This work is motivated by the sign problem in a logarithmic parameter of black hole entropy and the existing more massive white dwarfs than the Chandrasekhar mass limit. We examine the quadratic, linear, and linear–quadratic generalized uncertainty principle (GUP) models within the virtue of recent masses and radii of white dwarfs. We consider the modification generated by introducing the minimal length on the degenerate Fermi gas equation of state (EoS) and the hydrostatic equation. For the latter, we applied Verlinde’s proposal regarding entropic gravity to derive the quantum corrected Newtonian gravity, which is responsible for modifying the hydrostatic equation. Through the models’ chi-square analysis, we have found that the observation data favor the quadratic than linear GUP models without mass limit. However, for the quadratic–linear GUP model, we can obtain the positive value of the free parameter γ0 as well as we can get mass limit more massive than the Chandrasekhar limit. In the linear–quadratic GUP model, the formation of stable massive white dwarfs than the Chandrasekhar limit is possible only if both parameters are not equal.

中文翻译：

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白矮星和广义不确定性原理

这项工作的动机是黑洞熵的对数参数中的符号问题以及现有的比钱德拉塞卡质量限制更大的白矮星。我们根据最近的白矮星质量和半径检查二次、线性和线性二次广义不确定性原理 (GUP) 模型。我们考虑通过在简并费米气体状态方程（EoS）和流体静力方程上引入最小长度产生的修改。对于后者，我们应用 Verlinde 关于熵引力的提议来推导量子校正的牛顿引力，它负责修改流体静力方程。通过模型的卡方分析，我们发现观测数据更倾向于二次而不是没有质量限制的线性 GUP 模型。然而，γ0以及我们可以得到比钱德拉塞卡极限更大的质量极限。在线性二次 GUP 模型中，只有当两个参数不相等时，才有可能形成稳定的大质量白矮星而不是钱德拉塞卡极限。