References
- Hintz, P., Vasy, A. (2015). Semilinear wave equations on asymptotically de Sitter, Kerr–de Sitter and Minkowski spacetimes. Anal. PDE 8(8):1807–1890. DOI: 10.2140/apde.2015.8.1807.
- Hintz, P., Vasy, A. (2014). Non-trapping estimates near normally hyperbolic trapping. Math. Res. Lett. 21(6):1277–1304. DOI: 10.4310/MRL.2014.v21.n6.a5.
- Hintz, P., Vasy, A. (2016). Global analysis of quasilinear wave equations on asymptotically de Sitter spaces. Ann. de l’Institut Fourier 66(4):1285–1408. DOI: 10.5802/aif.3039.
- Hintz, P., Vasy, A. (2016). Global analysis of quasilinear wave equations on asymptotically Kerr–de Sitter spaces. Int. Math. Res. Not. IMRN 17:5355–5426. DOI: 10.1093/imrn/rnv311.
- Vasy, A. (2010). The wave equation on asymptotically de Sitter-like spaces. Adv. Math. 223(1):49–97. DOI: 10.1016/j.aim.2009.07.005.
- Vasy, A. (2013). Microlocal analysis of asymptotically hyperbolic and Kerr-de Sitter spaces (with an appendix by Semyon Dyatlov). Invent. Math. 194(2):381–513. DOI: 10.1007/s00222-012-0446-8.
- Bony, J.-F., Häfner, D. (2008). Decay and non-decay of the local energy for the wave equation on the de Sitter-Schwarzschild metric. Commun. Math. Phys. 282(3):697–719. DOI: 10.1007/s00220-008-0553-y.
- Dafermos, M., Rodnianski, I. (2010). A new physical-space approach to decay for the wave equation with applications to black hole spacetimes. In: XVIth International Congress on Mathematical Physics. Hackensack, NJ: World Scientific Publishing, pp. 421–432. DOI: 10.1142/9789814304634_0032.
- Dafermos, M., Rodnianski, I. (2007). A note on energy currents and decay for the wave equation on a Schwarzschild background. arXiv:0710.0171.
- Dafermos, M., Rodnianski, I. (2007). The wave equation on Schwarzschild-de Sitter spacetimes. arXiv:0709.2766.
- Melrose, R., Sá Barreto, A., Vasy, A. (2014). Asymptotics of solutions of the wave equation on de Sitter-Schwarzschild space. Commun. Partial Differ. Equ. 39(3):512–529. DOI: 10.1080/03605302.2013.866958.
- Dyatlov, S. (2011). Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole. Commun. Math. Phys. 306(1):119–163. DOI: 10.1007/s00220-011-1286-x.
- Dyatlov, S. (2011). Exponential energy decay for Kerr–de Sitter black holes beyond event horizons. Math. Res. Lett. 18(5):1023–1035. DOI: 10.4310/MRL.2011.v18.n5.a19.
- Hintz, P., Vasy, A. (2018). The global non-linear stability of the Kerr–de Sitter family of black holes. Acta Math. 220(1):1–206. DOI: 10.4310/ACTA.2018.v220.n1.a1.
- Schlue, V. (2021). Decay of the Weyl curvature in expanding black hole cosmologies. arXiv:1610.04172.
- Schlue, V. (2015). Global results for linear waves on expanding Kerr and Schwarzschild de Sitter cosmologies. Commun. Math. Phys. 334(2):977–1023. DOI: 10.1007/s00220-014-2154-2.
- Friedrich, H. (1986). On the existence of n-geodesically complete or future complete solutions of Einstein’s field equations with smooth asymptotic structure. Commun. Math. Phys. 107(4):587–609. DOI: 10.1007/BF01205488.
- Dafermos, M., Rodnianski, I. (2009). The red-shift effect and radiation decay on black hole spacetimes. Commun. Pure Appl. Math. 62(7):859–919. DOI: 10.1002/cpa.20281.
- Tataru, D., Tohaneanu, M. (2011). A local energy estimate on Kerr black hole backgrounds. Int. Math. Res. Not. 2:248–292. DOI: 10.1093/imrn/rnq069.
