Prof Robert Bartnik - Researcher Profile

Robert Bartnik

Address

School of Mathematical Sciences
Building 28, Clayton

Biography

Robert works in the School of Mathematical Sciences at Monash University as a Professor

Robert’s research areas of interest are:

•Differential geometry, analysis of partial differential equations, Einstein equations and
 general relativity: energy and quasi-local energy definitions and properties, numerical solution
 of Einstein equations, spacetime singularity formation.

Keywords

Differential geometry, Einstein equations, Partial differential equations

Qualifications

PHD
Institution: Princeton University
Year awarded: 1983
MSC
Institution: University of Melbourne
Year awarded: 1980
SCIENCE (HONS)
Institution: UNIVERSITY OF MELBOURNE
Year awarded: 1978

Publications

Book Chapters

Bartnik, R.A., Isenberg, J., 2004, The constraint equations, in The Einstein equations and the large scale behavior of gravitational fields : 50 years of the Cauchy problem in general relativity, eds P T Chrusciel, H. Friedrich, Birkhauser, Basel, Switzerland, pp. 1-34.

Journal Articles

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.

Bartnik, R.A., Tod, P., 2006, A note on static metrics, Classical and Quantum Gravity, vol 23, issue 2, IOP Publishing Ltd, Bristol England, pp. 569-571.

Bartnik, R.A., Isenberg, J., 2006, Spherically symmetric dynamical horizons, Classical and Quantum Gravity, vol 23, issue 7, IOP Publishing Ltd, Bristol England, pp. 2559-2569.

Bartnik, R.A., Chrusciel, P.T., 2005, Boundary value problems for Dirac-type equations, Journal fr die reine und angewandte Mathematik, Walter de Gruyter, Berlin Germany, pp. 13-73.

Bartnik, R.A., 2005, Phase space for the Einstein equations, Communications in Analysis and Geometry, vol 13, issue 5, International Press Co. Ltd, Irvine USA, pp. 845-885.

Bartnik, R.A., 2004, Gravity matters, Australian Mathematical Society Gazette, vol 31, issue 3, Australian Mathematical Society, Australia, pp. 161-164.

Bartnik, R.A., 2003, Bondi mass in the NQS gauge, Classical and Quantum Gravity, vol 21, issue 3, Institute of Physics Publishing, UK, pp. 59-71.

Bartnik, R.A., Norton, A., 2002, Numerical experiments at null infinity, Conformal Structure of Spacetime, vol 604, Springer, Berlin, pp. 313-326.

Bartnik, R.A., Oganessyan, G., 2000, A canonical gauge for the Einstein equations, General Relativity and Gravitation, vol 32, issue 3, Springer, Netherlands, pp. 459-470.

Bartnik, R.A., Norton, A., 2000, Numerical methods for the Einstein equations in null quasi-spherical coordinates, SIAM Journal Scientific Computing, vol 22, Society for Industrial and Applied Mathematics, Philadelphia USA, pp. 917-950.

Conference Proceedings

Bartnik, R.A., 2005, Assessing accuracy in a numerical Einstein solver, Differential Equations and Mathematical Physics UAB-GIT 99, 16/03/1999-20/03/1999, International Press, Birmingham, pp. 11-19.

Bartnik, R.A., 2002, Mass and 3-metrics of non-negative scalar curvature, Proceedings ICM 2002, pp. 231-240.

Postgraduate Research Supervisions

Current Supervision

Program of Study:
(DOCTORATE BY RESEARCH).
Thesis Title:
Energy, momentum and dynamics of general relativity with guage fields.
Supervisors:
Bartnik, R (Main), Miao, P (Associate).
Program of Study:
(DOCTORATE BY RESEARCH).
Thesis Title:
Introduction of backlund and darboux transformations.
Supervisors:
Bartnik, R (Main), Weinstein, G (Associate).
Program of Study:
(DOCTORATE BY RESEARCH).
Thesis Title:
The Einstein-Yang-Mills equations.
Supervisors:
Bartnik, R (Main), Oliynyk, T (Associate).

Completed Supervision

Student:
Fisher, M.
Program of Study:
The Einstein Yang-Mills equations: particle-like solutions for non-Abelian models. (PHD) 2010.
Supervisors:
Bartnik, R (Joint-Co), Oliynyk, T (Joint).
Student:
Kandanaarachchi, S.
Program of Study:
Algebra. 2007.
Supervisors:
Athanassenas, M (Main), Bartnik, R (Associate).
Student:
Kandanaarachchi, S.
Program of Study:
Axially symmetric volume preserving mean curvature flow. (PHD) 2011.
Supervisors:
Athanassenas, M (Main), Bartnik, R (Associate).