$\mathbf{f(T)}$引力场中规则黑洞的物质条件
Matter Conditions for Regular Black Holes in $\mathbf{f(T)}$ Gravity
摘要：
我们在远程平行引力的$f(T)$扩展中研究了一类球对称黑洞产生规则（非奇异）内部的条件。在广义相对论中，所研究的黑洞类必然是奇异的。我们导出了一个与黑洞内部相容的四元组，并利用这个四元组在引力运动方程中研究了黑洞内部。结果表明，在引力拉氏量可按幂级数$f(T)=T+\underset{n\neq 1}{\sum} b_{n}T^{n}$展开的情况下，黑洞在满足一定的能量条件下可以是非奇异的.因此，黑洞奇点可以被去除，引力运动方程可以在整个流形上保持有效。只要$n$是正的，这是正确的，但在理论的负扇区中不是正确的。因此，引力$f(T)$拉格朗日量可以泰勒展开为$T$的幂，它可以产生这种类型的规则黑洞。虽然我们发现这些黑洞在$f(T)$理论中可以被证明是非奇异的，但是我们猜想如果相应的$f(T)$黑洞是正则的，那么在广义相对论奇点的任意小邻域内，主能量条件被违反，这是一个温和的奇异性定理.这里的分析技术也可以应用于引力拉格朗日函数，而不是劳伦或泰勒可展开的。
英文摘要：
We study the conditions imposed on matter to produce a regular (non-singular) interior of a class of spherically symmetric black holes in the $f(T)$ extension of teleparallel gravity. The class of black holes studied is necessarily singular in general relativity. We derive a tetrad which is compatible with the black hole interior and utilize this tetrad in the gravitational equations of motion to study the black hole interior. It is shown that in the case where the gravitational Lagrangian is expandable in a power series $f(T)=T+\underset{n\neq 1}{\sum} b_{n}T^{n}$ that black holes can be non-singular while respecting certain energy conditions in the matter fields. Thus the black hole singularity may be removed and the gravitational equations of motion can remain valid throughout the manifold. This is true as long as $n$ is positive, but is not true in the negative sector of the theory. Hence, gravitational $f(T)$ Lagrangians which are Taylor expandable in powers of $T$ may yield regular black holes of this type. Although it is found that these black holes can be rendered non-singular in $f(T)$ theory, we conjecture that a mild singularity theorem holds in that the dominant energy condition is violated in an arbitrarily small neighborhood of the general relativity singular point if the corresponding $f(T)$ black hole is regular. The analytic techniques here can also be applied to gravitational Lagrangians which are not Laurent or Taylor expandable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
