Corichi Alejandro, Díaz-Polo Jacobo, Fernández-Borja Enrique
Instituto de Matemáticas, Unidad Morelia, Universidad Nacional Autónoma de México, UNAM-Campus Morelia, A. Postal 61-3, Morelia, Michoacán 58090, Mexico.
Phys Rev Lett. 2007 May 4;98(18):181301. doi: 10.1103/PhysRevLett.98.181301.
Ever since the pioneering works of Bekenstein and Hawking, black hole entropy has been known to have a quantum origin. Furthermore, it has long been argued by Bekenstein that entropy should be quantized in discrete (equidistant) steps given its identification with horizon area in (semi-)classical general relativity and the properties of area as an adiabatic invariant. This lead to the suggestion that the black hole area should also be quantized in equidistant steps to account for the discrete black hole entropy. Here we shall show that loop quantum gravity, in which area is not quantized in equidistant steps, can nevertheless be consistent with Bekenstein's equidistant entropy proposal in a subtle way. For that we perform a detailed analysis of the number of microstates compatible with a given area and show consistency with the Bekenstein framework when an oscillatory behavior in the entropy-area relation is properly interpreted.
自贝肯斯坦和霍金的开创性工作以来，人们就知道黑洞熵具有量子起源。此外，贝肯斯坦长期以来一直认为，鉴于熵在（半）经典广义相对论中与视界面积的等同性以及面积作为绝热不变量的性质，熵应以离散（等间距）步长进行量子化。这导致了这样的建议，即黑洞面积也应以等间距步长进行量子化，以解释离散的黑洞熵。在这里，我们将表明，尽管在圈量子引力中面积不是以等间距步长进行量子化的，但它仍能以一种微妙的方式与贝肯斯坦的等间距熵提议相一致。为此，我们对与给定面积兼容的微观态数量进行了详细分析，并表明当熵 - 面积关系中的振荡行为得到恰当解释时，与贝肯斯坦框架是一致的。
