Effective potential and stable circular orbits in magnetized Schwarzschild spacetime

LIU Wenfang; ZHOU Naying; ZHANG Hongxing; SUN Xin

doi:10.12299/jsues.22-0338

Volume 37 Issue 3

Sep. 2023

Turn off MathJax

Article Contents

Article Navigation > Journal of Shanghai University of Engineering Science > 2023 > 37(3): 247-254, 334

LIU Wenfang, ZHOU Naying, ZHANG Hongxing, SUN Xin. Effective potential and stable circular orbits in magnetized Schwarzschild spacetime[J]. Journal of Shanghai University of Engineering Science, 2023, 37(3): 247-254, 334. doi: 10.12299/jsues.22-0338

Citation:

LIU Wenfang, ZHOU Naying, ZHANG Hongxing, SUN Xin. Effective potential and stable circular orbits in magnetized Schwarzschild spacetime[J]. Journal of Shanghai University of Engineering Science, 2023, 37(3): 247-254, 334. doi: 10.12299/jsues.22-0338

Citation:

PDF( 2189 KB)

Effective potential and stable circular orbits in magnetized Schwarzschild spacetime

doi: 10.12299/jsues.22-0338

LIU Wenfang^{1a, 1b
,},
ZHOU Naying^{1a, 1b
,},
ZHANG Hongxing^{1a, 1b},
SUN Xin²

1a.
School of Mathematics, Physics and Statistics
1b.
Center of Application and Research of Computational Physics, Shanghai University of Engineering Science, Shanghai 201620, China
2.
School of Physical Science and Technology, Guangxi University, Nanning 530004, China

Received Date: 2022-11-11
Publish Date: 2023-09-30

Abstract

Abstract

An effective potential in the equatorial plane was used to study the circular motion of charged particles near the Schwarzschild black hole immersed into an external magnetic field. It is found that no stable circular orbits exist for some angular momenta and small magnetic fields. However, the stable circular orbit easily occurs and has small radius when the magnetic induction increases. The radius of stable circular orbit increases with an increase of the angular momentum. The relation between the angular momentum and a radial distance can show the features of circular orbits, as the relation between the effective potential and the radial distance can.
- black hole,
- magnetic field,
- effective potential,
- stable circular orbits

FullText(HTML)

References(27)

