修正熵力引力中的静态球对称解
Static Spherically Symmetric Solutions in Modified Entropic Gravity
- Amirkabir University of Technology（阿米尔卡比尔理工大学）
- Institute for Research in Fundamental Sciences (IPM)（伊朗基础科学研究院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究求解修正熵力引力中静态球对称时空的修正爱因斯坦方程，发现温度修正函数为$f(T)\boldsymbol{\times} T^2$时时空退化为闵可夫斯基度规，需轻微偏离二次依赖以获得引力修正，对数修正或影响弱场下的粒子运动。
AI中文摘要：
在Verlinde提出的熵力引力范式中，假设位于全息屏上的微观自由度遵循能量均分定律。然而，统计力学的含义表明，这种能量共享会获得依赖于温度的修正。考虑此类修正后，从热力学推导会得到修正后的引力场方程。我们求解静态球对称时空下的修正爱因斯坦方程，确定度规分量的一般结构。研究发现，若温度修正函数满足$f(T)\boldsymbol{\times} T^2$，对应时空几何会退化为平直的闵可夫斯基度规。因此，要得到与平直性的微小偏差，需考虑与纯二次温度依赖的轻微偏离，这种偏离可被解释为编码额外引力效应，可能与全息屏未完全描述的物质贡献相关。这些效应使有效引力势获得对数修正，可能导致偏离牛顿引力，这在极弱引力场区域尤为显著，此类修正可能影响粒子运动，并对天体物理和宇宙学场景具有启示意义。
英文摘要：
Within the entropic gravity paradigm introduced by Verlinde, one assumes that the microscopic degrees of freedom residing on the holographic screen obey the equipartition law of energy. Nevertheless, implications of statistical mechanics suggest that this energy sharing can acquire corrections that depend on temperature. Taking such modifications into account leads to altered gravitational field equations when derived from thermodynamic considerations. We solve the resulting modified Einstein equations in the case of a static, spherically symmetric spacetime and determine the general structure of the metric components. Our findings indicate that if the temperature correction function behaves as $f(T)\propto T^{2}$, the corresponding spacetime geometry reduces to the flat Minkowski metric. Therefore, to obtain small deviations from flatness, it is necessary to consider slight departures from this purely quadratic temperature dependence. Such deviations can be interpreted as encoding additional gravitational effects, potentially associated with matter contributions that are not entirely described by the holographic screen. As a result of these effects, the effective gravitational potential acquires a logarithmic correction, which can give rise to deviations from Newtonian gravity. This aspect is especially significant in the regime of very weak gravitational fields, where these corrections may affect particle motion and could carry implications for both astrophysical and cosmological contexts.
