College of Agriculture, Engineering
and Science (CAES)

Dr Daniel Krupanandan seen at his graduation, and pictured with his late son Rowan to whom he dedicated his PhD.

PhD in Applied Mathematics Undertaken in Son’s Memory

Dr Daniel Krupanandan was awarded a PhD in Applied Mathematics for his thesis titled: Exact Einstein and Higher Curvature Astrophysical Models. He dedicated his achievement to the memory of his son, Rowan.

‘The Einstein field equations governing the behaviour of astrophysical entities are notoriously complicated and difficult to solve,’ said his supervisor, Professor Sudan Hansraj. ‘In this work a new algorithm was devised which generated previously unknown solutions to Einstein’s equations.

‘Inspired by the success at the Einstein level, a similar approach was applied to the more formidable Einstein-Gauss-Bonnet (EGB) system incorporating higher curvature effects. Other physically reasonable models with equations of state were developed.’

Having completed his first teaching qualification in 1979 at the former University of Durban-Westville and an honours degree in Mathematics in 1995, Krupanandan started lecturing at Springfield College of Education in 1999. ‘The internationally recognised staff members within UKZN’s Mathematics Department prompted me to pursue my masters and doctoral studies at the Institution,’ he said.

During his MSc, Krupanandan investigated the modelling of compact objects such as neutron stars and pulsars in Einstein’s theory of general relativity. For his PhD he expanded on this research, extending the four-dimensional stellar models to modified theories of gravity, specifically the EGB five- and six-dimensional theories.

‘We successfully solved the EGB gravity equations to obtain models of hyperspheres,’ said Krupanandan. ‘These stellar models were subjected to rigorous physical viability tests and we showed that they describe realistic stellar stars in higher dimensions. We also showed that contributions from higher dimensions lead to higher stellar densities and higher redshifts. Our models provide explanations about stellar masses and radii which lie outside the realm of Newtonian and Einstein’s gravities.’

The work contained in Krupanandan’s thesis has resulted in four publications in well-known astrophysical journals with high impact factors.

Krupanandan’s motivation to complete his PhD was extremely personal: ‘My late son, Rowan Krupanandan mentioned before his untimely and tragic death whilst he was an Engineering student that he was getting better than me in mathematics. This was evident in his excellent matric and university results. I agreed with him but took a challenge that I would further my studies in applied mathematics to give him academic support. I also promised him that we would both graduate with higher scientific degrees.

‘During my lecturing years I worked with Professor Sudan Hansraj and was extremely impressed with his research activities at UKZN, especially in the area of Applied Mathematics. I knew that this was an extremely difficult area of scientific study. Listening to Professor Hansraj’s journey into the world of mathematics and research ignited my mind to look into pursuing research in the areas of gravity and stellar modelling. My son was also excited about these fields of study. Professor Hansraj took on the challenge of supervising me and gave me a project to work on solution-generating algorithms in Einstein’s general relativity.

‘My son passed away tragically in a car accident. It was difficult but I pushed through the pain and loss to complete my MSc in Mathematics and kept my promise to him about graduating. I stood in the same Graduation ceremony as my son’s friends and literally stood in for him on Graduation day.

‘Since my son’s death in 2009 I longed to study Mathematics as a tribute to his memory.’

Krupanandan believes the results contained in his thesis are important within the realm of theoretical astrophysics and gravitation. ‘The solutions are excellent descriptions of stellar models in higher dimensions,’ he explained. ‘As technology and observations improve, such models will play an important part in determining the fundamental physics of stars.

‘This work will encourage future postgraduate students and emerging researchers to seek new families of solutions describing more realistic matter distributions. The most rewarding and impactful part of this work will be future evidence of higher dimensions and the effects on stellar structure.’

With his PhD complete, Krupanandan plans to continue his work to develop school teachers and learners’ mathematical skills, to which he has devoted much of his career.

He thanked his family, supervisor and numerous colleagues for their support.

‘Some dreams seem impossible and scare us, but that’s only because they are bigger than us,’ he said.

‘I never thought that I would achieve my dream of obtaining a PhD in Applied Mathematics. Despite the difficulty and illusive nature of the field of research I was determined to finish the course of study. This achievement is a great lesson in life for anyone who has a dream, to continue striving for its realisation even if it scares you.

‘I was inspired by my late son as a challenge. At the age of 65 and with many health issues I persevered and kept focused on my dream. I encourage those who dream: you have the potential to succeed, just believe in yourself and trust God to do the rest.’

Words: Sally Frost

Photographs: Sandile Ndlovu and Supplied