Strings near BTZ black holes: A Carrollian Chronicle

Abstract

The BTZ black hole provides a tractable (2+1)-dimensional example for investigating string dynamics in curved spacetime. However, a systematic and robust analysis of the solution space of strings in the near-horizon region of BTZ black holes remains elusive in the literature. This work aims to fill this gap by employing the string-Carroll expansion. This formalism provides a natural setting for working with the near-horizon region, because near-horizon expansions for non-extremal black holes match string-Carroll expansions. Using this formalism, and expanding the string action and pullback fields in powers of an effective speed of light, we study the dynamics of closed bosonic strings in the near-horizon, non-extremal BTZ spacetime. Our approach classifies the general characteristics and further reveals some novel features of the families of string solutions.

Figures (9)

• Figure 1: This is a plot for $x^\rho(\sigma)$ vs $\sigma$ in \ref{['yoyo strings 2']} depicting "yo-yo" strings. The constants have been chosen to be $x^\rho_0 = 0.1$, $\vartheta = 4$ and $\alpha = 1$.
• Figure 2: Exaggerated depiction of the string folding onto itself radially and approaching the blackhole along $x^\phi=0$.
• Figure 3: This figure depicts the behaviour of the folded string worldsheet as it falls towards the event horizon of a BTZ black hole. The string tends to mimic the null Rindler geodesic as it approaches the event horizon. In this plot, we have taken $x^t_0 = 0$, $x^\rho_0 = 1$, $\alpha = \ell^2/2r_h=0.5$, $\beta = 0.2$ and $\theta = 3$. It can be noticed in the zoomed inset plot that the shrinking string asymptotes to \ref{['mimic rindler']}, rather than the pure null Rindler geodesic \ref{['static rindler geodesic']}.
• Figure 4: The full parameter space of magnetic strings with different classes of solutions marked.
• Figure 5: Snapshots of folded string of constant length revolving around the black hole at a fixed radius. The corresponding solution in the static case is given by ansatz \ref{['ansatz1']} with $\vartheta\neq0$, i.e. a static yo-yo like solution.