4 research outputs found
Gyromagnetic Ratio of Charged Kerr-Anti-de Sitter Black Holes
We examine the gyromagnetic ratios of rotating and charged AdS black holes in
four and higher spacetime dimensions. We compute the gyromagnetic ratio for
Kerr-AdS black holes with an arbitrary electric charge in four dimensions and
show that it corresponds to g=2 irrespective of the AdS nature of the
spacetime. We also compute the gyromagnetic ratio for Kerr-AdS black holes with
a single angular momentum and with a test electric charge in all higher
dimensions. The gyromagnetic ratio crucially depends on the dimensionless ratio
of the rotation parameter to the curvature radius of the AdS background. At the
critical limit, when the boundary Einstein universe is rotating at the speed of
light, it exhibits a striking feature leading to g=2 regardless of the
spacetime dimension. Next, we extend our consideration to include the exact
metric for five-dimensional rotating charged black holes in minimal gauged
supergravity. We show that the value of the gyromagnetic ratio found in the
"test-charge" approach remains unchanged for these black holes.Comment: New section added; 6 pages, RevTe
Kaluza-Klein Consistency, Killing Vectors, and Kahler Spaces
We make a detailed investigation of all spaces Q_{n_1... n_N}^{q_1... q_N} of
the form of U(1) bundles over arbitrary products \prod_i CP^{n_i} of complex
projective spaces, with arbitrary winding numbers q_i over each factor in the
base. Special cases, including Q_{11}^{11} (sometimes known as T^{11}),
Q_{111}^{111} and Q_{21}^{32}, are relevant for compactifications of type IIB
and D=11 supergravity. Remarkable ``conspiracies'' allow consistent
Kaluza-Klein S^5, S^4 and S^7 sphere reductions of these theories that retain
all the Yang-Mills fields of the isometry group in a massless truncation. We
prove that such conspiracies do not occur for the reductions on the Q_{n_1...
n_N}^{q_1... q_N} spaces, and that it is inconsistent to make a massless
truncation in which the non-abelian SU(n_i+1) factors in their isometry groups
are retained. In the course of proving this we derive many properties of the
spaces Q_{n_1... n_N}^{q_1... q_N} of more general utility. In particular, we
show that they always admit Einstein metrics, and that the spaces where
q_i=(n_i+1)/\ell all admit two Killing spinors. We also obtain an iterative
construction for real metrics on CP^n, and construct the Killing vectors on
Q_{n_1... n_N}^{q_1... q_N} in terms of scalar eigenfunctions on CP^{n_i}. We
derive bounds that allow us to prove that certain Killing-vector identities on
spheres, necessary for consistent Kaluza-Klein reductions, are never satisfied
on Q_{n_1... n_N}^{q_1... q_N}.Comment: Latex, 43 pages, references added and typos correcte