关于$f(\mathbb{Q})$引力的史瓦西分支上对数熵修正的热力学一致性及超辐射禁戒结果
Thermodynamic Consistency of Logarithmic Entropy Corrections on the Schwarzschild Branch of $f(\mathbb{Q})$ Gravity and a Superradiance No-Go Result
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中文总结 AI 辅助
研究对称遥平行引力史瓦西分支上对数熵修正的黑洞热力学及标量散射，构建相关方程，导出主导熵及修正，分析热容量等，还推导标量相关关系，得出无超辐射放大等结论。
中文摘要 AI 辅助
我们对对称遥平行引力的史瓦西分支上对数修正的黑洞热力学和标量散射进行了简洁明确的分析。将度规和无挠平坦仿射联络视为独立变量，构建相关非度规几何和场方程，表明线性分支在边界项之外与广义相对论动力学等效，真空解为史瓦西时空。通过诺特定理电荷法和经典第一定律导出主导熵并引入对数修正。固定几何和ADM质量时，几何霍金温度不变，修正第一定律定义的温度改变。热容量的明显发散出现在对数展开可靠范围之外，不能解释为物理相变。还推导了标量径向方程、有效势、守恒朗斯基行列式和反射透射关系。对于静态中性背景上的中性标量场，无超辐射放大，除非有真正的半经典反作用或明确的旋转或带电黑洞解，熵修正不会使散射振幅产生一阶变化。
英文摘要
We present a concise and explicit analysis of logarithmically corrected black-hole thermodynamics and scalar scattering on the Schwarzschild branch of symmetric teleparallel gravity. Treating the metric and the flat, torsion-free affine connection as independent variables, we formulate the relevant nonmetricity geometry and field equations and show that the linear branch is dynamically equivalent to general relativity up to a boundary term. The vacuum solution is therefore the Schwarzschild spacetime. The leading entropy is derived from both the Noether-charge method and the classical first law, after which a logarithmic correction is introduced. When the geometry and ADM mass are kept fixed, the geometric Hawking temperature remains unchanged, whereas the temperature defined through the corrected first law is modified. The apparent divergence of the heat capacity occurs outside the regime in which the logarithmic expansion is reliable and therefore cannot be interpreted as a physical phase transition. We also derive the scalar radial equation, effective potential, conserved Wronskian, and reflection-transmission relation. For a neutral scalar field on a static neutral background, no superradiant amplification occurs, and the entropy correction produces no first-order change in the scattering amplitudes unless a genuine semiclassical backreaction or an explicit rotating or charged black-hole solution is provided.
