标题： 热密度矩阵破坏了Page曲线 显示英文标题

标题： Thermal density matrix breaks down the Page curve

摘要： 在本文中，我们研究了被有限温度共形物质包围的永恒四维施瓦茨希尔德黑洞中的纠缠岛屿和Page曲线。 我们所说的有限温度共形物质是指由热密度矩阵描述的物质，而不是通常考虑的高于福克真空的物质。 我们将物质和黑洞置于不同的温度下，并使用s波近似计算这种设置下的纠缠熵。 结果表明，在晚期时间，岛屿公式会导致热真空中共形物质的纠缠熵指数增长。 显示英文摘要

摘要： In this paper, we study entanglement islands and the Page curve in the eternal four-dimensional Schwarzschild black hole surrounded by finite temperature conformal matter. By finite temperature conformal matter we mean the matter described by the thermal density matrix, rather than the usually considered matter above the Fock vacuum. We take the matter and the black hole at different temperatures and calculate the entanglement entropy for such a setup using the s-wave approximation. As a result, we obtain that at late times the island prescription leads to the exponential growth of the entanglement entropy of conformal matter in thermal vacuum.