Dr Todd Oliynyk - Researcher Profile

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Address

School of Mathematical Sciences
Building 28, Clayton

Contact Details

Tel: +61 3 990 54433

Email: todd.oliynyk@sci.monash.edu.au


Biography

A relatively complex puzzle

When you think of physics, you probably think of Isaac Newton and Albert Einstein. Their work forms the basis of gravitational theory as we know it, and still inspires thought. Dr Todd Oliynyk says Newton’s law of universal gravitation is relatively simple and well-established, while Einstein’s theory of general relativity is complex, but more accurate. Todd is using Newtonian gravity as a starting point to understand general relativity.

 

Newtonian gravity states that gravity is a force which for two point particles are proportional to the product of their masses, and inversely proportional to the square of the distance between them. Einstein’s theory of general relativity describes gravity as a geometric property of space and time. Todd says Newtonian gravity can help us understand general relativity theory.

“General relativity is complicated and we understand Newtonian gravity much better,” Todd says. “One way to try and understand general relativity is to start with this well-known theory of gravity and try to correct it to get closer to the real theory of gravity, which is general relativity. It’s better to start in regimes you understand.” 

“The idea is how to understand how these two theories are related, and how to develop a systematic way of building approximations in order to understand the more accurate theory of general relativity,” he says.

Todd says GPS navigation is a good example of the limitations of Newtonian gravity.

“Your GPS tells you where you are, but you need very accurate time measurements to get accurate space measurements. If you pretend this is Newtonian gravity, you would discover that your GPS wouldn’t work. You wouldn’t be anywhere close to where you think you are, as you have to include the general relativistic effects,” Todd says. 

Todd says physicists study the correspondence between Newtonian gravity and general relativity by assuming certain solutions with certain behaviours exist. He believes it is important to develop a mathematical theory that justifies these assumptions.

“I approach it from the mathematical side to try and prove solutions exist with that sort of behaviour. I’m trying to put it on firm mathematical foundations. I go to the beginning and try to show that solutions do or do not exist for these properties. Sometimes it’s more complicated, as they may have different behaviours to what you would expect.”

Todd has also received a Monash Researcher Accelerator grant to explore the contentious area of dark energy, which accounts for around 73 per cent of the total mass-energy of the universe. Many believe dark energy best explains why the universe is expanding at an increasingly fast rate.

“Until recently, the universe was thought of as homogeneous,” he says. “In the late 1990s they found out that it’s expanding in a certain accelerated way. They found something was causing this accelerated expansion, but we don’t know what it is. That’s dark energy. There also exists something mysterious that can’t be seen and acts like matter, known as dark matter. Together they dominate the behaviour of the universe,” he says.

Again, Todd believes there are too many assumptions about dark energy research.

“The question is whether this is happening, or whether we misunderstand how to use general relativity to model the universe,” Todd says. 

“One key problem is this idea of approximating or not approximating. People make approximations, study them and offer an answer – yes dark energy is real, or no it’s not. We don’t really know the right answer. It’s hard for anyone to make a convincing argument because nobody can show what follows from the equations.”

 

Research & Supervision Interests

    Partial differential equations: singular limits of symmetric hyperbolic systems, geometric PDEs. General relativity: Newtonian limit, post-Newtonian expansions, Einstein-Yang-Mills, gravitating perfect fluids and elastic bodies. Geometric flows: Ricci flow, renormalization group flow.

Qualifications

PHD IN MATHEMATICS
Institution: University of Alberta
Year awarded: 2002
MASTER OF SCIENCE IN APPLIED MATHEMATICS
Institution: University of Western Ontario
Year awarded: 1997
BACHELOR OF SCIENCE (HONS) IN PHYSICS
Institution: University of Calgary
Year awarded: 1995

Publications

Journal Articles

Oliynyk, T., 2012, Lagrange coordinates for the Einstein-Euler equations, Physical Review D: Particles and fields [P], vol 85, issue 4, American Physical Society, College Park MD United States, pp. 1-13.

Oliynyk, T., 2012, On the existence of solutions to the relativistic Euler equations in two spacetime dimensions with a vacuum boundary, Classical and Quantum Gravity [P], vol 29, issue 15, IOP Publishing, Bristol England, pp. 1-28.

Oliynyk, T., 2012, The fast Newtonian limit for perfect fluids, Advances in Theoretical and Mathematical Physics [P], vol 16, issue 2, International Press, Somerville USA, pp. 359-391.

Oliynyk, T., Fisher, M., 2012, There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for models with an Ableian residual group, Communications In Mathematical Physics [P], vol 312, issue 1, Springer, Heidelberg Germany, pp. 137-177.

Andersson, L., Oliynyk, T., Schmidt, B., 2011, Dynamical elastic bodies in newtonian gravity, Classical and Quantum Gravity [P], vol 28, Institute of Physics Publishing Ltd., UK, pp. 1-35.

