More on long string dynamics in gravity on ${\mathrm{AdS}}_3$: Spinning strings and rotating BTZ black holes

In this paper we study the classical dynamics of long strings in ${\mathrm{AdS}}_3$, generalizing our previous study, arXiv:1410.3424, to rotating strings and BTZ black holes. As in the nonrotating case, BTZ black holes are generated in the large tension limit, in which string backreaction must be taken into account. When backreaction is properly accounted for, collapsing heavy, physical, rotating strings do not generate naked singularities but only BTZ black holes, including extremal ones. The rotating string must contain world-sheet excitations in order to have consistent equations of motion; we describe such additional degrees of freedom implicitly in terms of an effective equation of state.

Figure 1

We redefine the argument of $V(y)$ as $(y+\frac{1}{2})(M{l}_{+}^2)$ so that the horizon is sitting at the origin, and we set $8G=1$. From (a), (c) and (e), one can see that the largest turning points occur near the horizon (the origin here). (b), (d) and (f) zoom in near the origin to show that the turning points are hidden behind the horizon. (a,b) $\tilde{T}=100,\alpha =1.0001$, (c,d) $\tilde{T}=1000,\alpha =1.00001$, (e,f) $\tilde{T}=7500,\alpha =1.00001$.