10,221 research outputs found
Milnor operations and the generalized Chern character
We have shown that the n-th Morava K-theory K^*(X) for a CW-spectrum X with
action of Morava stabilizer group G_n can be recovered from the system of some
height-(n+1) cohomology groups E^*(Z) with G_{n+1}-action indexed by finite
subspectra Z. In this note we reformulate and extend the above result. We
construct a symmetric monoidal functor F from the category of
E^{vee}_*(E)-precomodules to the category of K_{*}(K)-comodules. Then we show
that K^*(X) is naturally isomorphic to the inverse limit of F(E^*(Z)) as a
K_{*}(K)-comodule.Comment: This is the version published by Geometry & Topology Monographs on 18
April 200
Charged Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions
We study charged black hole solutions in Einstein-Gauss-Bonnet theory with
the dilaton field which is the low-energy effective theory of the heterotic
string. The spacetime is D-dimensional and assumed to be static and spherically
symmetric with the -dimensional constant curvature space and
asymptotically flat. The system of the basic equations is complex and the
solutions are obtained numerically. We identify the allowed parameter region
where the black hole solutions exist, and show configurations of the field
functions in D=4 -- 6 and 10. We also show the relations of the physical
quantities of the black holes such as the horizon radius, the mass, the
temperature, and so on, and find several results. The forms of the allowed
parameter regions are different depending on the dimension. There is no extreme
black hole solution with T=0 that can be obtained by taking the limit of the
non-extreme solutions within the parameter range we chose. Entropy of the black
holes in the dilatonic theory is always larger than that in the non-dilatonic
theory. Our analysis includes the higher order term of the dilaton field which
is not in our previous works. Its effect remarkably appears in five dimensions
and is given in the appendix. By our analysis it is found that the properties
of the black hole solutions strongly depend on the dimension, charge, existence
of the dilaton field. Hence both the detailed analyses of the individual
systems and the investigations from the systematic point of view are important.Comment: 23 pages, 14 figures. Typos corrected, references added, accepted in
PR
Global Structure of Black Holes in String Theory with Gauss-Bonnet Correction in Various Dimensions
We study global structures of black hole solutions in Einstein gravity with
Gauss-Bonnet term coupled to dilaton in various dimensions. In particular we
focus on the problem whether the singularity is weakened due to the
Gauss-Bonnet term and dilaton. We find that there appears the non-central
singularity between horizon and the center in many cases, where the metric does
not diverge but the Kretschmann invariant does diverge. Hence this is a
singularity, but we find the singularity is much milder than the Schwarzschild
solution and the non-dilatonic one. We discuss the origin of this "fat"
singularity. In other cases, we encounter singularity at the center which is
much stronger than the usual one. We find that our black hole solutions have
three different types of the global structures; the Schwarzschild,
Schwarzschild-AdS and "regular AdS black hole" types.Comment: 22 pages, 6 figure
Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions III -- Asymptotically AdS Black Holes with --
We study black hole solutions in the Einstein-Gauss-Bonnet gravity with the
dilaton and a negative ``cosmological constant''. We derive the field equations
for the static spherically symmetric () and hyperbolically symmetric
() spacetime in general dimensions. The system has some scaling
symmetries which are used in our analysis of the solutions. We find exact
solutions, i.e., regular AdS solution for and a massless black hole
solution for . Nontrivial asymptotically AdS solutions are obtained
numerically in D=4 -- 6 and 10 dimensional spacetimes. For spherically
symmetric solutions, there is the minimum horizon radius below which no
solution exists in D=4 -- 6. However in D=10, there is not such lower bound but
the solution continues to exist to zero horizon size. For hyperbolically
symmetric solution, there is the minimum horizon radius in all dimensions. Our
solution can be used for investigations of the boundary theory through AdS/CFT
correspondence.Comment: 25 pages, 16 figure
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