Mihalis Dafermos Μιχάλης Δαφέρμος

Research articles

• Exhaustions of complete manifolds of bounded curvature, Tsing-Hua lectures on geometry and analysis, 319–322, Int. Press Cambridge, MA, 1997
• Stability and instability of the Cauchy horizon for the spherically symmetric Einstein-Maxwell-scalar field equations, Ann. of Math. 158 (2003), no. 3, 875–928
• On "time-periodic" black-hole solutions to certain spherically symmetric Einstein-matter systems, Commun. Math. Phys. 238 (2003), 411–427
• Spherically symmetric spacetimes with a trapped surface, Class. Quantum Grav. 22 (2005), no. 11, 2221–2232
• The interior of charged black holes and the problem of uniqueness in general relativity, Comm. Pure Appl. Math. 58 (2005), 0445–0504
• with Igor Rodnianski, Small-amplitude nonlinear waves on a black hole background, J. Math. Pures Appl. 84 (2005), 1147–1172
• with Igor Rodnianski, A proof of Price's law for the collapse of a self-gravitating scalar field, Invent. Math. 162 (2005), 381–457
• with Alan Rendall, An extension principle for the Einstein-Vlasov system under spherical symmetry, Ann. Henri Poincare 6 (2005), 1137–1155
• with Alan Rendall, Inextendibility of expanding cosmological models with symmetry, Class. Quantum Grav. 22 (2005), no. 23, L143–L147
• A note on the collapse of small-data massless collisionless matter, J. Hyperbolic Differ. Equ. 3 (2006), no. 4, 589–598
• On naked singularities and the collapse of self-gravitating Higgs fields, Adv. Theor. Math. Phys. 9 (2005) 575–591
• Black hole formation from a complete regular past, Commun. Math. Phys. 289 (2009), no. 2, 579–596
• with Igor Rodnianski, A note on boundary value problems for black hole evolutions, available online at http://www.arxiv.org/abs/gr-qc/0403034, 8 pages
• with Gustav Holzegel, On the nonlinear stability of triaxial Bianchi IX black holes, Adv. Theor. Math. Phys. 10 (2006) 503–523
• with Igor Rodnianski, The redshift effect and radiation decay on black hole spacetimes, Comm. Pure Appl. Math. 62 (2009), no. 7, 859–919
• with Alan Rendall, Strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter, available online at http://www.arxiv.org/abs/gr-qc/0610075, 17 pages
• with Alan Rendall, Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter, Comm. Pure Appl. Math. 69 (2016) 815–908 (available also at http://www.arxiv.org/abs/gr-qc/0701034)
• with Igor Rodnianski, The wave equation on Schwarzschild-de Sitter spacetimes, available online at http://www.arxiv.org/abs/0709.2766, 48 pages
• with Igor Rodnianski, A note on energy currents and decay for the wave equation on a Schwarzschild background, available online at http://www.arxiv.org/abs/0710.0171, 10 pages
• with Igor Rodnianski, A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds, Invent. Math. 185 (2011), 467–559, (available also at http://www.arxiv.org/abs/0805.4309)
• with Igor Rodnianski, A new physical-space approach to decay for the wave equation with applications to black hole spacetimes, in XVIth International Congress on Mathematical Physics, P. Exner (ed.), World Scientific, London, 2009, pp. 421–433, related article available online at http://arxiv.org/abs/0910.4957
• with Igor Rodnianski, Decay for solutions of the wave equation on Kerr exterior spacetimes I-II: The Cases ∣a∣ ≪ M or axisymmetry, available online at http://www.arxiv.org/abs/1010.5132, 57 pages
• Black holes without spacelike singularities, Commun. Math. Phys. 332 (2014), 729–757 (available also at http://www.arxiv.org/abs/1201.1797)
• with Gustav Holzegel and Igor Rodnianski, A scattering theory construction of dynamical black hole spacetimes,  J. Differential Geom. 126(2): 633-740 (February 2024), available also at http://www.arxiv.org/abs/1306.5534
• with Igor Rodnianski and Yakov Shlapentokh-Rothman, Decay for solutions of the wave equation on Kerr exterior spacetimes III: the full subextremal case ∣a∣ < M, Ann. of Math., 183 (2016), 787–913 (available also at http://www.arxiv.org/abs/1402.7034)
• with Igor Rodnianski and Yakov Shlapenthokh-Rothman, A scattering theory for the wave equation on Kerr black hole exteriors, Ann. Sci. Éc. Norm. Supér. 51 (2018), 371–486 (available also at http://www.arxiv.org/abs/1412.8379)
• with Yakov Shlapentokh-Rothman, Time-translation invariance of scattering maps and blue-shift instabilities on Kerr black hole sapcetimes, available online at http://arxiv.org/abs/1512.08260, Commun. Math. Phys. 350 (2017), 985–1016
  
