Exploring Accelerating Hairy Black Holes in $2+1$ Dimensions: The Asymptotically Locally Anti-de Sitter Class and its Holography

TL;DR

This paper introduces new three-dimensional accelerating black hole solutions with scalar hair in asymptotically locally AdS spacetimes, extending geometric frameworks and holographic analysis to include scalar fields and domain walls.

Contribution

It presents novel families of accelerating hairy black holes in 3D AdS, incorporating scalar fields and domain walls, and develops a holographic stress tensor framework for these configurations.

Findings

Discovery of new accelerating hairy black hole solutions.

Extension of holographic stress tensor to scalar field configurations.

Construction of spacetimes with asymptotically locally flat, AdS, and dS geometries.

Abstract

In the realm of lower-dimensional accelerating spacetimes, it is well-established that the presence of domain walls, which are co-dimension one topological defects, is a necessary condition for their construction. We expand the geometric framework by adding a conformally coupled scalar field. This endeavor leads to the identification of several new families of three-dimensional accelerating spacetimes with asymptotically locally anti-de Sitter (AdS) behavior. Notably, one of these solutions showcases a hairy generalization of the accelerating BTZ black hole. This solution is constructed at both slow and rapid phases of acceleration, and its connection with established vacuum spacetime models is explicitly elucidated. The inclusion of the scalar field imparts a non-constant Ricci curvature to the domain wall, thereby rendering these configurations particularly suitable for the construction of two-dimensional quantum black holes. To establish a well-posed variational principle in the presence of the domain wall, two essential steps are undertaken. First, we extend the conventional renormalized AdS$_3$ action to accommodate the presence of the scalar field. Second, to establish a well-posed variational principle, we extend the renormalized AdS$_3$ action to include the scalar field and incorporate the Gibbons--Hawking--York term for internal boundaries and domain wall tension. We engage in holographic computations, thereby determining the explicit form of the holographic stress tensor. In this context, the stress tensor can be expressed as that of a perfect fluid situated on a curved background. Additionally, it paves the road to ascertain the spacetime mass. Finally, we close by demonstrating the existence of three-dimensional accelerating spacetimes with asymptotically locally flat and asymptotically locally de Sitter geometries, particularly those embodying black holes.