He was educated at Melbourne University and Massachusetts Institute of Technology, and held a post-doctoral research position at the University of Chicago, before taking an assistant professorship at Northwestern University in 1987.
A former Presidential Young Investigator and Sloan Research Fellow, he is the author of six books and 200 refereed articles on theoretical astrophysics and cosmology. Moving to the University of Arizona as an associate professor in 1991, he became a full professor in 1993. He became a Fellow of the American Physical Society in 2002.
He is also a Professorial Fellow in the School of Physics, Melbourne University. He is also the Chief Editor of the Theoretical Astrophysics series of books at the University of Chicago Press. In a career that has seen him publish 200 refereed research papers and several books, Melia has made important contributions in High Energy Astronomy and the physics of supermassive black holes.
He is especially known for his work on the galactic center, particularly developing a theoretical understanding of the central supermassive black hole, known as Sagittarius A*. With his students and collaborators, he was the first to propose that imaging this object with millimeter-interferometry, which should be feasible within a few years, should prove beyond doubt that it possesses the event horizon predicted by Einstein's theory of general relativity. In so doing, he and his students have developed the so-called R_h=ct Universe, a cosmological theory that has accounted for the observational data better than all other models proposed thus far.
In this cosmology, the Universe has no horizon problem, and therefore evolved without inflation. He is also a well-respected and popular publicist of astronomy and science in general, delivering many lectures at public venues, including museums and planetariums.
Member International Astronomical Union, American Astronomical Society, American Physical Society, American Association of University Professors.
Married Patricia S. Hsu, August 9, 1980. Children: Marcus, Eliana, Adrian.