Nuttier (A)dS Black Holes in Higher Dimensions

TL;DR

The paper develops a general framework to construct higher-dimensional Taub-NUT spacetimes with a cosmological constant by modeling them as $U(1)$-fibrations over Einstein–Kähler base spaces, including odd dimensions. It provides explicit metric ansätze and regularity (nut/bolt) conditions across dimensions $d=3,4,5,6,7$, revealing a deep coupling between the NUT charges and the cosmological constant that precludes simple asymptotically flat limits in higher dimensions. The authors explore a wide array of base-factor configurations (single and product spaces such as $S^{2}, T^{2}, H^{2}$, and CP$^{2}$-type manifolds) and derive Euclidean sections and regularity constraints, highlighting potential implications for the AdS/CFT correspondence and string theory. The work offers a catalog of explicit solutions and a methodological template for generating further higher-dimensional NUT-charged spacetimes with rich topologies, setting the stage for further thermodynamic and holographic investigations.

Abstract

We construct new solutions of the vacuum Einstein field equations with cosmological constant. These solutions describe spacetimes with non-trivial topology that are asymptotically dS, AdS or flat. For a negative cosmological constant these solutions are NUT charged generalizations of the topological black hole solutions in higher dimensions. We also point out the existence of such NUT charged spacetimes in odd dimensions and we explicitly construct such spaces in 5 and 7 dimensions. The existence of such spacetimes with non-trivial topology is closely related to the existence of the cosmological constant. Finally, we discuss the global structure of such solutions and possible applications in string theory.