论文标题
关于Immirzi参数和地平线熵的值
On the value of the Immirzi parameter and the horizon entropy
论文作者
论文摘要
在循环量子重力（LQG）中，一般相对性的定量导致对几何可观察物（例如体积和面积）的特征值的精确预测，直到理论的唯一自由参数，即Barbero-Immmirzi（BI）参数。 LQG在区域操作员的特征值方程的帮助下，成功得出了带有隔离视野的大型黑洞的Bekenstein-Hawking熵，将BI参数固定为BI参数为$γ\约0.274 $。在本文中，我们显示了一些证据表明，具有角动量$ \ hbar $和Planck Mass的黑洞是该区域操作员的特征，前提是$γ= \ sqrt {3}/6 \大约1.05 \ times 0.274 $。由于黑洞是极端的，因此没有鹰辐射，并且地平线是隔离的。我们还建议，可以在质量状态$ m_2 $的两个平行标准模型中微子的正面散射中形成这样一个黑洞（假设$ m_1 = 0 $）。此外，我们使用所获得的BI参数来计算隔离视野的熵，而区域的区域范围为$ 250 \，l_p^2 $，通过计算与给定区域相关的微态数量。与Bekenstein-Hawking Entropy同意，结果熵具有领先的项$ {\ cal s} \大约0.25 \，{\ cal a} $。由于上述本征态的识别基于经典区域和量子区域特征值之间的匹配，因此，我们还基于Schwarzschild黑洞的有效量子模型，该模型最近提出了Ashtekar，OlMedo和Singh，这是一个孤立水平量子校正面积的表达式，对任何黑洞质量有效。对于经典区域，量子校正对于普朗克质量黑洞的量子校正可以忽略不计。
In Loop Quantum Gravity (LQG) the quantisation of General Relativity leads to precise predictions for the eigenvalues of geometrical observables like volume and area, up to the value of the only free parameter of the theory, the Barbero-Immirzi (BI) parameter. With the help of the eigenvalues equation for the area operator, LQG successfully derives the Bekenstein-Hawking entropy of large black holes with isolated horizons, fixing at this limit the BI parameter as $γ\approx 0.274$. In the present paper we show some evidence that a black hole with angular momentum $\hbar$ and Planck mass is an eigenstate of the area operator provided that $γ= \sqrt{3}/6 \approx 1.05 \times 0.274$. As the black hole is extremal, there is no Hawking radiation and the horizon is isolated. We also suggest that such a black hole can be formed in the head-on scattering of two parallel Standard Model neutrinos in the mass state $m_2$ (assuming $m_1 = 0$). Furthermore, we use the obtained BI parameter to numerically compute the entropy of isolated horizons with areas ranging up to $250\,l_P^2$, by counting the number of micro-states associated to a given area. The resulting entropy has a leading term ${\cal S} \approx 0.25\, {\cal A}$, in agreement to the Bekenstein-Hawking entropy. As the identification of the above eigenstate rests on the matching between classical areas and quantum area eigenvalues, we also present, on the basis of an effective quantum model for the Schwarzschild black hole recently proposed by Ashtekar, Olmedo and Singh, an expression for the quantum corrected area of isolated horizons, valid for any black hole mass. Quantum corrections are shown to be negligible for a Planck mass black hole, of order $10^{-3}$ relative to the classical area.
