非对易引力黑洞研究与时空基本长度的探测

As a new hot topic, the noncommutative gravity is a phenomenological gravity model which has a strong motivation of Quantum Gravity. This project try to study on some related problems of the noncommutative gravity black holes under the frame of coordinate coherent state and, investigate probing the fundmental length of spacetime. Firstly, by using the variational principle, we seek for modifications of some field equations such as gravitational field, scalar field, Dirac field, electromagnetic field, etc., and try to obtain some new black hole solutions and some field evolution equations under the background of noncommutative spacetime. Secondly, by using some methods such as Hamilton-Jacobi process, we study some thermodynamic properties of noncommutative gravity black holes, such as Hawking temperature, Hawking radiation, entropy, etc. By using the perturbation theory, we study the evolutions of some perturbation fields in the spacetime of noncommutative gravity black holes. Then by comparing them with some corresponding conclusions under the background of commutative spacetime, we try to get some signals about Quantum Gravity and, provide some theoretical supports for seeking black hole via astronomical way. Lastly, by studying the spacetime noncommutative effect on black holes as gravitational lens, we try to obtain some relevant informations about the fundamental length of spacetime by the way of astronomy. All these studies will benefit to change and develop some conceptions of spacetime, will promote the study of Quantum Gravity, and will benefit to the development of black hole physics which is the intersection of many disciplines.

作为一个新兴的热点课题，非对易引力是一个具有很强量子引力动机的唯象引力模型。本项目试图探讨坐标相干态框架下的非对易引力黑洞相关问题，并研究时空基本长度的探测。首先采用变分原理研究在非对易时空背景下的引力场、标量场、Dirac 场、电磁场等不同场方程的修正，试图得到新的黑洞解和场的演化方程。然后采用哈密顿-雅克比等方法研究非对易引力黑洞的霍金温度、霍金辐射、熵等黑洞热力学性质；采用微扰理论研究非对易引力黑洞时空中微扰场的演化，与对易时空背景下的相关结论进行比较，试图获得关于量子引力的信号，为天文寻找黑洞提供理论支持。最后，研究时空非对易性效应对黑洞作为引力透镜的影响，试图从天文途径获得关于时空基本长度的相关信息。这些研究将有利于变革、发展人们的时空观念，促进量子引力的研究，有利于黑洞物理学——这门诸多学科的交叉点的发展。

引力的量子效应是人们当前关注的热点之一。本项目研究了时空非对易性效应、黑洞量子辐射、破坏Lorentz对称性的黑洞以及黑洞引力透镜等内容。通过研究，我们得到了这些发现。(1) 当考虑引力的量子效应时，黑洞作为加速器，不会使粒子获得无限高能量，除非黑洞质量无限大。(2) 在通常的坐标系下得出了黑洞背景对辐射粒子的散射作用和黑洞与辐射粒子整个系统的熵增，且物理图像更加清晰。(3) 在爱因斯坦-麦克斯韦-以太理论的框架下，我们发现了两类荷电黑洞的精确解，它们都是渐近平直的，并且都有万有视界和Killing视界，可以容许超光速粒子存在。(4) phantom暗能量对黑洞引力透镜方面的影响：它的作用有点像RN黑洞中的电荷，即光线偏折角和角分离度随着phantom常数增加而增加；但是，其它观测量却与RN黑洞情形的相反，即暗能量将普通黑洞压缩得更小，更强烈的吸引光子等。