The Research Management Center congratulates undergraduates Chen Zihang and Deng Bojun from Mathematics and Applied Mathematics programme, on the publication of “Orbital mechanics and quasiperiodic oscillation resonances of black holes in Einstein-Æther theory” in SCI Q1 Journal - Physical Review D, 102 (2020) 044028. This research was done under the guidance of Associate Professor Dr. Lim Yen Kheng and is part of an international collaboration between XMUM and universities from Turkey, Pakistan and China. 

The dark matter problem is currently among the biggest unsolved problems in physics. Progress in understanding the modifications of gravitational theories, along with the study of the orbits around black holes will shed light into this issue. Furthermore, calculations of the orbital properties will produce parameters that can be tested against observations. This is becoming increasingly relevant with recent breakthroughs of the direct detection of gravitational waves in 2015 and the direct imaging of a black hole in 2019.

In this work, the team of collaborators studied the orbital motion around a black hole predicted by a modified form of Einstein’s theory of gravity, called Einstein-Æther theory. This is a theory developed to address the shortcomings of Einstein’s original theory, which failed to explain the behaviour of rotation speeds of galaxies. This issue has since been called the “dark matter problem” in physics. The theory postulates the existence of a time-like Æther field which is responsible for the additional gravitational forces that mimics the effects of dark matter.

Among the results obtained in the project are the conditions under which periodic orbits can occur. A particle in periodic orbit would trace out shapes as below.

Periodic orbits are important elements in the general study of relativistic motion around black holes. As any general orbit can be approximated to a periodic orbit, each orbit can be classified by an index of three numbers (for vertex, zoom, and whirl) and arranged in a chemistry-like Periodic Table coined by Levin and Perez-Giz in 2008, for which, interestingly, the term “periodic” now works as a double-entendre.

The paper is available online at https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.044028.

Associate Professor Dr. Lim Yen Kheng is from the Department of Mathematics, XMUM. Dr. Lim received his PhD from National University of Singapore in December 2015, where he also worked as an instructor. He has published more than 15 journals in Physical Review D, Classical and Quantum Gravity, and the International Journal of Modern Physics. His research interests are black holes, cosmology, and theoretical/mathematical physics.