On the properties of a deformed extension of the NUT space-time
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Regular Article - Theoretical Physics
On the properties of a deformed extension of the NUT space-time Bakhtiyor Narzilloev1,2,a , Daniele Malafarina3,b , Ahmadjon Abdujabbarov2,4,5,6,7,c , Cosimo Bambi1,d 1
Center for Field Theory and Particle Physics and Department of Physics, Fudan University, Shanghai 200438, China Ulugh Beg Astronomical Institute, Astronomicheskaya 33, Tashkent 100052, Uzbekistan 3 Department of Physics, Nazarbayev University, 53 Kabanbay Batyr Avenue, 010000 Astana, Kazakhstan 4 Shanghai Astronomical Observatory, 80 Nandan Road, Shanghai 200030, China 5 National University of Uzbekistan, Tashkent 100174, Uzbekistan 6 Institute of Nuclear Physics, Ulugbek 1, Tashkent 100214, Uzbekistan 7 Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kori Niyoziy, 39, Tashkent 100000, Uzbekistan
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Received: 7 May 2020 / Accepted: 16 August 2020 © The Author(s) 2020
Abstract We consider a class of space-times given by a stationary extension of the Zipoy–Voorhees metric that was found by Halilsoy. We show that the solutions do not describe rotating sources but must be interpreted, similarly to the NUT case, as deformed sources endowed with a gravitomagnetic charge. We show that the Halilsoy family is directly linked to the NUT space-time, which can be obtained in the limit of vanishing deformations. We investigate the motion of test particles and photons in this class of space-times, in particular the innermost stable circular orbits and photon capture radius. Finally we show that this class of solutions possesses a submanifold where closed time-like curves are allowed.
1 Introduction Vacuum, exact solutions describing stationary space-times are of great importance in General Relativity since they can describe the field outside a rotating compact source. The most famous of such solutions is the well known Kerr metric which describes the field of a rotating black hole [1]. However other solutions do exist and investigating their properties and to what extent they may describe the exterior of physical sources, is important in order to establish the extent to which a solution may be considered physically viable and, as a consequence, whether astrophysical black hole candidates are well described by mathematical black hole solutions [2–5]. An important class of exact solutions of Einstein’s equations that describes deviations from black a e-mail:
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hole space-times is the so-called Weyl class of static axially symmetric vacuum solutions [6,7]. Given the one-to-one correspondence between metrics belonging to Weyl’s class and solutions of Laplace equation in flat two-dimensional space, all static axially symmetric solutions are in principle known [8,9]. For example in recent times some attention has been given to the Zipoy–Voorhees (ZV) metric which is a static generalization of the Schwarzschild solution to inclu
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