Fluctuations of the AdS3 C-metric

TL;DR

This work analyzes the dilaton fluctuations and holographic structure of three classes of AdS$_3$ C-metric solutions with two defects. By employing Fefferman–Graham expansions and Brown–Henneaux-type asymptotic analysis, it establishes a Virasoro symmetry with central charge $c=rac{3l}{2G_3}$ and derives a JT gravity description on the string worldvolume from fluctuations, while incorporating higher-curvature corrections. In the large-acceleration (small-$l$) regime, the effective action on the strings contains JT and Weyl-anomaly (Wald–Dong) contributions, with the generalized entropy expanded as $S_{ m BH}=S_{ m WD}+S_{ m JT}+ ext{O}( u^2)$, where the Weyl anomaly provides the leading term. The results offer a coherent holographic picture for AdS$_3$ C-metrics with defects, linking boundary CFT data, dilaton gravity on the brane, and entropy corrections, and suggest several avenues for future work (dS/CFT, additional symmetries, matter couplings, and entanglement/complexity analyses).

Abstract

We investigate the dilaton fluctuations near the string based on three classes of solutions of the 3D C-metric within the framework of the string-world holography. As a setup of holography, we focus on the asymptotic symmetry, recover the Virasoro algebra by central extension and get the central charge of the AdS3. Then we reduce the gravity on the brane as a JT gravity model by introducing a fluctuation. As an extension of the braneworld, we also investigate the higher curvature correction to the brane under some conditions. Finally, we make an expansion on generalized entropy of black hole solution with respect to small l and find that the leading term comes from Weyl anomaly, which is different from that in 4-dimensional C-metric.

Figures (11)

• Figure 1: Two copies of the geometry with each cut by two strings in Class I.
• Figure 2: The spatial slice of the Class I solutions in $(r,x)$.
• Figure 3: Two copies of the geometry with each cut by two strings in Class I. (a): Class $\rm I_{b1}$ solutions; (b): Class $\rm I_{b2}$ solutions. The black and green lines represent the conformal boundary ($x=y$) and the strings, respectively. The orange double line represents the event horizon. The grey regions are cut from the entire manifold. The orange lines denote the constant-$y$ lines, and the arrows indicate the directions of increasing $x$ in the two patches.
• Figure 4: The spatial slice of the (a): Class $\rm I_{b1}$ solutions, and (b): Class $\rm I_{b2}$ solutions in the $(r,x)$ coordinates. The orange dashed curves are constant-$r$ lines. The Orange double curve denotes the horizons. The blue curves are constant-$x$ lines. The green dot-dash lines are strings. The black dot is the original point. The black circle is the conformal boundary ($x=y$). The grey shadow region is the part that we cut from the entire manifold as the bulk. The string at $x=x_{2}$ ($x=x_{1}$) is a strut (wall). The red arrows indicate the directions of increasing $x$.
• Figure 5: The geometry of (a) class $\rm II_{b1}$ and (b) class $\rm II_{b2}$ solutions. The dark lines represent the conformal boundaries at $x=y$, the green dash-dotted lines denote strings, the orange double lines mark the position of the horizon, and the blue lines depict the lines of constant-$x$. The string at $x=x_{2}$ is a strut, while at $x=x_{1}$ is a wall. The grey-shaded region indicates the remaining manifold after the CCG process. The orange arrows indicate the directions of increasing $x$ in the two patches.