Universe

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11 pages, 296 KiB

Open AccessArticle

On the Euler–Type Gravitomagnetic Orbital Effects in the Field of a Precessing Body

by Lorenzo Iorio

Universe 2024, 10(9), 375; https://doi.org/10.3390/universe10090375 - 21 Sep 2024

Cited by 1 | Viewed by 519

To the first post–Newtonian order, the gravitational action of mass–energy currents is encoded by the off–diagonal gravitomagnetic components of the spacetime metric tensor. If they are time–dependent, a further acceleration enters the equations of motion of a moving test particle. Let the source [...] Read more.

To the first post–Newtonian order, the gravitational action of mass–energy currents is encoded by the off–diagonal gravitomagnetic components of the spacetime metric tensor. If they are time–dependent, a further acceleration enters the equations of motion of a moving test particle. Let the source of the gravitational field be an isolated, massive body rigidly rotating whose spin angular momentum experiences a slow precessional motion. The impact of the aforementioned acceleration on the orbital motion of a test particle is analytically worked out in full generality. The resulting averaged rates of change are valid for any orbital configuration of the satellite; furthermore, they hold for an arbitrary orientation of the precessional velocity vector of the spin of the central object. In general, all the orbital elements, with the exception of the mean anomaly at epoch, undergo nonvanishing long–term variations which, in the case of the Juno spacecraft currently orbiting Jupiter and the double pulsar PSR J0737–3039 A/B turn out to be quite small. Such effects might become much more relevant in a star–supermassive black hole scenario; as an example, the relative change of the semimajor axis of a putative test particle orbiting a Kerr black hole as massive as the one at the Galactic Centre at, say, 100 Schwarzschild radii may amount up to about

7 %

per year if the hole’s spin precessional frequency is

10 %

of the particle’s orbital one. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

18 pages, 8503 KiB

Open AccessArticle

Effects of Two Quantum Correction Parameters on Chaotic Dynamics of Particles near Renormalized Group Improved Schwarzschild Black Holes

by Junjie Lu and Xin Wu

Universe 2024, 10(7), 277; https://doi.org/10.3390/universe10070277 - 26 Jun 2024

Viewed by 1274

Abstract

A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter

γ

represents the identification of cutoff of the distance scale, and another parameter

Ω

stems from nonperturbative renormalization group theory. The two parameters are constrained by the data [...] Read more.

A renormalized group improved Schwarzschild black hole spacetime contains two quantum correction parameters. One parameter

γ

represents the identification of cutoff of the distance scale, and another parameter

Ω

stems from nonperturbative renormalization group theory. The two parameters are constrained by the data from the shadow of M87* central black hole. The dynamics of electrically charged test particles around the black hole are integrable. However, when the black hole is immersed in an external asymptotically uniform magnetic field, the dynamics are not integrable and may allow for the occurrence of chaos. Employing an explicit symplectic integrator, we survey the contributions of the two parameters to the chaotic dynamical behavior. It is found that a small change of the parameter

γ

constrained by the shadow of M87* black hole has an almost negligible effect on the dynamical transition of particles from order to chaos. However, a small decrease in the parameter

Ω

leads to an enhancement in the strength of chaos from the global phase space structure. A theoretical interpretation is given to the different contributions. The term with the parameter

Ω

dominates the term with the parameter

γ

, even if the two parameters have same values. In particular, the parameter

Ω

acts as a repulsive force, and its decrease means a weakening of the repulsive force or equivalently enhancing the attractive force from the black hole. On the other hand, there is a positive Lyapunov exponent that is universally given by the surface gravity of the black hole when

Ω \geq 0

is small and the external magnetic field vanishes. In this case, the horizon would influence chaotic behavior in the motion of charged particles around the black hole surrounded by the external magnetic field. This point can explain why a smaller value of the renormalization group parameter would much easily induce chaos than a larger value. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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12 pages, 8396 KiB

Open AccessEditor’s ChoiceArticle

Effects of Coupling Constants on Chaos of Charged Particles in the Einstein–Æther Theory

by Caiyu Liu and Xin Wu

Universe 2023, 9(8), 365; https://doi.org/10.3390/universe9080365 - 7 Aug 2023

Cited by 3 | Viewed by 1114

Abstract

There are two free coupling parameters

c_{13}

and

c_{14}

in the Einstein–Æther metric describing a non-rotating black hole. This metric is the Reissner–Nordström black hole solution when

0 \leq 2 c_{13} < c_{14} < 2

, but it is [...] Read more.

