Abstract
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 B-field 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 the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston’s geometries of E^3, S^3, H^3, H^2 times E^1, widetilde{{SL_2R}}, 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.
Highlights
The equations of motion of low energy string frame effective action are equivalent to the one-loop β-function equations which are the conformal invariance condition of the corresponding σ -model
In this paper we focus on D = 5 case, looking for black hole solutions of low energy string theory effective equations of motion on five-dimensional spacetimes where the r and t constant hypersurfaces are given by homogeneous space corresponding to a Bianchi types
We have constructed five-dimensional topological black hole solutions at leading order of string effective action in presence of dilaton and antisymmetric B-field associated with a magnetic charge
Summary
The equations of motion of low energy string frame effective action are equivalent to the one-loop β-function equations which are the conformal invariance condition of the corresponding σ -model. In some cases, the scalar field can have a non-trivial profile introducing a dilaton charge which is not an extra independent characteristic of the black hole This is usually referred as the scalar hair of second kind [51]. An intriguing physical discussion about the variation of φ∞ is presented in [58], where using the solution phase space method and integrability of charge variations, it is shown that for black hole solutions of Einstein–Maxwell–(Axion)-Dilaton theories the φ∞ is a redundant (non-physical) parameter, whose variation is not included in the first law of thermodynamics. 3, the string equations of motion are solved to obtain new five-dimensional black hole solutions whose horizons are homogeneous spaces corresponding to the Bianchi types.
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