Abstract
In this work, we perform a detailed analysis of the equatorial motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime. By working out the orbit equation in the radial direction, we examine possible orbit types. We investigate the conditions for existence of bound orbits in causality-preserving region as well as the conditions for existence of circular orbits for charged and uncharged particles. We also study the effect of NUT parameter on Newtonian orbits. Finally, we give exact analytical solutions of equations of equatorial motion for a charged test particle.
Similar content being viewed by others
References
Newman, E., Tamburino, L., Unti, T.: Empty space generalization of the Schwarzschild metric. J. Math. Phys. 4, 915 (1963)
Demiański, M., Newman, E.T.: A combined Kerr–NUT solution of the Einstein field equations. Bull. Acad. Polon. Sci. Math. Astron. Phys. 14, 653 (1966)
Misner, C.W.: The flatter regions of Newman, Unti and Tamburino’s generalized Schwarzschild space. J. Math. Phys. 4, 924 (1963)
Bonnor, W.B.: A new interpretation of the NUT metric in general relativity. Math. Proc. Camb. Philos. Soc. 66, 145 (1969)
Miller, J.G.: Global analysis of the Kerr–Taub–NUT metric. J. Math. Phys. 14, 486 (1973)
Nouri-Zonoz, M., Lynden-Bell, D.: Gravitomagnetic lensing by NUT space. Mon. Not. Astron. Soc. 292, 714 (1997)
Lynden-Bell, D., Nouri-Zonoz, M.: Classical monopoles: Newton, NUT space, gravitomagnetic lensing and atomic spectra. Rev. Mod. Phys. 70, 427 (1998)
Bini, D., Cherubini, C., Jantzen, R.T.: On the interaction of massless fields with a gravitomagnetic monopole. Class. Quant. Grav. 19, 5265 (2002)
Bini, D., Cherubini, C., Jantzen, R.T., Mashhoon, B.: Gravitomagnetism in the Kerr–Newman–Taub–NUT spacetime. Class. Quant. Grav. 20, 457 (2003)
Aliev, A.N.: Rotating spacetimes with asymptotic non-flat structure and the gyromagnetic ratio. Phys. Rev. D 77, 044038 (2008)
Esmer, G.D.: Separability and hidden symmetries of Kerr–Taub–NUT spacetime in Kaluza–Klein theory. Grav. Cosmol. 19, 139 (2013)
Liu, C., Chen, S., Ding, C., Jing, J.: Particle acceleration on the background of the Kerr–Taub–NUT Spacetime. Phys. Lett. B 701, 285 (2011)
Zimmerman, R.L., Shahir, B.Y.: Geodesics for the NUT metric and gravitational monopoles. Gen. Relativ. Gravit. 21(8), 821 (1989)
Kagramanova, V., Kunz, J., Hackmann, E., Lämmerzahl, C.: Analytic treatment of complete and incomplete geodesics in Taub–NUT space–times. Phys. Rev. D 81, 124044 (2010)
Abdujabbarov, A.A., Ahmedov, B.J., Kagramanova, V.G.: Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge. Gen. Relativ. Gravit. 40, 2515 (2008)
Abdujabbarov, A.A., Ahmedov, B.J., Shaymatov, S.R., Rakhmatov, A.S.: Penrose process in Kerr–Taub–NUT spacetime. Astrophys. Space Sci. 334, 237 (2011)
Grenzebach, A., Perlick, V., Lämmerzahl, C.: Photon regions and shadows of Kerr–Newman–NUT black holes with a cosmological constant. Phys. Rev. D 89, 124004 (2014)
Pradhan, P.: Circular geodesics in the Kerr–Newman–Taub–NUT spacetime. Class. Quant. Grav. 32, 165001 (2015)
Jefremov, P.I., Perlick, V.: Circular motion in NUT space–time. Class. Quant. Grav. 33, 245014 (2016)
Clément, G., Guenouche, M.: Motion of charged particles in a NUTty Einstein–Maxwell spacetime and causality violation. Gen. Relativ. Gravit 50, 60 (2018)
Mukharjee, S., Chakraborty, S., Dadhich, N.: On some novel features of the Kerr–Newman–NUT spacetime. Eur. Phys. J. C 79, 161 (2019)
Abbott, B.P., et al.: LIGO Scientific and Virgo Collaborations, Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)
Grunau, S., Kagramanova, V.: Geodesics of electrically and magnetically charged test particles in the Reissner–Nordström spacetime: analytical solutions. Phys. Rev. D 83, 044009 (2011)
Flathmann, K., Grunau, S.: Analytic solutions of the geodesic equation for Einstein–Maxwell–dilaton–axion black holes. Phys. Rev. D 92, 104027 (2015)
Pugliese, D., Quevedo, H., Ruffini, R.: Motion of charged test particles in Reissner–Nordström spacetime. Phys. Rev. D 83, 104052 (2011)
