BTZ黑洞背景下Dirac场的量子性质
Quantum properties of the Dirac field on BTZ black hole backgrounds
摘要：
本文考虑$(1 + 2)$维不带电BTZ黑洞背景上的Dirac场.我们首先找出了狄拉克哈密顿量，并研究了它的自伴性。我们发现，在类似的Kerr-Newman-AdS狄拉克哈密尔顿在$(1+3)$维，本质上的自伴$C_0^{\infty}(r_+,\infty)^2$的约化（径向）哈密尔顿实现，只有当一个合适的关系之间的质量$μ$的狄拉克场和宇宙半径$l$成立。$r=\infty$类似边界行为的存在是这个问题的根源。此外，我们确定在一个完整的方式定性的光谱性质的非极值的情况下，我们可以推断的狄拉克场的量子束缚态的情况下。接下来，我们研究了$(1 + 2)$维不带电BTZ黑洞角动量量子损失的可能性。与相应的固定四维解不同，能级交叉机制的形式处理要简单得多。我们发现，即使在极端的情况下，没有水平交叉发生。因此，不允许通过粒子对产生的角动量的量子损失。
英文摘要：
We consider a Dirac field on a $(1 + 2)$-dimensional uncharged BTZ black hole background. We first find out the Dirac Hamiltonian, and study its self-adjointness properties. We find that, in analogy to the Kerr-Newman-AdS Dirac Hamiltonian in $(1+3)$ dimensions, essential self-adjointness on $C_0^{\infty}(r_+,\infty)^2$ of the reduced (radial) Hamiltonian is implemented only if a suitable relation between the mass $μ$ of the Dirac field and the cosmological radius $l$ holds true. The very presence of a boundary-like behaviour of $r=\infty$ is at the root of this problem. Also, we determine in a complete way qualitative spectral properties for the non-extremal case, for which we can infer the absence of quantum bound states for the Dirac field. Next, we investigate the possibility of a quantum loss of angular momentum for the $(1 + 2)$-dimensional uncharged BTZ black hole. Unlike the corresponding stationary four-dimensional solutions, the formal treatment of the level crossing mechanism is much simpler. We find that, even in the extremal case, no level crossing takes place. Therefore, no quantum loss of angular momentum via particle pair production is allowed.
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