论文标题
连接形式主义中各个属的非交通性黑洞
Non-commutative black holes of various genera in the connection formalism
论文作者
论文摘要
我们认为在非共同几何形状范式内的任意属数的黑洞内部。该研究以两种方式进行：一种方法是对黑洞内物质分布的简单涂抹。所得结构在文献中通常被称为“受非共同几何形状启发的模型”。第二种方法涉及一种更基本的方法，其中使用了哈密顿形式主义，并在自由度的配置程度之间以及规范的自由度之间引入了非平凡的泊松支架。这是根据连接变量而不是更常见的ADM变量来完成的。在这里使用连接变量，因为非交通效应通常是从量子理论中启发的，并且连接变量在某些更有希望的量子引力的现代理论中使用。我们发现，在第一项研究中，很容易去除黑洞的奇异性。在第二项研究中，我们发现在连接（配置变量）之间引入非平凡的支架可能会延迟奇异性，但不一定会消除它。但是，通过在密度三合会（规范动量变量）之间引入非平凡的支架，通常可以去除奇异性。在某些情况下，由于非交换性，新的视野也出现。
We consider black hole interiors of arbitrary genus number within the paradigm of non-commutative geometry. The study is performed in two ways: One way is a simple smearing of a matter distribution within the black hole. The resulting structure is often known in the literature as a "model inspired by non-commutative geometry". The second method involves a more fundamental approach, in which the Hamiltonian formalism is utilized and a non-trivial Poisson bracket is introduced between the configuration degrees of freedom, as well as between the canonical momentum degrees of freedom. This is done in terms of connection variables instead of the more common ADM variables. Connection variables are utilized here since non-commutative effects are usually inspired from the quantum theory, and it is the connection variables that are used in some of the more promising modern theories of quantum gravity. We find that in the first study, the singularity of the black holes can easily be removed. In the second study, we find that introducing a non-trivial bracket between the connections (the configuration variables) may delay the singularity, but not necessarily eliminate it. However, by introducing a non-trivial bracket between the densitized triads (the canonical momentum variables) the singularity can generally be removed. In some cases, new horizons also appear due to the non-commutativity.
