On properties of vacuum axially symmetric spacetime of gravitomagnetic monopole in cylindrical coordinates

Abstract

We investigate general relativistic effects associated with the gravitomagnetic monopole moment of gravitational source through the analysis of the motion of test particles and electromagnetic fields distribution in the spacetime around nonrotating cylindrical NUT source. We consider the circular motion of test particles in NUT spacetime, their characteristics and the dependence of effective potential on the radial coordinate for the different values of NUT parameter and orbital momentum of test particles. It is shown that the bounds of stability for circular orbits are displaced toward the event horizon with the growth of monopole moment of the NUT object. In addition, we obtain exact analytical solutions of Maxwell equations for magnetized and charged cylindrical NUT stars.

Particle motion and electromagnetic fields of rotating compact gravitating objects with gravitomagnetic charge

“…(33) and (34), when NUT parameter is equal to zero, for different values of the constants of motion, orbital radii, the rotation parameter a, as well as the strength parameter of the magnetic field. The problem of existence of stable orbits in NUT space-time [25] and other properties of particles motion are also discussed in our preceding paper [26]. The radius of marginal stability, the associated energy and angular momentum of the circular orbits can be derived from the simultaneous solution of the condition L, r, b, a, l) ∂r…”

Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times

“…The separation constant k is known as Carter constant. A study of the geodesic equation in Weyl coordinates has been performed in [21].…”

“…Here the influence of the independent variation of n ( fig.1(a)-(d)), and k ( fig.1(e)-(i)) on the zeros of R is presented. The dashed region denotes the prohibited values of E andL following from the inequalities (21). Here C = 0.…”

Does the gravitomagnetic monopole exist? A clue from a black hole x-ray binary

“…Since we use the KTN spacetime instead of the Kerr spacetime, here we use the expressions of these frequencies (see Eqs. [3][4][5] ) using these three fundamental frequencies. Besides, the condition to derive the radius of the innermost stable circular orbit r ISCO and the expression of the gravitational redshift for the KTN spacetime are given by Eq.…”

“…The gravitational analogue of Dirac's magnetic monopole [1,2] is known as the gravitomagnetic monopole [3], which, if detected, can open a new area of research in physics. Historically, Newmann et al discovered a stationary and spherically symmetric exact solution (now known as the NUT solution) of Einstein equation, that contains the gravitomagnetic monopole or the so-called NUT (Newman, Unti and Tamburino [4]) parameter [5,6]. Note that Einstein-Hilbert action requires no modification [7] to accommodate the gravitomagnetic monopole.…”