Charged rotating black holes in Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant

Abstract

We consider rotating black hole solutions in five-dimensional Einstein-Maxwell-Chern-Simons theory with a negative cosmological constant and a generic value of the Chern-Simons coupling constant λ. Using both analytical and numerical techniques, we focus on cohomogeneity-1 configurations, with two equalmagnitude angular momenta, which approach at infinity a globally anti-de Sitter background. We find that the generic solutions share a number of basic properties with the known Cvetič, Lü, and Pope black holes which have λ ¼ 1. New features occur as well; for example, when the Chern-Simons coupling constant exceeds a critical value, the solutions are no longer uniquely determined by their global charges. Moreover, the black holes possess radial excitations which can be labelled by the node number of the magnetic gauge potential function. Solutions with small values of λ possess other distinct features. For instance, the extremal black holes there form two disconnected branches, while not all near-horizon solutions are associated with global solutions.

Radially Excited AdS5 Black Holes in Einstein–Maxwell–Chern–Simons Theory

“…For instance, we will see that the extremal RN-AdS solution becomes isolated from the rest of extremal rotating and charged black holes. Similarly to what happens in the small CS coupling regime, the extremal MP-AdS black hole cannot be continuosly connected with the extremal RN-AdS configuration [9]. However, instead of two disconnected branches, here one finds infinitely many branches between the MP-AdS and the RN-AdS black holes.…”

“…At this critical point, the black hole has zero area and the geometry of the horizon changes from AdS 2 × S 3 to AdS 3 × S 2 . This type of zero-area configuration is common in the EMCS theories, and, in particular, it is present in the CPL black hole [9]. A H J B [1,2] B [1,2] B * [1,2] B * [1,2] C [1,2] C [1,2] C [3,4] C [3,4] C nh C nh n=1, 2, 3, ... [1,2] , B * [1,2] ) (B [1,2] , B * [1,2] ) (B [2,3] , B * [2,3] ) (B [2,3] , B * [2,3] ) C [1,2] C [1,2] C [3,4] C [3,4] The extremal MP branch is shown in Figure 1a as a dashed red line.…”

“…The typical size of the mesh is around 10 3 -10 4 points, and the solutions have a relative accuracy of 10 −8 -10 −10 , which we test by evaluating several constraints from the field equations, conserved charges and relations at the boundaries, such as the relation (17). Note this procedure has been successfully used before to study other regimes of the EMCS-AdS theory [9].…”

“…It is interesting to note that the rotating generalization of the RN-AdS black hole (i.e., the AdS 5 equivalent of the Kerr-Newmann black hole) is not known analytically, and has been investigated numerically for equal magnitude angular momenta in the non-extremal [8] and extremal cases [9]. In addition, asymptotically AdS black holes in D > 4 can have an event horizon topology different from spherical, e.g., black ring solutions [10].…”

“…The case for large CS coupling was considered before in the asymptotically flat case, where it was shown that when λ > 2λ SG , a complicated branch structure of solutions surrounding the static black hole exists [20,21]. The case for large CS coupling with the AdS 5 asymptotics was briefly introduced in [9] too, where it was mentioned that similar features to the asymptotically flat case can also be found. It is the purpose of this paper to study in a systematic way the space of solutions in the large CS coupling regime with the AdS 5 asymptotics, a study, which, to the best of our knowledge, has not been done before.…”