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Exact interpretation of the NUT parameter becomes possible when a static Schwarzchild mass is immersed in a stationary, source free electromagnetic universe. We explain this on the basis of our solution (Halilsoy and AlBadawi in Class Quantum Grav 12:3013, 1995), which represents the non-linear superposition of the Schwarzschild solution and the generalized Bertotti-Robinson solution.The physical meaning of the NUT parameter, characterizing the NUT solution as well as all the solutions including this as a limiting case, needs clarification. Is the so-called NUT parameter a gravomagnetic monopole parameter of the central mass [2], or a twisting property of the surrounding spacetime? Does it characterize the environment, rather than its connection to a central mass immersed in it? These questions find a response when we consider a static Schwarschild (S) mass coupled to an externally powered twisting electromagnetic (em) universe. We gave a solution [1] that described this situation which interpolates between the S solution and a generalized Bertotti-Robinson (BR) solution. Our metric was given by−r 2 f (r) dθ 2 + sin 2 θ dφ 2 ,

The exact solutions of the Dirac equation that describe a massive, non-charged particle with spin− 1 2 in the curved spacetime geometry of regular Bardeen black hole surrounded by quintessence (BBHSQ) are investigated. We first derive the Dirac equation in the BBHSQ background using a null tetrad in the Newman-Penrose formalism. Afterward, we separate the Dirac equation into ordinary differential equations for the radial and angular parts. The angular equations are solved exactly in terms of standard spherical harmonics. The radial part equations are transformed into a Schrödinger like differential wave equations with effective potentials. The effect of the quintessence on the regular Bardeen black hole is studied by understanding the physical behavior of the effective potentials. In addition, the potentials are plotted with changing the quintessence parameters, magnetic monopole charge parameter and the frequency of the particle in the physically acceptable regions. Finally, we study the greybody radiation of spin−0 particles from the BBHSQ.2

We present the metric of a Schwarzschild (S) black hole coupled to an external, stationary electromagnetic Bertotti - Robinson (BR) solution. This metric generalizes a previous metric that served to unify the S and BR solutions. Limiting cases of our metric include the case of a stationary electromagnetic universe in which conformal curvature arises due to rotation.

We study the Dirac equation in a spacetime that represents the nonlinear superposition of the Schwarzchild solution to an external, stationary electromagnetic Berttoti-Robinson solution. We separate the Dirac equation into radial and angular equations using Newman-Penrose formalism. We obtain exact analytical solutions of the angular equations. We manage to obtain the radial wave equations with effective potentials. Finally, we study the potentials by plotting them as a function of radial distance and examine the effect of the twisting parameter and the frequencies on the potentials. Recently, Dirac equation was examined in Kerr-Taub-NUT spacetime [14]. In