On the BTZ black hole and the spinning cosmic string

Abstract

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 $g_{\mu \nu }=\omega ^2 {\tilde{g}}_{\mu \nu }$, is horizon free and has an ergo-circle, while ${\tilde{g}}_{\mu \nu }$ is the BTZ solution. The dilaton $\omega$ 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.