37 research outputs found
Five Dimensional Rotating Black Hole in a Uniform Magnetic Field. The Gyromagnetic Ratio
In four dimensional general relativity, the fact that a Killing vector in a
vacuum spacetime serves as a vector potential for a test Maxwell field provides
one with an elegant way of describing the behaviour of electromagnetic fields
near a rotating Kerr black hole immersed in a uniform magnetic field. We use a
similar approach to examine the case of a five dimensional rotating black hole
placed in a uniform magnetic field of configuration with bi-azimuthal symmetry,
that is aligned with the angular momenta of the Myers-Perry spacetime. Assuming
that the black hole may also possess a small electric charge we construct the
5-vector potential of the electromagnetic field in the Myers-Perry metric using
its three commuting Killing vector fields. We show that, like its four
dimensional counterparts, the five dimensional Myers-Perry black hole rotating
in a uniform magnetic field produces an inductive potential difference between
the event horizon and an infinitely distant surface. This potential difference
is determined by a superposition of two independent Coulomb fields consistent
with the two angular momenta of the black hole and two nonvanishing components
of the magnetic field. We also show that a weakly charged rotating black hole
in five dimensions possesses two independent magnetic dipole moments specified
in terms of its electric charge, mass, and angular momentum parameters. We
prove that a five dimensional weakly charged Myers-Perry black hole must have
the value of the gyromagnetic ratio g=3.Comment: 23 pages, REVTEX, v2: Minor changes, v3: Minor change
Closed Timelike Curves and Holography in Compact Plane Waves
We discuss plane wave backgrounds of string theory and their relation to
Goedel-like universes. This involves a twisted compactification along the
direction of propagation of the wave, which induces closed timelike curves. We
show, however, that no such curves are geodesic. The particle geodesics and the
preferred holographic screens we find are qualitatively different from those in
the Goedel-like universes. Of the two types of preferred screen, only one is
suited to dimensional reduction and/or T-duality, and this provides a
``holographic protection'' of chronology. The other type of screen, relevant to
an observer localized in all directions, is constructed both for the compact
and non-compact plane waves, a result of possible independent interest. We
comment on the consistency of field theory in such spaces, in which there are
closed timelike (and null) curves but no closed timelike (or null) geodesics.Comment: 21 pages, 3 figures, LaTe
Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions
We compute logarithmic corrections to the entropy of rotating extremal black
holes using quantum entropy function i.e. Euclidean quantum gravity approach.
Our analysis includes five dimensional supersymmetric BMPV black holes in type
IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL
models, and also non-supersymmetric extremal Kerr black hole and slowly
rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black
holes our results are in perfect agreement with the microscopic results derived
from string theory. In particular we reproduce correctly the dependence of the
logarithmic corrections on the number of U(1) gauge fields in the theory, and
on the angular momentum carried by the black hole in different scaling limits.
We also explain the shortcomings of the Cardy limit in explaining the
logarithmic corrections in the limit in which the (super)gravity description of
these black holes becomes a valid approximation. For non-supersymmetric
extremal black holes, e.g. for the extremal Kerr black hole in four dimensions,
our result provides a stringent testing ground for any microscopic explanation
of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation
between boundary condition and choice of ensemble, modified analysis for
slowly rotating black holes, all results remain unchanged, typos corrected;
v3: minor additions and correction