There are two free coupling parameters

c_{13}

and

c_{14}

in the Einstein–Æther metric describing a non-rotating black hole. This metric is the Reissner–Nordström black hole solution when

0 \leq 2 c_{13} < c_{14} < 2

, but it is not for

0 \leq c_{14} < 2 c_{13} < 2

. When the black hole is immersed in an external asymptotically uniform magnetic field, the Hamiltonian system describing the motion of charged particles around the black hole is not integrable; however, the Hamiltonian allows for the construction of explicit symplectic integrators. The proposed fourth-order explicit symplectic scheme is used to investigate the dynamics of charged particles because it exhibits excellent long-term performance in conserving the Hamiltonian. No universal rule can be given to the dependence of regular and chaotic dynamics on varying one or two parameters

c_{13}

and

c_{14}

in the two cases of

0 \leq 2 c_{13} < c_{14} < 2

and

0 \leq c_{14} < 2 c_{13} < 2

. The distributions of order and chaos in the binary parameter space

(c_{13}, c_{14})

rely on different combinations of the other parameters and the initial conditions. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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30 pages, 4164 KiB

Open AccessArticle

Analysis of Resonant Periodic Orbits in the Framework of the Perturbed Restricted Three Bodies Problem

by Bhavika M. Patel, Niraj M. Pathak and Elbaz I. Abouelmagd

Universe 2023, 9(5), 239; https://doi.org/10.3390/universe9050239 - 18 May 2023

Cited by 2 | Viewed by 1228

Abstract

In this work, the perturbed equations of motion of the infinitesimal body are constructed in the framework of the circular restricted three-body problem when the main two bodies are oblate and radiating. Under the perturbations effects of the oblateness and the radiation pressure [...] Read more.

In this work, the perturbed equations of motion of the infinitesimal body are constructed in the framework of the circular restricted three-body problem when the main two bodies are oblate and radiating. Under the perturbations effects of the oblateness and the radiation pressure the positions of collinear Lagrange points are evaluated, the interior and exterior first-order resonant periodic orbits are also studied. In addition, the initial positions of the periodic orbits and the size of loops have been estimated under these effects. Thus, the characteristics of periodic orbits have been studied under the combine effects of two, three and four perturbations for all the possible combinations of the perturbed parameters. The different order of resonant periodic orbits have been also analysed under the effects of Jacobi constant, mass factor, order of resonance and number of loops. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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16 pages, 2659 KiB

Open AccessArticle

Strong Deflection Gravitational Lensing for the Photons Coupled to the Weyl Tensor in a Conformal Gravity Black Hole

by Ghulam Abbas, Ali Övgün, Asif Mahmood and Muhammad Zubair

Universe 2023, 9(3), 130; https://doi.org/10.3390/universe9030130 - 2 Mar 2023

Viewed by 1435

Abstract

In the present paper, strong deflection gravitational lensing is studied in a conformal gravity black hole. With the help of geometric optics limits, we have formulated the light cone conditions for the photons coupled to the Weyl tensor in a conformal gravity black [...] Read more.

