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Abstract
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We construct black hole solutions to the leading
order of string effective action in five dimensions with
the source given by dilaton and magnetically charged antisymmetric
gauge B-field. Presence of the considered Bfield
leads to the unusual asymptotic behavior of the solutions
which are neither asymptotically flat nor asymptotically
(A)dS.We consider the three-dimensional space part to correspond
to theBianchi classes and so the horizons of these topological
black hole solutions are modeled by seven homogeneous
Thurston’s geometries of E3, S3, H3, H2×E1,
SL2R,
nilgeometry, and solvegeometry. Calculating the quasi-local
mass, temperature, entropy, dilaton charge, and magnetic
potential, we show that the first law of black hole thermodynamics
is satisfied by these quantities and the dilaton charge
is not independent of mass and magnetic charge. Furthermore,
for Bianchi type V, the T -dual black hole solution is
obtained which carries no charge associated with B-field and
the entropy turns to be invariant under the T -duality..
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