AI 中文总结
研究希格斯场在史瓦西时空中行为，通过引入普朗克抑制耦合，表明时空曲率改变希格斯有效势，导出临界曲率等，确定事件视界内电弱对称性恢复区域，提供联系强引力场与希格斯真空的解析框架。
AI 中文摘要
通过引入希格斯场与克雷奇曼标量之间的普朗克抑制耦合，研究了希格斯场在史瓦西时空中的行为。结果表明时空曲率改变了希格斯有效势，导致真空期望值随曲率增加而连续下降。导出了临界曲率，此时希格斯真空期望值消失，标志着电弱对称性的曲率诱导恢复。对于史瓦西黑洞，得到了临界曲率、相应的相变半径和标志量子引力效应开始的普朗克曲率半径的解析表达式。这些结果确定了事件视界内一个自洽区域，其中电弱对称性恢复而有效描述仍然适用。该模型提供了一个简单的解析框架，通过单一无量纲曲率 - 希格斯耦合将强引力场与希格斯真空联系起来。
英文摘要
I investigate the behaviour of the Higgs field in Schwarzschild spacetime by introducing a Planck-suppressed coupling between the Higgs field and the Kretschmann scalar, the leading curvature invariant in Ricci-flat geometries. I show that spacetime curvature modifies the Higgs effective potential, causing the vacuum expectation value to decrease continuously with increasing curvature. A critical curvature is derived at which the Higgs vacuum expectation value vanishes, signalling a curvature-induced restoration of electroweak symmetry. For Schwarzschild black holes, we obtain analytical expressions for the critical curvature, the corresponding phase-transition radius, and the Planck-curvature radius that marks the onset of quantum-gravity effects. These results identify a self-consistent region inside the event horizon in which electroweak symmetry is restored while the effective description remains applicable. The model provides a simple analytical framework linking strong gravitational fields to the Higgs vacuum through a single dimensionless curvature-Higgs coupling.
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