I am an applied mathematician working on problems in analysis, PDEs and geometry many of which are motivated by mathematical physics, especially general relativity and cosmology. I am a member of the Gravity group of the University of Otago.
Since November 2022, I am the Associate Dean International (Sciences).
My research is about asymptotics and singular limits of solutions to partial differential equations (PDEs), especially so-called Fuchsian PDEs. These are nonlinear systems of wave equations appearing frequently in mathematics and mathematical physics where some of the coefficients may have characteristic “1/t-singularities”.
The main concerns of my research are, (i), global existence, stability and asymptotics of solutions of the Cauchy problem evolved towards the singular time t=0 from some initial time T>0, and, (ii), singular initial value problems where one seeks solutions that are launched from the singular time t=0 into the increasing time direction.
Mathematical/computational general relativity/cosmology
I am interested in fundamental questions, like nonlinear stability of cosmological models, Roger Penrose's cosmic censorship conjecture, asymptotic simplicity and Mixmaster dynamics.
Publications
Beyer, F., Marshall, E., & Oliynyk, T. A. (2023). Future instability of FLRW fluid solutions for linear equations of state p = Kp with 1/3 < K < 1. Physical Review D, 107, 104030. doi: 10.1103/PhysRevD.107.104030
Journal - Research Article
Beyer, F., & Ritchie, J. (2022). Asymptotically hyperboloidal initial data sets from a parabolic-hyperbolic formulation of the Einstein vacuum constraints. Classical & Quantum Gravity. Advance online publication. doi: 10.1088/1361-6382/ac79f1
Journal - Research Article
Ames, E., Beyer, F., Isenberg, J., & Oliynyk, T. A. (2022). Stability of asymptotic behaviour within polarized T2-symmetric vacuum solutions with cosmological constant. Philosophical Transactions of the Royal Society A, 380, 20210173. doi: 10.1098/rsta.2021.0173
Journal - Research Article
Ames, E., Beyer, F., Isenberg, J., & Oliynyk, T. A. (2022). Stability of AVTD behavior within the polarized Τ2-symmetric vacuum spacetimes. Annales Henri Poincaré, 23, 2299-2343. doi: 10.1007/s00023-021-01142-0
Journal - Research Article
Beyer, F., & LeFloch, P. G. (2021). A numerical algorithm for Fuchsian equations and fluid flows on cosmological spacetimes. Journal of Computational Physics, 431, 110145. doi: 10.1016/j.jcp.2021.110145
Journal - Research Article
Beyer, F., Oliynyk, T. A., & Olvera-Santamaría, J. A. (2021). The Fuchsian approach to global existence for hyperbolic equations. Communications in Partial Differential Equations, 46(5), 864-934. doi: 10.1080/03605302.2020.1857402
Journal - Research Article
Beyer, F., Frauendiener, J., & Hennig, J. (2020). Explorations of the infinite regions of spacetime. International Journal of Modern Physics D, 29(10), 2030007. doi: 10.1142/S0218271820300074
Journal - Research Article
Beyer, F., Frauendiener, J., & Ritchie, J. (2020). Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations. Physical Review D, 101, 084013. doi: 10.1103/PhysRevD.101.084013
Journal - Research Article
Ames, E., Beyer, F., & Isenberg, J. (2019). Contracting asymptotics of the linearized lapse-scalar field sub-system of the Einstein-scalar field equations. Journal of Mathematical Physics, 60, 102504. doi: 10.1063/1.5115104
Journal - Research Article
Beyer, F., Escobar, L., Frauendiener, J., & Ritchie, J. (2019). Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations. Classical & Quantum Gravity, 36(17), 175005. doi: 10.1088/1361-6382/ab3482
Journal - Research Article
Ames, E., Beyer, F., & Isenberg, J. (2019). Contracting asymptotics of the lapse-scalar field sub-system of the Einstein-scalar field equations. arXiv. Retrieved from https://arxiv.org/abs/1904.02854
Working Paper; Discussion Paper; Technical Report
Beyer, F., Oliynyk, T. A., & Olvera-Santamaría, J. A. (2019). The Fuchsian approach to global existence for hyperbolic equations. arXiv. Retrieved from https://arxiv.org/abs/1907.04071
Working Paper; Discussion Paper; Technical Report
Beyer, F., & Paetz, T.-T. (2018). Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor. Journal of Mathematical Physics, 59, 022501. doi: 10.1063/1.4996700
Journal - Research Article
Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2017). A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges. Journal of Geometry & Physics, 121, 42-71. doi: 10.1016/j.geomphys.2017.06.005
Journal - Research Article
Beyer, F., & LeFloch, P. G. (2017). Self–gravitating fluid flows with Gowdy symmetry near cosmological singularities. Communications in Partial Differential Equations, 42(8), 1199-1248. doi: 10.1080/03605302.2017.1345938
Journal - Research Article
Beyer, F., Escobar, L., & Frauendiener, J. (2017). Asymptotics of solutions of a hyperbolic formulation of the constraint equations. Classical & Quantum Gravity, 34(20), 205014. doi: 10.1088/1361-6382/aa8be6
Journal - Research Article
Beyer, F., Escobar, L., & Frauendiener, J. (2017). Criticality of inhomogeneous Nariai-like cosmological models. Physical Review D, 95(8), 084030. doi: 10.1103/PhysRevD.95.084030
Journal - Research Article
Beyer, F., Frauendiener, J., Stevens, C., & Whale, B. (2017). Numerical initial boundary value problem for the generalized conformal field equations. Physical Review D, 96(8), 084020. doi: 10.1103/PhysRevD.96.084020
Journal - Research Article
Beyer, F., & Paetz, T.-T. (2017). Analysis of a Bianchi-like equation satisfied by the Mars-Simon tensor. arXiv. Retrieved from https://arxiv.org/abs/1707.05201
Working Paper; Discussion Paper; Technical Report
Beyer, F., Escobar, L., & Frauendiener, J. (2017). Criticality of inhomogeneous Nariai-like cosmological models. arXiv. Retrieved from https://arxiv.org/abs/1702.02694
Working Paper; Discussion Paper; Technical Report
Beyer, F., Escobar, L., & Frauendiener, J. (2016). Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1). Physical Review D, 93, 043009. doi: 10.1103/PhysRevD.93.043009
Journal - Research Article
Beyer, F., Daszuta, B., & Frauendiener, J. (2015). A spectral method for half-integer spin fields based on spin-weighted spherical harmonics. Classical & Quantum Gravity, 32(17), 175013. doi: 10.1088/0264-9381/32/17/175013
Journal - Research Article
Beyer, F., & LeFloch, P. G. (2015). "Matter does not matter" for self-gravitating perfect fluids? [Extended abstract]. Proceedings of the Mathematisches Forschungsinstitut Oberwolfach Workshop: Mathematical Aspects of General Relativity [Report No. 33/2015].12(3), (pp. 1867-1935). Zürich, Switzerland: European Mathematical Society. doi: 10.4171/OWR/2015/33
Conference Contribution - Published proceedings: Abstract
Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2015). A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges. arXiv. Retrieved from http://arxiv.org/abs/1602.03018
Working Paper; Discussion Paper; Technical Report
Beyer, F., & LeFloch, P. G. (2015). Dynamics of self-gravitating fluids in Gowdy-symmetric spacetimes near cosmological singularities. arXiv. Retrieved from http://arxiv.org/abs/1512.07187
Working Paper; Discussion Paper; Technical Report
Beyer, F., Escobar, L., & Frauendiener, J. (2015). Numerical solutions of Einstein's equations for cosmological spacetimes with spatial topology S3 and symmetry group U(1). arXiv. Retrieved from http://arxiv.org/abs/1505.05920v1
Working Paper; Discussion Paper; Technical Report
Beyer, F., & Hennig, J. (2014). An exact smooth Gowdy-symmetric generalized Taub–NUT solution. Classical & Quantum Gravity, 31(9), 095010. doi: 10.1088/0264-9381/31/9/095010
Journal - Research Article
Beyer, F., Daszuta, B., Frauendiener, J., & Whale, B. (2014). Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics. Classical & Quantum Gravity, 31, 075019. doi: 10.1088/0264-9381/31/7/075019
Journal - Research Article
Beyer, F., Doulis, G., Frauendiener, J., & Whale, B. (2014). Linearized gravitational waves near space-like and null infinity. In A. Garcia-Parrado, F. C. Mena, R. Moura & E. Vas (Eds.), Progress in Mathematical Relativity, Gravitation and Cosmology (Vol. 60). (pp. 3-17). Berlin: Springer. doi: 10.1007/978-3-642-40157-2_1
Conference Contribution - Published proceedings: Full paper
Beyer, F., Doulis, G., Frauendiener, J., & Whale, B. (2014). The spin-2 equation on Minkowski background. In A. Garcia-Parrado, F. C. Mena, R. Moura & E. Vas (Eds.), Progress in Mathematical Relativity, Gravitation and Cosmology (Vol. 60). (pp. 465-468). Berlin: Springer. doi: 10.1007/978-3-642-40157-2_71
Conference Contribution - Published proceedings: Full paper
