{
  "id": "2407.08997",
  "version": "v1",
  "published": "2024-07-12T05:32:21.000Z",
  "updated": "2024-07-12T05:32:21.000Z",
  "title": "Asymptotic Expansions for Semilinear Waves on Asymptotically Flat Spacetimes",
  "authors": [
    "Shi-Zhuo Looi",
    "Haoren Xiong"
  ],
  "categories": [
    "math.AP",
    "gr-qc"
  ],
  "abstract": "We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. For cubic nonlinearities $a(t,x)\\phi^3$, we prove $\\phi(t, x) = 2c_0 t^{-2} + O(t^{-3+})$ in compact spatial regions, with $c_0$ computable. For $a(t,x)\\phi^p$ with $p \\geq 4$, we show $\\phi(t, x) = d t^{-3} + O(t^{-4+})$, extending Price's law to the nonlinear setting. Our approach combines radiation field analysis with a generalized low-energy resolvent expansion, providing a bridge between spectral and physical space methods. These results sharpen previous decay estimates and yield complete asymptotics across the entire spacetime, including black hole backgrounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-12T05:32:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotically flat spacetimes",
      "black hole backgrounds",
      "radiation field analysis",
      "semilinear wave equations",
      "establish precise asymptotic expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}