References

[1]	EINSTEIN A. Sitzungsberichte der köiglich preuschen $ \beta $ akademie der wissenschaften [M]. Berlin: Deutsche Akademie der Wissenschaften zu Berlin, 1915: 425.
[2]	EINSTEIN A, SITZUNGSBER K. Eine neue formale deutung der maxwellschen feldgleichungen der elektrodynamik [M]. New York: Sons John Wiley and Sons, 1916: 688.
[3]	EATOUGH R P, FALCKE H, KARUPPUSAMY R. A strong magnetic field around the supermassive black hole at the centre of the Galaxy[J] . Nature,2013,501:391 − 394. doi: 10.1038/nature12499
[4]	ZHANG H X, ZHOU N Y, LIU W F, et al. Charged particle motions near non-Schwarzschild black holes with external magnetic fields in modified theories of gravity[J] . Universe,2021,7(12):488. doi: 10.3390/universe7120488
[5]	SUN W, WANG Y, LIU F Y, et al. Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole[J] . European Physical Journal C,2021,81:785.
[6]	LI D, WANG Y, DENG C, et al. Coherent post-Newtonian Lagrangian equations of motion[J] . European Physical Journal Plus,2020,135:390. doi: 10.1140/epjp/s13360-020-00407-7
[7]	WU X, ZHANG H. Chaotic dynamics in a superposed Weyl spacetime[J] . The Astrophysical Journal,2006,652(2):1466. doi: 10.1086/508129
[8]	WANG Y, SUN W, LIU F Y, et al. Construction of explicit symplectic integrators in general relativity. I. Schwarzschild black holes[J] . The Astrophysical Journal,2021,907(2):66. doi: 10.3847/1538-4357/abcb8d
[9]	WANG Y, SUN W, LIU F Y, et al. Construction of explicit symplectic integrators in general relativity. III. Reissner–Nordström-(anti)-de sitter black holes[J] . The Astrophysical Journal Supplement Series,2021,254(1):8. doi: 10.3847/1538-4365/abf116
[10]	WU X, WANG Y, SUN W, et al. Construction of explicit symplectic integrators in general relativity. IV. Kerr black holes[J] . The Astrophysical Journal,2021,914(1):63. doi: 10.3847/1538-4357/abfc45
[11]	ZHOU N Y, ZHANG H X, LIU W F, et al. A note on the construction of explicit symplectic integrators for Schwarzschild spacetimes[J] . The Astrophysical Journal,2022,927(2):160. doi: 10.3847/1538-4357/ac497f
[12]	YANG D Q, CAO W F, ZHOU N Y, et al. Chaos in a magnetized modified gravity Schwarzschild spacetime[J] . Universe,2022,8(6):320. doi: 10.3390/universe8060320
[13]	HU A R, HANG G Q. Dynamics of charged particles in the magnetized γ spacetime[J] . European Physical Journal Plus,2021,136:1210. doi: 10.1140/epjp/s13360-021-02194-1
[14]	SUN X, WU X, WANG Y, et al. Dynamics of charged particles moving around Kerr black hole with inductive charge and external magnetic field[J] . Universe,2021,7:410. doi: 10.3390/universe7110410
[15]	YI M, WU X. Dynamics of charged particles around a magnetically deformed Schwarzschild black hole[J] . Physica Scripta,2020,95:085008. doi: 10.1088/1402-4896/aba4c2
[16]	NARAYAN R, JOHNSON M D, GAMMIE C F. The shadow of a spherically accreting black hole[J] . The Astrophysical Journal Letters,2019,885:L33. doi: 10.3847/2041-8213/ab518c
[17]	GRALLA S E, HOLZ D E, WALD R M. Black hole shadows, photon rings, and lensing rings[J] . Physical Review D,2019,100:024018. doi: 10.1103/PhysRevD.100.024018
[18]	PENG J, GUO M Y, FENG X H. Influence of quantum correction on the black hole shadows, photon rings and lensing rings[J] . Chinese Physics C,2021,45:085103.
[19]	HU S Y, DENG C, LI D, et al. Observational signatures of Schwarzschild-MOG black holes in scalar -tensor -vector gravity: shadows and rings with different accretions[J] . European Physical Journal C,2022,82:885. doi: 10.1140/epjc/s10052-022-10868-y
[20]	ZHANG H X, ZHOU N Y, LIU W F, et al. Equivalence between two charged black holes in dynamics of orbits outside the event horizons[J] . General Relativity and Gravitation,2022,54:110. doi: 10.1007/s10714-022-02998-1
[21]	CAO W F, LIU W F, WU X. Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field[J] . Physical Review D,2022,105:124039. doi: 10.1103/PhysRevD.105.124039
[22]	KOVÁŘ J, SLANÝ P, CREMASCHINI C, et al. Electrically charged matter in rigid rotation around magnetized black hole[J] . Physical Review D,2014,90:044029. doi: 10.1103/PhysRevD.90.044029
[23]	HAWLEY J F, BALBUS S A. A powerful local shear instability in weakly magnetized disks. I-Linear analysis. II-Nonlinear evolution[J] . The Astrophysical Journal,1991,376:223. doi: 10.1086/170271
[24]	CAEMASCHINI C, STUCHLÍK Z. Magnetic loop generation by collisionless gravitationally bound plasmas in axisymmetric tori[J] . Physical Review E,2013,87:043113. doi: 10.1103/PhysRevE.87.043113
[25]	KOLOŠ. Quasi-harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform magnetic field[J] . Classical Quantum Gravity,2015,32:165009. doi: 10.1088/0264-9381/32/16/165009
[26]	WANG Y, SUN W, LIU F Y, et al. Construction of explicit symplectic integrators in general relativity. II. Reissner–Nordström black holes[J] . The Astrophysical Journal,2021,909(1):22. doi: 10.3847/1538-4357/abd701
[27]	Wald R M. General Relativity [M]. Chicago: University of Chicago Press, 1984: 317.