Olivares, M., Saavedra, J., Leiva, C., Villanueva, J.: Motion of charged particles on the Reissner–Nordström (Anti)–de Sitter black holes. Mod. Phys. Lett. A 26, 2923 (2011)
Hackmann, E., Xu, H.: Charged particle motion in Kerr–Newmann space–times. Phys. Rev. D 87, 124030 (2013)
Soroushfar, S., Saffari, R., Kazempour, S., Grunau, S., Kunz, J.: Detailed study of geodesics in the Kerr–Newman–(A)dS spacetime and the rotating charged black hole spacetime in \(f(R)\) gravity. Phys. Rev. D 94, 024052 (2016)
Cebeci, H., Özdemir, N., Şentorun, S.: Motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime and analytical solutions. Phys. Rev. D 93, 104031 (2016)
Bardeen, J.M., Press, W.H., Teukolsky, S.A.: Rotating black holes: locally nonrotating frames, energy extraction and scalar synchrotron radiation. Astrophys. J. 178, 347 (1972)
Dadhich, N., Kale, P.P.: Equatorial circular geodesics in the Kerr–Newman geometry. J. Math. Phys. 18, 1727 (1977)
Pugliese, D., Quevedo, H., Ruffini, R.: Equatorial circular orbits of neutral test particles in the Kerr–Newman spacetime. Phys. Rev. D 88, 024042 (2013)
Stuchlík, Z., Slaný, P.: Equatorial circular orbits in the Kerr–de Sitter spacetimes. Phys. Rev. D 69, 064001 (2004)
Slaný, P., Pokorná, M., Stuchlík, Z.: Equatorial circular orbits in Kerr–anti-de Sitter spacetimes. Gen. Relativ. Gravit 45, 2611 (2013)
Wald, R.M.: General Relativity. The University of Chicago Press, Chicago (1984)
Chandrasekhar, S.: The Mathematical Theory of Black Holes. Clarendon Press, London (1983)
Carter, B.: Hamilton–Jacobi and Schrodinger separable solutions of Einstein’s equations. Commun. Math. Phys. 10, 280 (1968)
Carter, B.: Global structure of the Kerr family of gravitational fields. Phys. Rev. 174, 1559 (1968)
Debever, R., Kamran, N., Mc Lenaghan, R.G.: Exhaustive integration and a single expression for the general solution of the type D vacuum and electrovac field equations with cosmological constant for a nonsingular aligned Maxwell field. J. Math. Phys. 25, 1955 (1984)
Frolov, V.P., Krtous, P., Kubizňák, D.: Separability of Hamilton–Jacobi and Klein–Gordon equations in general Kerr–NUT–AdS spacetimes. J. High Energy Phys. 02, 005 (2007)
Zakharov, A.F.: On the hotspot near a Kerr black hole: Monte Carlo simulations. Mon. Not. R. Astron. Soc. 269, 283 (1994)
Mino, Y.: Perturbative approach to an orbital evolution around a supermassive black hole. Phys. Rev. D 67, 084027 (2003)
Pugliese, D., Quevedo, H.: The ergoregion in the Kerr spacetime: properties of the equatorial circular motion. Eur. Phys. J. C 75, 234 (2015)
Pugliese, D., Quevedo, H.: Observers in Kerr spacetimes. Eur. Phys. J. C 78, 69 (2018)
O’Neill, B.: The Geometry of Kerr Black Holes. A K Peters/CRC Press, Wellesley (1995)
Wilkins, D.C.: Bound geodesics in the Kerr metric. Phys. Rev. D 5, 814 (1972)
Dereli, T., Tucker, R.W.: On the detection of scalar field induced space–time torsion. Mod. Phys. Lett. A 17, 421 (2002)
Cebeci, H., Dereli, T., Tucker, R.W.: Autoparallel orbits in Kerr Brans–Dicke spacetimes. Int. J. Mod. Phys. D 13, 137 (2004)
Wang, Z.X., Guo, D.R.: Special Functions. World Scientific Publishing Co., Singapore (1989)
Drasco, S., Hughes, S.A.: Rotating black hole orbit functionals in the frequency domain. Phys. Rev. D 69, 044015 (2004)
Fujita, R., Hikida, W.: Analytical solutions of bound timelike geodesic orbits in Kerr spacetime. Class. Quant. Grav. 26, 135002 (2009)
Hackmann, E., Lämmerzahl, C.: Observables for bound orbital motion in axially symmetric space–times. Phys. Rev. D 85, 044049 (2012)
Chakraborty, C., Bhattacharyya, S.: Does the gravitomagnetic monopole exist? A clue from a black hole X-ray binary. Phys. Rev. D 98, 043021 (2018)
Acknowledgements
We would like to thank anonymous reviewers for their suggestions and comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Cebeci, H., Özdemir, N. & Şentorun, S. The equatorial motion of the charged test particles in Kerr–Newman–Taub–NUT spacetime. Gen Relativ Gravit 51, 85 (2019). https://doi.org/10.1007/s10714-019-2569-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s10714-019-2569-3