• with Gustav Holzegel and Igor Rodnianski, The linear stability of the Schwarzschild solution to gravitational perturbations, Acta Math., 222 (2019), 1–214 (available also at http://arxiv.org/abs/1601.06467)
• with Jonathan Luk, The interior of dynamical vacuum black holes I: The C⁰-stability of the Kerr Cauchy horizon, available online at http://arxiv.org/abs/1710.01772, 217 pages, to appear in Ann. of Math.
• with Gustav Holzegel and Igor Rodnianski, Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M, Annals of PDE (2019) 5:2 (available also at http://arxiv.org/abs/1711.07944)
• with Yakov Shlapentokh-Rothman, Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ>0, Class. Quantum Grav. 35 (2018) 195010 (available also at http://arxiv.org/abs/1805.08764)
• with Gustav Holzegel, Igor Rodnianski and Martin Taylor, The non-linear stability of the Schwarzschild family of black holes, available online at https://arxiv.org/abs/2104.08222, 513 pages
• with Gustav Holzegel, Igor Rodnianski and Martin Taylor, Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes, available online at https://arxiv.org/abs/2212.14093, 98 pages, to appear in Analysis and PDE
• with Gustav Holzegel, Igor Rodnianski and Martin Taylor, Quasilinear wave equations on Kerr black holes in the full subextremal range ∣a∣ < M, available online at https://arxiv.org/abs/2410.03639, 99 pages

Survey articles

• Stability and Instability of the Reissner-Nordstrom Cauchy horizon and the problem of uniqueness in general relativity, Contemp. Math. 350 (2004), 99–113, related article available online at http://www.arxiv.org/abs/gr-qc/0209052
• Price's law, mass inflation, and strong cosmic censorship, in Racz, I., ed. Relativity today: Proceedings of the Seventh Hungarian Relativity Workshop, Budapest, 2004, pp. 79--90, related article available online at http://www.arxiv.org/abs/gr-qc/0401121
• The wave equation on axisymmetric stationary black hole backgrounds, AIP Conf. Proc. 1122, (2009) 19–38, available online at http://www.arxiv.org/abs/0901.4125
• The evolution problem in General Relativity, Current Developments in Mathematics 2008, 1–66, Int. Press, Somerville, MA, 2009
• with Igor Rodnianski, The black hole stability problem for linear scalar perturbations, in Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, T. Damour et al (ed.), World Scientific, Singapore, 2011, pp. 132–189, related article available online at http://www.arxiv.org/abs/1010.5137
• The mathematical analysis of black holes in general relativity, Proceedings of the ICM, Seoul 2014, Vol III, pp. 747–772

Essays

• Penrose's incompletenss theorem, Newsletter of the LMS
• The stability problem for extremal black holes,  General Relativity and Gravitation (2025) 57:60 (available also at https://arxiv.org/abs/2410.14414

Lecture notes

• with Igor Rodnianski, Lectures on black holes and linear waves, in Evolution equations, Clay Mathematics Proceedings, Vol. 17. Amer. Math. Soc., Providence, RI, 2013, pp. 97–205, previous version at http://www.arxiv.org/abs/0811.0354

Unpublished

• with Gustav Holzegel, Dynamic instability of solitons in 4 + 1-dimensional gravity with negative cosmological constant, February 2006

Bourbaki exposé

• The formation of black holes in General Relativity [after D. Christodoulou], Astérisque 352 (2013), Exp. No. 1051, viii, 243–313

Book articles

• General relativity and the Einstein equations, in Princeton Companion to Mathematics (T. Gowers, ed.), Princeton Univ. Press 2008

Book review

• Book Review: On the topology and future stability of the universe, by Hans Ringström, Classical and Quantum Gravity Plus

Obituary

• Obituary for Yvonne Choquet-Bruhat, Nature, Vol 642, 12 June 2025, p. 298

Oberwolfach reports

• Linear and non-linear waves in general relativity, Oberwolfach Rep. 2 (2005), pp. 1399–1403
• Stability of black holes and singularities in general relativity, Oberwolfach Rep. 4 (2007), pp. 2381–2387
• The black hole stability problem, Oberwolfach Rep. 6 (2009), pp. 2589–2594
• Superradiance, trapping, and decay of waves on Kerr spacetimes in the general subextremal range |a| < M, Oberwolfach Rep. 7 (2010), pp. 2407–2413
• Construction of dynamical vacuum black holes without symmetries, Oberwolfach Rep. 9 (2012), pp. 1573–1575
• ed. with Jim Isenberg and Hans Rinsgström, Mathematical Aspects of General Relativity, Oberwolfach Rep. 9 (2012), pp. 2269–2333
• ed. with Jim Isenberg and Hans Rinsgström, Mathematical Aspects of General Relativity, Oberwolfach Rep. 12 (2015), pp. 1867–1935
• ed. with Carla Cederbaum, Jim Isenberg and Hans Rinsgström, Mathematical Aspects of General Relativity, Oberwolfach Rep. 15 (2018), pp. 2157–2251
• ed. with Carla Cederbaum, Jim Isenberg and Hans Rinsgström, Mathematical Aspects of General Relativity, Oberwolfach Rep. 18 (2021), no. 3, pp. 2157–2267
• ed. with Carla Cederbaum, Jim Isenberg and Hans Rinsgström, Mathematical Aspects of General Relativity, Oberwolfach Rep. 21 (2024), no. 3, pp. 2033–2112