AI 中文总结
本文通过计算机辅助证明，严格验证了爱因斯坦-外尔引力中一个非施瓦西黑洞解的存在性，采用级数、泰勒模型与稳定流形结合的方法，并利用庞加莱-米兰达定理确认匹配零点。
AI 中文摘要
静态、渐近平坦的四维爱因斯坦-外尔引力中的非施瓦西黑洞此前已通过数值打靶法构造，而局部场方程允许任意阶的视界和渐近展开。我们给出一个非施瓦西解的计算机辅助存在性证明，该解的无量纲视界半径在以有质量自旋-2尺度为单位下等于1，其参数接近先前报道的数值分支。外部区域被划分为一个收敛的视界级数域、一个由带定向舍入的参数相关泰勒模型包围的紧致核心，以及一个作为中心稳定流形不动点问题处理的无穷渐近域。由此产生的核心与尾部之间的五维匹配映射在严格指定的盒子上连续。在精确有理预条件处理后，相对面上的符号满足庞加莱-米兰达定理的假设，从而证明存在匹配零点。该解具有正则非退化视界、无额外外部视界、里奇标量消失且里奇张量非零。该证明确立了存在性，但不保证匹配零点的唯一性。
英文摘要
Static, asymptotically flat, non-Schwarzschild black holes in four-dimensional Einstein--Weyl gravity have previously been constructed by numerical shooting, while the local field equations admit horizon and asymptotic expansions to all orders. We give a computer assisted existence proof for a non-Schwarzschild solution whose dimensionless horizon radius is one in units of the massive spin-two scale, with parameters close to the previously reported numerical branch. The exterior is divided into a convergent horizon series domain, a compact core enclosed by a parameter dependent Taylor model with directed rounding, and an infinite asymptotic domain treated as a centered stable manifold fixed point problem. The resulting five-dimensional matching map between the core and tail is continuous on a rigorously specified box. After exact rational preconditioning, the signs on opposite faces satisfy the hypotheses of the Poincaré--Miranda theorem and therefore certify a matching zero. The solution has a regular nondegenerate horizon, no additional exterior horizon, vanishing Ricci scalar, and nonvanishing Ricci tensor. The proof establishes existence, but not uniqueness of the matching zero.
Comments39 pages
