Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law
Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law
复制标题
DOI：
10.1103/physrevd.70.107501
复制
发表时间：
2004-05
影响因子：
5
通讯作者：
G. Amelino-Camelia;M. Arzano;Andrea Procaccini
中科院分区：
文献类型：
--
作者：
G. Amelino-Camelia;M. Arzano;Andrea Procaccini
我们探讨了最近文献中广泛研究的圈量子引力的两个方面之间的可能联系：黑洞面积熵定律和能量动量色散关系。我们观察到，原来的贝肯斯坦面积熵定律的论点隐含地需要信息的能量动量色散关系和位置动量的不确定性关系。最近的结果表明，在一级近似下，圈量子引力中的黑洞熵与面积呈线性关系，小的修正项与面积呈对数或反幂关系。在环圈量子引力中，色散关系应该包含与普朗克长度线性相关的项，但没有发现位置-动量不确定关系被修正的证据.我们发现，色散关系的普朗克长度线性修正和位置-动量不确定关系未修正的情况与黑洞熵的结果是不相容的，因为它会在熵公式中产生一个项，类似于面积的平方根。
We explore a possible connection between two aspects of loop quantum gravity which have been extensively studied in the recent literature: the black-hole area-entropy law and the energy-momentum dispersion relation. We observe that the original Bekenstein argument for the area-entropy law implicitly requires information on the energy-momentum dispersion relation and on the position-momentum uncertainty relation. Recent results show that in first approximation black-hole entropy in loop quantum gravity depends linearly on the area, with small correction terms which have logarithmic or inverse-power dependence on the area. And it has been argued that in loop quantum gravity the dispersion relation should include terms that depend linearly on the Planck length, while no evidence of modification of the position-momentum uncertainty relation has been found. We observe that this scenario with Planck-length-linear modification of the dispersion relation and unmodified position-momentum uncertainty relation is incompatible with the black-hole-entropy results, since it would give rise to a term in the entropy formula going like the square root of the area.