本论文主要含有两方面内容，一个是分别讨论了带电BTZ黑洞和非对易黑洞内标量场熵在Hawking辐射下的演化性质，一个是推导了SchwarzschilddS时空中光线的偏折角并讨论了宇宙学常数对它的影响。

在第二章中，我们按照Christodoulou和Rovelli所提出的黑洞体积定义，先计算了带电BTZ黑洞的内部体积，结果显示它会随着时间的增大而增大。然后我们又推导了定义在该内部体积上的标量场熵，并考虑Hawking辐射过程，在两条假设的基础上进一步得到了标量场熵和Bekenstein-Hawking熵两者变化率之间的关系，以比例函数为体现。当黑洞质量很大时，带电BTZ黑洞的比例函数会与质量近似成正比例关系。这与Reissner-Nordstrom黑洞的情况不同，后者的比例函数会近似为常数。除此之外，我们将以上计算过程推广到了Massive Gravity理论下的带电BTZ黑洞上，发现足够大的MassiveGravity参数会使比例函数在质量很大时近似于常值。在第三章中，通过计算非对易黑洞内标量场的熵，我们构建了该熵和Bekenstein-Hawking熵两者在Hawking辐射下的变化关系。与Schwarzschild黑洞相比，由于我们引入了非对易性，该计算过程的有效性可以拓展至Hawking辐射后期。经过分析我们发现，在Hawking辐射的前期，非对易黑洞的比例函数退化为Schwarzschild黑洞情况，近似与质量无关。随着Hawking辐射进入到后期，非对易性开始主导比例函数的行为。在该阶段中，比例函数随着黑洞质量的减小而逐渐减小。当非对易黑洞演化至其终态时，内部体积会收敛为一个有限值，这意味着黑洞蒸发过程中所丢失的信息最终会存储在内部体积中。最后我们在第四章沿用Rinder的思路，分别计算了Schwarzschild时空和Schwarzschild-dS时空中光线轨迹上任意一点的偏折角。这种计算方法理论上可应用于其他具有球对称性的非渐近平直时空中。为了讨论宇宙学常数对偏折角的影响，我们考虑光源、透镜天体和观测者它们的相对位置已知，计算光线从光源到观测者所发生的偏折。最终我们得出结论，宇宙学常数的存在会削弱光线的偏折效应，减小光线的偏折角。

There are two main contents in this thesis: one is the discussion about the properties of the scalar field’s entropy inside a charged BTZ black hole and a noncommutative black hole. The other is the discussion about the deflection angle of light in the Schwarzschild-dS spacetime and the influence on deflection angle by the cosmological constant.

In Chapter 2, using the definition of a black hole’s volume introduced by Christodoulou and Rovelli, we calculate the interior volume of a (2+1)-dimensional charged Banados Teitelboim Zanelli (BTZ) black hole, and find that the volume increases linearly with Eddington time. Then, we calculate a massless scalar field’s entropy inside the black hole and the result indicates that the entropy will be also increasing with time infinitely. Moreover, the ratio of variation of the scalar field’s entropy to the variation of Bekenstein-Hawking entropy under Hawking radiation is approximately a linear function of mass when the mass is relatively large, which is quite different from a Reissner-Nordstrom black hole. Besides, we extend the calculations above to a massive BTZ black hole and find that as the Massive Gravity parameter becomes big enough, the proportion function will tend to be a constant. In Chapter 3, by calculating the scalar field’s entropy in the interior volume of a noncommutative black hole, we construct a proportion function which reflects the evolution relation between the scalar field entropy and Bekenstein-Hawking entropy under Hawking radiation. Comparing with the case of a Schwarzschild black hole, the new physics of this research is an extension to the later stage of Hawking radiation. From the result, we find that the proportion function is still a constant in the earlier stage of the radiation process, which is identical to the case of a Schwarzschild black hole. As Hawking radiation goes into the later stage, the noncommutative effect will dominate the behavior of the function. In this circumstance, the proportion function is no longer a constant and decreases with the evaporation process. When the noncommutative black hole evolves into its final state, the interior volume will converge to a certain value, which implies that the information loss of the black hole during the evaporation process will finally be stored in the limited interior volume. In Chapter 4, following Rindler’s idea, we calculate the deflection angles of any point on the light in Schwarzschild spacetime and Schwarzschild-dS spacetime. Theoretically, this calculation can be used in any non-asymptotically flat spherically symmetric spacetime. In order to investigate the influence on the deflection angle by cosmological constant, we consider that the relative positions of light source, lens and observer are all known, and calculate the deflection angle of light from the source to the observer. The result indicates that the existence of a cosmological constant will weaken the light deflection.