Revisiting a family of five-dimensional charged, rotating black holes

TL;DR

This work analyzes five-dimensional Einstein-Maxwell-Chern-Simons theory and a broad Ferraro family of charged, rotating black holes. It demonstrates that the Ferraro metrics are locally equivalent to the Chong-Cvetič-Lü-Pope (CCLP) solution via a coordinate map and complex parameter redefinitions, covering AdS and dS cases and clarifying global properties. Conserved charges are computed both through Komar integrals (with a carefully chosen frame) and via a near-horizon formalism, with the Chern-Simons term properly incorporated; in both approaches the results agree with the CCLP values. The findings provide a unified interpretation of these 5D EMCS black holes and establish a first near-horizon Noether-charge derivation in this setting, highlighting the robustness of the near-horizon method beyond four dimensions.

Abstract

In the absence of a higher-dimensional analogue to the Kerr-Newman black hole, 5-dimensional Einstein-Maxwell theory with a Chern-Simons term has become a natural setting for studying charged, stationary solutions. A prominent example is the Chong-Cvetič-Lü-Pope (CCLP) solution, which describes a non-extremal black hole with electric charge and two independent angular momenta. This solution has been widely studied, and generalizations have been proposed. In this paper, we revisit a large family of five-dimensional black hole solutions to Einstein-Maxwell-Chern-Simons (EMCS) field equations, which admits to be written in terms of a generalized Plebański-Demiański ansatz and includes the CCLP and the Kerr-NUT-Anti-de Sitter solutions as particular cases. We show that the complete family can be brought to the CCLP form by means of a suitable coordinate transformation and a complex redefinition of parameters. Then, we compute the conserved charges associated to the CCLP form of the metric by analyzing the near-horizon asymptotic symmetries. We show that the zero-mode of the near-horizon charges exactly match the result of the Komar integrals.

Figures (3)

• Figure 1: The intersection between $u_1^2+u_2^2=R^2$ (green) and the cubic curve $t_0t_1t_2=F^2$ (orange), in the region $\{t_0>0\wedge{t_1>0}\wedge{t_2>0}\}$(blue). It can be observed that the radius has to be less than $\sqrt{2}$ for there to be a non-empty intersection.
• Figure 2: For $\alpha>1+\lambda(a^2+b^2)$, the intersection between $u_1^2+u_2^2=R^2$ (green) and the cubic curve $t_0t_1t_2=F^2<0$ (orange), in the region $\{t_0<0\wedge{t_1>0}\wedge{t_2>0}\}$(blue). In the right figure it can be observed that the radius has to be larger than $\frac{1}{\sqrt{2}}$ for there to be a non-empty intersection.
• Figure 3: For $\alpha<1+\lambda(a^2+b^2)$, the intersection between $u_1^2+u_2^2=R^2$ (green) and the cubic curve $t_0t_1t_2=F^2<0$ (orange), in the region $\{t_0<0\wedge{t_1>0}\wedge{t_2>0}\}$(blue). In the right figure it can be observed that the radius has to be larger than $\sqrt{2}$ for there to be a non-empty intersection.