed quantities in the case of equatorial circular orbits either when the black hole is static or is moving with respect to a distant observer. Furthermore, we incorporate the gravitational dragging effect generated by the rotating nature of the Kerr black hole into the analysis and elucidate its non-trivial contribution to the expression for the light bending parameter and the frequency shifts of photons emitted by orbiting particles that renders simple symmetric expressions for the kinematic redshift and blueshift. We also incorporate the dependency of the frequency shift on the azimuthal angle, a fact that allows one to express the total redshift/blueshift along any point of the orbit of the revolving particle for the cases when the black hole is both static or moving with respect to us. These formulas allow one to compute the Kerr black hole parameters by applying this general relativistic formalism to astrophysical systems like the megamaser accretion disks orbiting supermassive black holes at the core of active galactic nuclei. Our results open a new window to implement parameter estimation studies to constrain black hole variables, and they can be generalized to black hole solutions beyond Einstein gravity.
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.
Strong gravity Lense–Thirring precession in Kerr and Kerr–Taub–NUT spacetimes
Classical and Quantum Gravity, 2014
An exact expression derived in the literature for the rate of dragging of inertial frames (Lense-Thirring (LT) precession) in a general stationary spacetime, is reviewed. The exact LT precession frequencies for Kerr, Kerr-Taub-NUT and Taub-NUT spacetimes are explicitly derived. Remarkably, in the case of the zero angular momentum Taub-NUT spacetime, the frame-dragging effect is shown not to vanish, when considered for spinning test gyroscopes. The result becomes sharper for the case of vanishing ADM mass of that spacetime. We clarify how our results are consistent with claims in the recent literature of null orbital plane precession for NUT spacetimes.