We review the Baňados–Teitelboim–Zanelli (BTZ) black hole solution in connection with the spinning string solution. We find a new exact solution, which can be related to the (2 + 1)-dimensional spinning point particle solution. There is no need for a cosmological constant, and so the solution can be up-lifted to (3 + 1) dimensions. The exact solution in a conformally invariant gravity model, where the space–time is written as $$g_{\mu \nu }=\omega ^2 {\tilde{g}}_{\mu \nu }$$ g μ ν = ω 2 g ~ μ ν , is horizon free and has an ergo-circle, while $${\tilde{g}}_{\mu \nu }$$ g ~ μ ν is the BTZ solution. The dilaton $$\omega $$ ω determines the scale of the model. It is conjectured that the conformally invariant non-vacuum BTZ solution will solve the boundary and causality problems which one encounters in spinning cosmic string solutions.

中文翻译：

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在 BTZ 黑洞和旋转的宇宙弦上

我们回顾了 Baňados–Teitelboim–Zanelli (BTZ) 黑洞解决方案以及旋转弦解决方案。我们找到了一个新的精确解，它可以与（2 + 1）维自旋点粒子解有关。不需要宇宙常数，因此可以将解提升到 (3 + 1) 维。共形不变引力模型中的精确解，其中时空写为 $$g_{\mu \nu }=\omega ^2 {\tilde{g}}_{\mu \nu }$$ g μ ν = ω 2 g ~ μ ν 是无视界的，有一个ergo-circle，而 $${\tilde{g}}}_{\mu \nu }$$ g ~ μ ν 是 BTZ 解。dilaton $$\omega $$ ω 决定了模型的尺度。据推测，共形不变的非真空BTZ解将解决旋转宇宙弦解中遇到的边界和因果关系问题。