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arXiv 2007.10601gr-qc
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宇宙审查猜想违反:半经典方法

Cosmic Censorship Conjecture violation: A semiclassical approach

Rodrigo L. Fernandez

摘要:

宇宙审查猜想(Cosmic Censorship Conjecture,CCC)指出,每个奇点(除了宇宙奇点)都必须在宇宙中“穿着”。这个陈述是由罗杰·彭罗斯(Roger Penrose,1969)提出的,意思是宇宙中的每一个奇点(除了大爆炸)都必须隐藏在一个事件视界中。在数学上,这可以用不等式$M^2 \geqslant Q^2 + a^2$(在几何单位系统中)来描述,其中$M$是黑洞的质量,$Q$是它的电荷,$a := J/M$是它的比角动量。从本质上讲,这三个量唯一地决定了一个黑洞,正如无毛定理所述。研究了静态带电黑洞对大质量($m_w$)不带电标量波包(粒子的半经典近似)的发射几率。我们表明,对于质量$\mathcal{M} := M+δM$的几个值,(其中$M$是质量的固定值,$δM$是以$m_w$的顺序对$M$的小变化),对于黑洞,具有不同的$δM$值和固定电荷$Q$,一旦宇宙审查猜想接近被违反,发射概率趋于零,即,当所发射的分组使得新量$\mathcal{M}' := \mathcal{M}-m_w$将违反不等式$\mathcal{M}' > Q$时。

英文摘要:

The Cosmic Censorship Conjecture (CCC) states that every singularity (except the cosmological one) must appear "dressed" in the universe. This statement was introduced by Roger Penrose (Penrose, 1969), meaning that every singularity (except the Big Bang) in the universe must be hidden inside an Event Horizon. Mathematically, this is described by the inequality $M^2 \geqslant Q^2 + a^2$ (in geometrized unit system), with $M$ being the mass of the black hole, $Q$ its charge and $a := J/M$ its specific angular momentum. Essentially, this three quantities determines uniquely a black hole, as stated by the no-hair theorem. We study the emission probability of a massive ($m_w$) uncharged scalar wave packet, a semi-classical approximation for a particle, by a static, charged black hole. We show that for a few values of the mass $\mathcal{M} := M+δM$ (where $M$ is the fixed value for the mass and $δM$ being a small variation to $M$ in the order of $m_w$) with different values for $δM$ and fixed charge $Q$ for the black hole, the emission probability tends to zero once the Cosmic Censorship Conjecture is close to be violated, that is, when the emitted packet is such that the new quantity $\mathcal{M}' := \mathcal{M}-m_w$ would violate the inequality $\mathcal{M}' > Q$.

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