School of Mathematics, Statistics & Computer Science

Applied Mathematics PhD graduate, Dr Njabulo Mkhize.

PhD Tackles Mathematical Models of the Universe

Doctoral graduate Dr Njabulo Mkhize aims to understand the universe’s deepest mysteries. His PhD in Applied Mathematics, titled: Exact Solutions in Some Modified Gravity Theories, centred on the field of cosmology, which delves into the complex tapestry of the universe and its celestial inhabitants, including stars, planets and the sun.

Mkhize focused on General Relativity (GR), the ground-breaking theory introduced by Albert Einstein in 1915. There is strong evidence that GR is in need of modification and amongst the various options Einstein-Gauss-Bonnet (EGB) gravity is considered a worthy successor. EGB theory introduces new mathematical descriptions, with the aim of refining our understanding of the universe beyond the borders of GR. In his PhD research, Mkhize uncovered new exact solutions within the EGB theory, developed models and meticulously probed the physical implications of these discoveries.

Mkhize’s fascination with celestial structures and their behaviour can be traced back to the profound questions that have intrigued humanity for generations. How did the universe come into existence? What lies beyond the boundaries of our solar system? What forces drive the observed accelerated expansion of the cosmos? The significance of his work lies in its potential to shed light on the impact of higher curvature terms in the EGB gravity theory. Understanding whether these terms influence the behaviour of celestial models can lead to ground-breaking revelations about the cosmos and reshape our comprehension of the universe’s fundamental laws.

Looking ahead, Mkhize aspires to grow his research portfolio in Applied Mathematics and establish himself as a prominent researcher in this field, making lasting contributions to our understanding of the universe’s inner workings.

Acknowledging the importance of mentorship in his journey, Mkhize expressed his gratitude to his supervisor, Professor Sudan Hansraj who not only provided invaluable guidance but also served as a wellspring of encouragement. He also extended his heartfelt appreciation to his supportive friends and family.

‘Njabulo has been a dedicated and focused student,’ said Hansraj. ‘He set his goals early and made a determined effort to achieve them. The problems he worked on were nontrivial and required deep insight. He was resolute and enthusiastic about finding solutions that had pleasing physical attributes. The area of Einstein-Gauss-Bonnet gravity originated in many respects at UKZN in the 1970s during the days of celebrated applied mathematician Hanno Rund. It is particularly pleasing that we were able to extend those ideas to the area of relativistic astrophysical modelling. To his credit, his academic outputs appear in top-tier journals.’

Outside the world of mathematics and celestial contemplation, Mkhize finds solace in the rhythms of music and the joy of dancing.

Words: Siphesihle Shezi

Photograph: Sethu Dlamini