In the present paper, strong deflection gravitational lensing is studied in a conformal gravity black hole. With the help of geometric optics limits, we have formulated the light cone conditions for the photons coupled to the Weyl tensor in a conformal gravity black hole. It is explicitly found that strong deflection gravitational lensing depends on the coupling with the Weyl tensor, the polarization directions, and the black hole configuration parameters. We have applied the results of the strong deflection gravitational lensing to the supermassive black holes

S g r A^{*}

and

M 87^{*}

and studied the possibility of encountering quantum improvement. It is not practicable to recognize similar black holes through the strong deflection gravitational lensing observables in the near future, except for the possible size of the black hole’s shadow. We also notice that by directly adopting the constraint of the measured shadow of

M 87^{*}

, the quantum effect demands immense care. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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7 pages, 314 KiB

Open AccessCommunication

Might the 2PN Perihelion Precession of Mercury Become Measurable in the Next Future?

by Lorenzo Iorio

Universe 2023, 9(1), 37; https://doi.org/10.3390/universe9010037 - 4 Jan 2023

Cited by 1 | Viewed by 1468

Abstract

The Hermean average perihelion rate

{\dot{ω}}^{2} PN

, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from

- 18

to

- 4

microarcseconds per century

(μ as {cty}^{- 1})

[...] Read more.

The Hermean average perihelion rate

{\dot{ω}}^{2} PN

, calculated to the second post-Newtonian (2PN) order with the Gauss perturbing equations and the osculating Keplerian orbital elements, ranges from

- 18

to

- 4

microarcseconds per century

(μ as {cty}^{- 1})

, depending on the true anomaly at epoch

f_{0}

. It is the sum of four contributions: one of them is the direct consequence of the 2PN acceleration entering the equations of motion, while the other three are indirect effects of the 1PN component of the Sun’s gravitational field. An evaluation of the merely formal uncertainty of the experimental Mercury’s perihelion rate

{\dot{ω}}_{\exp}

recently published by the present author, based on 51 years of radiotechnical data processed with the EPM2017 planetary ephemerides by the astronomers E.V. Pitjeva and N.P. Pitjev, is

σ_{{\dot{ω}}_{\exp}} ≃ 8 μ as {cty}^{- 1}

, corresponding to a relative accuracy of

2 \times 10^{- 7}

for the combination

(2 + 2 γ - β) / 3

of the PPN parameters

β

and

γ

scaling the well known 1PN perihelion precession. In fact, the realistic uncertainty may be up to ≃10–50 times larger, despite reprocessing the now available raw data of the former MESSENGER mission with a recently improved solar corona model should ameliorate our knowledge of the Hermean orbit. The BepiColombo spacecraft, currently en route to Mercury, might reach a

≃ 10^{- 7}

accuracy level in constraining

β

and

γ

in an extended mission, despite

≃ 10^{- 6}

seems more likely according to most of the simulations currently available in the literature. Thus, it might be that in the not-too-distant future, it will be necessary to include the 2PN acceleration in the Solar System’s dynamics as well. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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12 pages, 639 KiB

Open AccessArticle

Quantum Hairy Black Hole Formation and Horizon Quantum Mechanics

by Rogerio Teixeira Cavalcanti and Julio Marny Hoff da Silva

Universe 2023, 9(1), 23; https://doi.org/10.3390/universe9010023 - 30 Dec 2022

Cited by 1 | Viewed by 1506

Abstract

After introducing the gravitational decoupling method and the hairy black hole recently derived from it, we investigate the formation of quantum hairy black holes by applying the horizon quantum mechanics formalism. It enables us to determine how external fields, characterized by hairy parameters, [...] Read more.

After introducing the gravitational decoupling method and the hairy black hole recently derived from it, we investigate the formation of quantum hairy black holes by applying the horizon quantum mechanics formalism. It enables us to determine how external fields, characterized by hairy parameters, affect the probability of spherically symmetric black hole formation and the generalized uncertainty principle. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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16 pages, 4642 KiB

Open AccessArticle

Chaos in a Magnetized Brane-World Spacetime Using Explicit Symplectic Integrators

by Airong Hu and Guoqing Huang

Universe 2022, 8(7), 369; https://doi.org/10.3390/universe8070369 - 4 Jul 2022

Cited by 2 | Viewed by 1653

Abstract

A brane-world metric with an external magnetic field is a modified theory of gravity. It is suitable for the description of compact sources on the brane such as stars and black holes. We design a class of explicit symplectic integrators for this spacetime [...] Read more.

