Selected Publications

• Collingbourne, Sam C.; Holzegel, Gustav Uniform Boundedness for Solutions to the Teukolsky Equation on Schwarzschild from Conservation Laws of Linearised Gravity. Communications in Mathematical Physics Vol. 405, 2024 online
• Dafermos, Mihalis; Holzegel, Gustav; Rodnianski, Igor Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M. Annals of PDE Vol. 5, 2019, pp Paper No. 2, 118 online
• Dafermos, Mihalis; Holzegel, Gustav; Rodnianski, Igor The linear stability of the Schwarzschild solution to gravitational perturbations. Acta Mathematica Vol. 222 (1), 2019 online
• Graf, Olivier; Holzegel, Gustav Mode stability results for the Teukolsky equations on Kerr-anti-de Sitter spacetimes. Classical and Quantum Gravity Vol. 40 (4), 2023 online
• Holzegel, Gustav Conservation laws and flux bounds for gravitational perturbations of the Schwarzschild metric. Classical and Quantum Gravity Vol. 33 (20), 2016, pp 205004 online
• Holzegel, Gustav The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms. Journal of Hyperbolic Differential Equations Vol. 20 (4), 2023 online
• Holzegel, Gustav; Luk, Jonathan; Smulevici, Jacques; Warnick, Claude Asymptotic properties of linear field equations in anti-de Sitter space. Communications in Mathematical Physics Vol. 374, 2020, pp 1125-1178 online
• Holzegel, Gustav; Shao, Arick Unique continuation from infinity in asymptotically anti-de Sitter spacetimes. Communications in Mathematical Physics Vol. 347 (3), 2016 online
• Holzegel, Gustav; Shao, Arick The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes. Archive for Rational Mechanics and Analysis Vol. 247 (3), 2023 online
• Speck, Jared; Holzegel, Gustav; Luk, Jonathan; Wong, Willie Stable Shock Formation for Nearly Simple Outgoing Plane Symmetric Waves. Annals of PDE Vol. 2 (2), 2016 online

Recent Publications

Recent Publications of Prof. Dr. Gustav Holzegel

$\bullet $ Olivier Graf and Gustav Holzegel. Linear stability of Schwarzschild-Anti-de Sitter spacetimes III: Quasimodes and sharp decay of gravitational perturbations. arXiv e-prints, October 2024. arXiv:2410.21994.

$\bullet $ Mihalis Dafermos, Gustav Holzegel, Igor Rodnianski, and Martin Taylor. Quasilinear wave equations on Kerr black holes in the full subextremal range $|a|<M$. arXiv e-prints, October 2024. arXiv:2410.03639.

$\bullet $ Olivier Graf and Gustav Holzegel. Linear stability of Schwarzschild-Anti-de Sitter spacetimes II: Logarithmic decay of solutions to the Teukolsky system. arXiv e-prints, August 2024. arXiv:2408.02252.

$\bullet $ Olivier Graf and Gustav Holzegel. Linear stability of Schwarzschild-Anti-de Sitter spacetimes I: The system of gravitational perturbations. arXiv e-prints, August 2024. arXiv:2408.02251.

$\bullet $ Sam C. Collingbourne and Gustav Holzegel. Uniform boundedness for solutions to the Teukolsky equation on Schwarzschild from conservation laws of linearised gravity. Communications in Mathematical Physics, 405:Paper No. 138, May 2024. doi:10.1007/s00220-024-04999-4.

$\bullet $ Gustav Holzegel, Georgios Mavrogiannis, and Renato Velozo Ruiz. A note on integrated local energy decay estimates for spherically symmetric black hole spacetimes. arXiv e-prints, March 2024. arXiv:2403.02533.

$\bullet $ Mihalis Dafermos, Gustav Holzegel, and Igor Rodnianski. A scattering theory construction of dynamical vacuum black holes. Journal of Differential Geometry, February 2024. doi:10.4310/jdg/1712344221.

$\bullet $ Gustav Holzegel and Christopher Kauffman. The wave equation on the Schwarzschild spacetime with small non-decaying first-order terms. Journal of Hyperbolic Differential Equations, 20(04):825–834, December 2023. doi:10.1142/s0219891623500273.

$\bullet $ Gustav Holzegel and Arick Shao. The bulk-boundary correspondence for the Einstein equations in asymptotically anti-de Sitter spacetimes. Archive for Rational Mechanics and Analysis, 247(3):56, May 2023. doi:10.1007/s00205-023-01890-9.

$\bullet $ Gustav Holzegel and Christopher Kauffman. The wave equation on subextremal Kerr spacetimes with small non-decaying first order terms. arXiv e-prints, February 2023. arXiv:2302.06387.

$\bullet $ Olivier Graf and Gustav Holzegel. Mode stability results for the Teukolsky equations on Kerr–anti-de Sitter spacetimes. Classical and Quantum Gravity, 40(4):045003, January 2023. doi:10.1088/1361-6382/acb0ac.

$\bullet $ Mihalis Dafermos, Gustav Holzegel, Igor Rodnianski, and Martin Taylor. Quasilinear wave equations on asymptotically flat spacetimes with applications to Kerr black holes. arXiv e-prints, December 2022. arXiv:2212.14093.

$\bullet $ Mihalis Dafermos, Gustav Holzegel, Igor Rodnianski, and Martin Taylor. The non-linear stability of the Schwarzschild family of black holes. arXiv e-prints, April 2021. arXiv:2104.08222.

$\bullet $ Gustav Holzegel, Jonathan Luk, Jacques Smulevici, and Claude Warnick. Asymptotic properties of linear field equations in anti–de Sitter space. Comm. Math. Phys., 374(2):1125–1178, March 2020. doi:10.1007/s00220-019-03601-6.

$\bullet $ Mihalis Dafermos, Gustav Holzegel, and Igor Rodnianski. The linear stability of the Schwarzschild solution to gravitational perturbations. Acta Math., 222(1):1–214, April 2019. doi:10.4310/ACTA.2019.v222.n1.a1.

$\bullet $ Mihalis Dafermos, Gustav Holzegel, and Igor Rodnianski. Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: The case $|a| \ll m$. Ann. PDE, 5(1):2–2, January 2019. doi:10.1007/s40818-018-0058-8.