By extending a standard mathematical technique, exact solutions describing how particles behave within a rotating charged dust distribution described by Som, Raychaudhuri space-time have been obtained. An extended Nikiforov-Uvarov method, a systematic algebraic approach, solved equations governing relativistic particle dynamics in this environment for both linear and Cornell potential models. Precise solutions for how particles behave in rotating, charged environments are now available, specifically within Som, Raychaudhuri space-time which models rotating dust distributions.

The team successfully solved equations describing particle movement using an extended Nikiforov-Uvarov method, a systematic algebraic process, for both straight line and Cornell potential scenarios. This enables detailed examination of energy levels and associated wave functions under these conditions. They developed a technique for solving complex equations describing how particles behave in rotating, charged environments; specifically within what can be imagined as warped fabric of space and time created by spinning dust clouds known as Som, Raychaudhuri space-time.

An extended Nikiforov-Uvarov method, a systematic algebraic approach, employed to find exact solutions for both straight line and Cornell potential scenarios, allowing detailed examination of particle energy levels. An eigenstate solution uniquely identifies each possible energy level of the particle under these conditions. The work focuses on the generalised Klein-Gordon oscillator, a simplified model representing vibrating tiny particles while accounting for relativity. They successfully determined external magnetic fields and interaction potentials affecting this system; however, further investigation is needed to determine if this framework can be applied more broadly across relativistic quantum mechanics.

Analytical eigenstate determination clarifies particle dynamics near cosmic strings and intense gravitation

The extended Nikiforov-Uvarov method yielded exact eigenstate solutions, a key improvement over standard approaches which frequently rely on approximations, for linear and Cornell potentials within Som-Raychaudhuri space-time. Previously obtaining analytical solutions for these complex scenarios proved intractable due to mathematical difficulties inherent in relativistic quantum mechanics. These findings detail how particles behave under combined gravitational, electromagnetic, and topological influences; energy spectra demonstrate strong dependence upon radial and angular quantum numbers alongside the ‘topological parameter’ α describing cosmic string effects.

A team of researchers demonstrated precise calculations of particle behaviour within complex gravitational fields, specifically obtaining exact solutions describing motion influenced by gravity, magnetism, and theoretical one-dimensional objects called ‘cosmic strings’ possessing immense density. They determined energy level values for a simple linear force and a more realistic Cornell potential, a combination mimicking atomic interactions, revealing shifts dependent on both quantum numbers defining particle state and the strength of topological effects represented by α. This analytical approach bypasses common approximation techniques used in relativistic quantum mechanics, yielding results rather than numerical estimations for both potentials.

Analytical progress constrains modelling of non-uniform magnetism and diverse potentials

The extended Nikiforov-Uvarov method delivers precise solutions describing particle behaviour within rotating charged dust distributions, and Som-Raychaudhuri space-time, although its current form is limited to uniform magnetic fields and only two specific interaction potentials: a simple linear attraction or Cornell potential mimicking atomic forces. Tackling more complicated scenarios involving varying field strengths presents an important mathematical hurdle requiring further investigation. This analytical solution advances understanding of particle behaviour in warped fabric created by spinning matter; Som-Raychaudhuri space-time describes these environments as derived from Einstein’s theory combined with electromagnetism. Extending the standard Nikiforov-Uvarov technique allowed them to calculate precise energy levels for particles experiencing both simple attraction and complex forces resembling those found between atoms using the Cornell potential. Obtaining exact eigenstate solutions, unique ‘fingerprints’ identifying each possible energy level, avoids reliance on approximations often needed when modelling quantum systems within curved spaces like this one.

The researchers obtained exact mathematical descriptions of how particles behave in a rotating environment combining gravity and magnetism, specifically within Som-Raychaudhuri space-time. Energy values changed predictably as the strength of magnetic effects varied for tested combinations of angular momentum and radial numbers. The authors suggest further work is necessary to extend these solutions to more complex scenarios involving non-uniform magnetic fields.

👉 More information
🗞 Analytical Solutions of the Generalized Klein-Gordon Oscillator in Som-Raychaudhuri Space-Time via the Extended Nikiforov-Uvarov Method
✍️ Hale Karayer, Tolga Celik and Dogan Demirhan
🧠 ArXiv: https://arxiv.org/abs/2608.20273

More like this