A brane-world metric with an external magnetic field is a modified theory of gravity. It is suitable for the description of compact sources on the brane such as stars and black holes. We design a class of explicit symplectic integrators for this spacetime and use one of the integrators to investigate how variations of the parameters affect the motion of test particles. When the magnetic field does not vanish, the integrability of the system is destroyed. Thus, the onset of chaos can be allowed under some circumstances. Chaos easily occurs when the electromagnetic parameter becomes large enough. Dark matter acts as a gravitational force, so that chaotic motion can become more obvious as dark matter increases. The gravity of the black hole is weakened with an increasing positive cosmological parameter; therefore, the extent of chaos can be also strengthened. The proposed symplectic integrator is applied to a ray-tracing method and the study of such chaotic dynamics will be a possible reference for future studies of brane-world black hole shadows with chaotic patterns of self-similar fractal structures based on the Event Horizon Telescope data for M87* and Sagittarius A*. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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12 pages, 3691 KiB

Open AccessArticle

Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime

by Daqi Yang, Wenfu Cao, Naying Zhou, Hongxing Zhang, Wenfang Liu and Xin Wu

Universe 2022, 8(6), 320; https://doi.org/10.3390/universe8060320 - 8 Jun 2022

Cited by 18 | Viewed by 1848

Abstract

Based on the scalar–tensor–vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational [...] Read more.

Based on the scalar–tensor–vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational constant and the black hole charge. In this sense, the modified gravity parameter acts as not only an enhanced gravitational effect but also a gravitational repulsive force contribution to a test particle moving around the black hole. Because the modified Schwarzschild spacetime is static spherical symmetric, it is integrable. However, the spherical symmetry and the integrability are destroyed when the black hole is immersed in an external asymptotic uniform magnetic field and the particle is charged. Although the magnetized modified Schwarzschild spacetime is nonintegrable and inseparable, it allows for the application of explicit symplectic integrators when its Hamiltonian is split into five explicitly integrable parts. Taking one of the proposed explicit symplectic integrators and the techniques of Poincaré sections and fast Lyapunov indicators as numerical tools, we show that the charged particle can have chaotic motions under some circumstances. Chaos is strengthened with an increase of the modified gravity parameter from the global phase space structures. There are similar results when the magnetic field parameter and the particle energy increase. However, an increase of the particle angular momentum weakens the strength of chaos. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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23 pages, 1022 KiB

Open AccessArticle

Bound Orbits and Epicyclic Motions around Renormalization Group Improved Schwarzschild Black Holes

by Hou-Yu Lin and Xue-Mei Deng

Universe 2022, 8(5), 278; https://doi.org/10.3390/universe8050278 - 10 May 2022

Cited by 21 | Viewed by 2795

Abstract

We study timelike particles’ bound orbits around renormalization group improved Schwarzschild black holes (RGISBHs), which originate from renormalization group improvement of the Einstein–Hilbert action by using the running Newton constant. By considering the secular periastron precession for the timelike particles orbiting around RGISBHs, [...] Read more.

We study timelike particles’ bound orbits around renormalization group improved Schwarzschild black holes (RGISBHs), which originate from renormalization group improvement of the Einstein–Hilbert action by using the running Newton constant. By considering the secular periastron precession for the timelike particles orbiting around RGISBHs, we found that it is not feasible to distinguish such black holes from Schwarzschild ones in the weak gravitational field. However, in the strong gravitational field, periodic orbits for the particles are investigated by employing a taxonomy. This suggests that the variation of the parameters in RGISBHs can change the taxonomy. This leads to a transition from periodic motion around Schwarzschild black holes to a quasi-periodic motion around these black holes. After that, the epicyclic motions of charged particles around RGISBHs immersed in an external asymptotically uniform magnetic field are taken into account with respect to the observed twin peak quasi-periodic oscillations’ frequencies. The epicyclic motions of charged particles around such black holes in the external magnetic field can give one possible explanation for the 3:2 resonance in three low-mass X-ray binaries. Our results might provide some hints to distinguish RGISBHs from the classical black holes by using periodic orbits and epicyclic motions around the strong gravitational field. Full article

(This article belongs to the Special Issue Testing General Relativity from the Solar System, Black Holes to Cosmology)

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