辐射在黑洞视界附近的性质与热力学第二定律

考虑把一个装满某种内能为E,熵为S的物质的盒子缓慢地向黑洞降落,Bekenstein认为热力学第二定律成立的必要条件为S/E≤2πR(R为盒子的有效半径),而Unruh和Wald认为Hawking辐射的存在保证了广义热力学第二定律的成立,无需条件S/E≤2πR。我们指出:Hawking辐射和S/E≤2πR都无法保证热力学第二定律的成立。我们根据充分的理由提出:引力场会影响物质的态方程。当盒子中装的为辐射时,我们得出了辐射在视界附近时的态方程,它和平直时空的辐射的态方程很不一样。只要将方程中的某个参量加上适当的限制,即可保证热力学第二定律的成立。 关键词：

THE PROPERTIES OF RADIATION NEAR THE BLACK HOLE'S HORIZON AND THE SEDOND LAW OF THERMODYNAMICS

By considering a gedankenexperiment of adiabatically lowering a box containing matter with rest energy E and entropy S to a black hole, Bekenstein claimed that the necessary condition for the validity of the generalized second law of thermodynamics is S/E ≤ 2πR, where R is the effective radius of the box, Unruh and Wald claimed that this condition is not necessary but the acceleration radiation can guarantee the generalized second law. In this paper, we point out that Unruh and Wald's conclusion does not hold because the Hawking radiation near the horizon is not thermal. Bekenstein's conclusion also does not hold because the thin box approximation is not correct near the horizon. Neither Hawking radiation nor S/E ≤ 2πR. can guarantee the second law. We have sufficient reasons to conjecture that the gravitation can influence the state equation of matter. For radiation, the usual state equation ρ = αT⁴ and s =4/3αT³ do not hold in the strong gravitation field, e.g., near theblackhole's horizon. We have derived the state equation for radiation near ths horizon and find that it is very different from that in flat spacetime. The second law may be valid if some restrictions on one parameter of the state equation are imbo-sed. As a corollary, an upper bound on S/E which resembles the Bekenatein's result is found.