Near-extremal black holes at late times, backreacted

Abstract

Black holes display universal behavior near extremality. One such feature is the late-time blowup of derivatives of linearized perturbations across the horizon. For generic initial data, this instability is regulated by backreaction, and the final state is a near-extremal black hole. The aim of this paper is to study the late time behavior of such black holes analytically using the weakly broken conformal symmetry of their near-horizon region. In particular, gravitational backreaction is accounted for within the Jackiw-Teitelboim model for near-horizon, near-extremal dynamics coupled to bulk matter.

Figures (3)

• Figure 1: Penrose diagram displaying the isometry (\ref{['coordinate trans ads2->ads2']}). The coordinates $\{T,R\}$ cover the upper Poincaré patch with metric (\ref{['near horizon metric']}), while the coordinates $\{\tt,\tilde{R}\}$ cover the lower Poincaré patch. The dashed null line represents a possible initial data surface, and the dotted circle highlights the neighborhood of $\tilde{V}\to\infty$ on which we are focusing. This point is the future endpoint of the future horizon and of the boundary of the patch $\{\tt,\tilde{R}\}$.
• Figure 2: Penrose diagram displaying the mapping (\ref{['coordinate trans ads2->Nads2']}). The coordinates $\{T,R\}$ cover the Poincaré patch $0<R<\infty$ with metric (\ref{['near horizon metric']}), while the coordinates $\{t,r\}$ cover the Rindler patch $0<r<\infty$ with metric (\ref{['nads2 solution']}). The dashed null line represents a possible initial data surface.
• Figure 3: Penrose diagram illustrating the near-horizon computation of late-time behavior including the effects of backreaction. The physical boundary, in solid blue, is promoted to a degree of freedom encoding the black hole's (small) deviation from extremality. The red solid lines are the future and past horizons. The magenta dashed line depicts a possible initial data surface, or an advanced time in which the BH is perturbed from afar. The dotted green line shows the later part of the boundary trajectory had the scalar field not been excited. The late-time behavior of fields, as in fig. \ref{['figure2']}, is determined by analyzing the neighborhood of the point $T=T_\infty$.