Beyer, F. (2014). AVTD solutions of Einstein's field equations. Proceedings of the 8th Australia and New Zealand Mathematics Convention (AustMS and NZMS). (pp. 97). Retrieved from http://www.austms2014.ms.unimelb.edu.au/
Conference Contribution - Published proceedings: Abstract
Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2013). Quasilinear hyperbolic Fuchsian systems and AVTD behavior in T2-symmetric vacuum spacetimes. Annales Henri Poincaré, 14(6), 1445-1523. doi: 10.1007/s00023-012-0228-2
Journal - Research Article
Beyer, F., & Escobar, L. (2013). Graceful exit from inflation for minimally coupled Bianchi A scalar field models. Classical & Quantum Gravity, 30, 195020. doi: 10.1088/0264-9381/30/19/195020
Journal - Research Article
Ames, E., Beyer, F., Isenberg, J., & LeFloch, P. G. (2013). Quasilinear symmetric hyperbolic Fuchsian systems in several space dimensions. Contemporary Mathematics, 591, (pp. 25-43). doi: 10.1090/comm/591/11824
Conference Contribution - Published proceedings: Full paper
Ames, E., Isenberg, J., & Beyer, F. (2013). What is the singular behavior of the gravitational field near generic big-bang type events? Proceedings of the Annual Meeting of the Four Corners Section of the APS: Bulletin of the American Physical Society.58(12). Retrieved from http://meetings.aps.org/Meeting/4CF13/Session/D2.6
Conference Contribution - Published proceedings: Abstract
Beyer, F., Doulis, G., Frauendiener, J., & Whale, B. (2012). Numerical space-times near space-like and null infinity: The spin-2 system on Minkowski space. Classical & Quantum Gravity, 29(24), 245013. doi: 10.1088/0264-9381/29/24/245013
Journal - Research Article
Beyer, F. (2012). The cosmic no-hair conjecture: A study of the Nariai solutions. In T. Damour & R. T. Jantzen (Eds.), Proceedings of the Twelfth Marcel Grossman Meeting: On Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories. (pp. 759-761). Singapore: World Scientific. [Full Paper]
Conference Contribution - Published proceedings: Full paper
Beyer, F. (2012). Guided tour through AVTD regions of the BKL world. Proceedings of the Sixth Australasian Conference on General Relativity and Gravitation. Retrieved from http://www.maths.otago.ac.nz/acgrg6/
Conference Contribution - Published proceedings: Abstract
Beyer, F. (2012, December). AVTD solutions of Einstein's field equations. Verbal presentation at the New Zealand Mathematical Society Colloquium, Palmerston North, New Zealand.
Conference Contribution - Verbal presentation and other Conference outputs
Beyer, F. (2012, February). Guided tour through AVTD regions of the BKL world. Plenary presentation at the Sixth Australasian Conference on General Relativity and Gravitation, Queenstown, New Zealand.
Conference Contribution - Verbal presentation and other Conference outputs
Beyer, F., & LeFloch, P. G. (2011). Second-order hyperbolic Fuchsian systems: Asymptotic behavior of geodesics in Gowdy spacetimes. Physical Review D, 84, 084036. doi: 10.1103/PhysRevD.84.084036
Journal - Research Article
Beyer, F., & LeFloch, P. G. (2010). Second-order hyperbolic Fuchsian systems and applications. Classical & Quantum Gravity, 27(24), 245012. doi: 10.1088/0264-9381/27/24/245012
Journal - Research Article
Beyer, F. (2009). A spectral solver for evolution problems with spatial S3-topology. Journal of Computational Physics, 228, 6496-6513. doi: 10.1016/j.jcp.2009.05.037
Journal - Research Article
Beyer, F. (2009). Non-genericity of the Nariai solutions: I. Asymptotics and spatially homogeneous perturbations. Classical & Quantum Gravity, 26, 235015. doi: 10.1088/0264-9381/26/23/235015
Journal - Research Article
Beyer, F. (2009). Non-genericity of the Nariai solutions: II. Investigations within the Gowdy class. Classical & Quantum Gravity, 26, 235016. doi: 10.1088/0264-9381/26/23/235016
Journal - Research Article
Beyer, F. (2008). Investigations of solutions of Einstein’s field equations close to λ-Taub–NUT. Classical & Quantum Gravity, 25, 235005. doi: 10.1088/0264-9381/25/23/235005
Journal - Research Article
Schnetter, E., Krishnan, B., & Beyer, F. (2006). Introduction to dynamical horizons in numerical relativity. Physical Review D, 74, 024028. doi: 10.1103/PhysRevD.74.024028
Journal - Research Article
Bishop, N. T., Beyer, F., & Koppitz, M. (2004). Black hole initial data from a nonconformal decomposition. Physical Review D, 69, 064010. doi: 10.1103/PhysRevD.69.064010
Journal - Research Article