Oliynyk, T., 2010, A rigorous formulation of the cosmological Newtonian limit without averaging, Journal of Hyperbolic Differential Equations [P], vol 7, issue 3, World Scientific Publishing Company, Singapore, pp. 405-431.

Oliynyk, T.A., 2010, Cosmological post-Newtonian expansions to arbitrary order, Communications in Mathematical Physics [E], vol 295, issue 2, Springer Berlin, Heidelberg Germany, pp. 431-463.

Gulcev, L., Oliynyk, T., Woolgar, E., 2010, On long-time existence for the flow of static metrics with rotational symmetry, Communications in Analysis and Geometry [P], vol 18, issue 4, International Press of Boston, USA, pp. 705-741.

Bartnik, R.A., Fisher, M., Oliynyk, T., 2010, Static spherically symmetric solutions of the SO(5) Einstein Yang-Mills equations, Journal Of Mathematical Physics [P], vol 51, issue 3, American Institute of Physics, Melville New York USA, pp. 1-10.

Oliynyk, T., Schmidt, B., 2009, Existence of families of spacetimes with a Newtonian limit, General Relativity And Gravitation [P], vol 41, issue 9, Springer/Plenum Publishers, New York USA, pp. 2093-2111.

Oliynyk, T., 2009, Post-Newtonian expansions for perfect fluids, Communications In Mathematical Physics [P], vol 288, issue 3, Springer, New York USA, pp. 847-886.

Oliynyk, T., 2009, The second-order renormalization group flow for nonlinear sigma models in two dimensions, Letters In Mathematical Physics [P], vol 26, issue 10, IOP Publishing Ltd, Bristol UK, pp. 105020-105027.

Guenther, C., Oliynyk, T., 2008, Stability of the (two-loop) renormalization group flow for nonlinear sigma models, Letters in Mathematical Physics, vol 84, issue 2-3, Springer Netherlands, Dordrecht Netherlands, pp. 149-157.

Oliynyk, T., Suneeta, V., Woolgar, E., 2007, Metric for gradient renormalization group flow of the worldsheet sigma model beyond first order, Physical Review D, vol 76, issue 1, American Physical Society, USA, pp. 1-7.

Oliynyk, T., Woolgar, E., 2007, Rotationally symmetric Ricci flow on asymptotically flat manifolds, Communications in Analysis and Geometry, vol 15, issue 3, International Press, Hong Kong, pp. 535-568.

Oliynyk, T.A., 2007, The Newtonian limit for perfect fluids, Communications in Mathematical Physics, vol 276, issue 1, Springer, Germany, pp. 131-188.

Oliynyk, T., Suneeta, V., Woolgar, E., 2006, A gradient flow for worldsheet nonlinear sigma models, Nuclear Physics B, vol 739, issue 3, Elsevier Science BV, Amsterdam Netherlands, pp. 441-458.

Oliynyk, T.A., 2006, An existence proof for the gravitating BPS Monopole, Annales Henri Poincare, vol 7, issue 2, Birkaeuser Verlag AG, Basel Switzerland, pp. 199-232.

Kunzle, H.P., Oliynyk, T., 2006, Spherical symmetry of generalized EYMH fields, Journal of Geometry and Physics, vol 56, issue 9, Elsevier BV, Netherlands, pp. 1856-1874.

Oliynyk, T.A., 2005, Hidden measurements, hidden variables and the volume representation of transition probabilities, Foundations of Physics, vol 35, issue 1, Spinger Science and Business Media Inc, New York USA, pp. 85-107.

Oliynyk, T.A., Suneeta, V., Woolgar, E., 2005, Irreversibility of world-sheet renormalization group flow, Physics Letters B, vol 610, Elsevier, Netherlands, pp. 115-121.

Oliynyk, T., 2005, Newtonian perturbations and the Einstein-Yang-Mills-dilaton equations, Classical and Quantum Gravity, vol 22, issue 11, Institute of Physics Publishing Ltd, Bristol UK, pp. 2269-2294.

Kunzle, H.P., Oliynyk, T., 2005, Spherically symmetric Einstein-Yang-Mills-Higgs fields for general compact gauge groups, Nonlinear Analysis, vol 63, issue 5-7, Elsevier, UK, pp. 473-480.

Oliynyk, T., Kunzle, H.P., 2003, On global properties of static spherically symmetric EYM fields with compact gauge groups, Classical and Quantum Gravity, vol 20, issue 21, Institute of Physics Publishing Ltd, Bristol UK, pp. 4653-4682.

Oliynyk, T., Kunzle, H.P., 2002, Local existence proofs for the boundary value problem for static spherically symmetric Einstein-Yang-Mills fields with compact gauge groups, Journal of Mathematical Physics, vol 43, issue 5, American Institute of Physics, Melville USA, pp. 2363-2393.

Oliynyk, T., Kunzle, H.P., 2002, On all possible static spherically symmetric EYM solitons and black holes, Classical and Quantum Gravity, vol 19, issue 3, Institute of Physics Publishing Ltd, Bristol UK, pp. 457-482.