Carroll black holes

Abstract

Despite the absence of a lightcone structure, some solutions of Carroll gravity show black hole-like behaviour. We define Carroll black holes as solutions of Carroll gravity that exhibit Carroll thermal properties and have a Carroll extremal surface, notions introduced in our work. The latter is a Carroll analogue of a Lorentzian extremal surface. As examples, we discuss the Carroll versions of Schwarzschild, Reissner-Nordstroem, and BTZ black holes and black hole solutions of generic 1+1 dimensional Carroll dilaton gravity, including Carroll JT and Carroll Witten black holes.

Figures (7)

• Figure 1: Left (orange): Lorentzian theories. Right (yellow): Carroll theories.
• Figure 2: Kruskal diagram of Lorentzian eternal black hole
• Figure 3: Three diagrams to visualize Carroll black holes
• Figure 4: Target space picture of Carroll JT by plotting the level sets of \ref{['eq:car112']}, restricted to the region $X\geq 0$. Extremal points are red circles and exist only for $M> 0$. The solutions given in \ref{['eq:sols_newgauge']} cover the lower half of this diagram.
• Figure 5: Target space picture of spherically reduced Carroll--Schwarzschild black hole. Extremal points are red circles and exist only for $M> 0$. The other symplectic leaves do not exhibit such points as for $M=0$ the point would be at $X=0$ and for $M<0$ the leaves do not contain points with $X_{\textrm{\tiny H}} =0$ at all (they are not simply connected). The black hole sector is thus given by $M>0$. The solutions \ref{['eq:CSS_1']}-\ref{['eq:CSS_3']} describe the lower half of the diagram.