- Dafermos, M., Rodnianski, I., Shlapentokh-Rothman, Y. (2016). Decay for solutions of the wave equation on Kerr exterior spacetimes III: The full subextremal case |a|<M . Ann. Math. (2) 183(3):787–913.
- Luk, J. (2013). The null condition and global existence for nonlinear wave equations on slowly rotating Kerr spacetimes. J. Eur. Math. Soc. (JEMS) 15(5):1629–1700. DOI: 10.4171/jems/400.
- Lindblad, H., Tohaneanu, M. (2018). Global existence for quasilinear wave equations close to Schwarzschild. Commun. Partial Differ. Equ. 43(6):893–944. DOI: 10.1080/03605302.2018.1476529.
- Klainerman, S. (1986). The null condition and global existence to nonlinear wave equations. In: Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 (Santa Fe, N.M., 1984), volume 23 of Lectures in Applied Mathematics. Providence, RI: American Mathematical Society, pp. 293–326.
- Dafermos, M., Holzegel, G., Rodnianski, I. (2019). The linear stability of the Schwarzschild solution to gravitational perturbations. Acta Math. 222(1):1–214. DOI: 10.4310/ACTA.2019.v222.n1.a1.
- Shlapentokh-Rothman, Y., Teixeira da Costa, R. (2020). Boundedness and decay for the Teukolsky equation on Kerr in the full subextremal range |a|<M : frequency space analysis. arXiv:2005.13644.
- Häfner, D., Hintz, P., Vasy, A. (2021). Linear stability of slowly rotating Kerr black holes. Invent. Math. 223(3):1227–1406. DOI: 10.1007/s00222-020-01002-4.
- Andersson, L., Bäckdahl, T., Blue, P., Ma, S. (2019). Stability for linearized gravity on the Kerr spacetime. arXiv:1903.03859.
- Klainerman, S., Szeftel, J. (2020). Global Nonlinear Stability of Schwarzschild Spacetime under Polarized Perturbations, volume 210 of Annals of Mathematics Studies. Princeton, NJ: Princeton University Press.
- Dafermos, M., Holzegel, G., Rodnianski, I., Taylor, M. (2021). The non-linear stability of the Schwarzschild family of black holes. arXiv:2104.08222.
- Dafermos, M., Holzegel, G., Rodnianski, I. (2019). Boundedness and decay for the Teukolsky equation on Kerr spacetimes I: the case |a|≪M . Ann. PDE 5(1):Paper No. 2, 118.
- Mavrogiannis, G. Morawetz estimates without relative degeneration and exponential decay on Schwarzschild de Sitter spacetimes. preprint.
- Holzegel, G., Kauffman, C. (2020). A note on the wave equation on black hole spacetimes with small non-decaying first order terms. arXiv:2005.13644.
- Sá Barreto, A., Zworski, M. (1997). Distribution of resonances for spherical black holes. Math. Res. Lett. 4(1):103–121. DOI: 10.4310/MRL.1997.v4.n1.a10.
- Burq, N. (2004). Smoothing effect for Schrödinger boundary value problems. Duke Math. J. 123(2):403–427. DOI: 10.1215/S0012-7094-04-12326-7.
- Burq, N., Guillarmou, C., Hassell, A. (2010). Strichartz estimates without loss on manifolds with hyperbolic trapped geodesics. Geom. Funct. Anal. 20(3):627–656. DOI: 10.1007/s00039-010-0076-5.
- Ikawa, M. (1988). Decay of solutions of the wave equation in the exterior of several convex bodies. Ann. Inst. Fourier (Grenoble) 38(2):113–146. DOI: 10.5802/aif.1137.
- Nonnenmacher, S., Zworski, M. (2009). Quantum decay rates in chaotic scattering. Acta Math. 203(2):149–233. DOI: 10.1007/s11511-009-0041-z.
- Dyatlov, S. (2016). Spectral gaps for normally hyperbolic trapping. Ann. Inst. Fourier (Grenoble) 66(1):55–82. DOI: 10.5802/aif.3005.
- Mavrogiannis, G. Relatively non degenerate estimates on Kerr de Sitter and applications. in preparation.
- Dafermos, M., Rodnianski, I. (2013). Lectures on black holes and linear waves. In: Evolution Equations, volume 17 of Clay Mathematics Proceedings. Providence, RI: American Mathematical Society, pp. 97–205.