New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory

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 Thurstons geometries of E 3 , S 3 , H 3 , H 2 × E 1 , 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 presented in [25,26], whose horizons are not compactificable and their described spacetimes are rotating black branes [27].Usually, the horizon geometries of topological black hole solutions are considered to be spherical, hyperbolic or flat. For the five-dimensional black hole solutions the situation can be more extensive. The geometries of three-dimensional homogeneous manifolds has been classified by Thurston into eight types [28], where in addition to three isotropic constant curvature cases of spherical S 3 , Hyperbolic H 3 , and Euclidean E 3 , there are five anisotropic alternative three-dimensional geometries of S 2 × R, H 2 × R, SL 2 R, solvegeometry, and nilgeometry. Admitting homogeneous metrics, these model geometries have close correspondence with the homogeneous geometries of Bianchi types and Kantowski-Sachs [29,30]. The Bianchi types are defined based on the simply-transitive three-dimensional Lie groups classification. Since the isometries of the Riemannian manifold form a Lie group, the Bianchi classification is widely used for studying the spatially homogeneous spacetimes in relativity and cosmology [31,32,33,34,35]. The spacetimes in these models are assumed to possess a symmetry, namely the spatial homogeneity [36]. Families of five-dimensional black hole solutions of gravity theories where the horizons are modeled by some of the Thurston 3-geometries have been presented in [37,38,39,40,41]. Also, extremal black branes whose geometries are classified by nine Bianchi types have been studied in [42].Recently, the black hole solutions in string theory have attracted an increasing interest [43,44,45,46,47,48,49]. Nevertheless, the effect of the magnetically charged B-field has not been discussed so much in previous works [7,6,8,9,10,11]. In this work, we are interested in five-dimensional black hole solutions in string theory including a dilaton field and a 3-form field strength tensor of B-field associated with a magnetic charge. The inclusion of B-field in this class wil...

Thermodynamically stable asymptotically flat hairy black holes with a dilaton potential

“…For recent discussions on the scalar charges and their role on the first law of thermodynamics, see[45,49,50] 9. The nomenclature T∞ comes from the fact that the heat capacity CΦ diverges at that temperature.…”

Classical and quantum $$(2+1)$$-dimensional spatially homogeneous string cosmology

“…In this work, we are going to present cosmological solutions at classical and quantum levels on (2 + 1)-dimensional space-times where the two-dimensional space part has the symmetries of two-dimensional Lie algebra and admits a homogeneous metric. In (3 + 1)-dimensions, the homogeneous space-times, usually referred as Bianchi type spacetimes, which are assumed to possess the symmetry of spatial homogeneity and defined based on the simply-transitive three-dimensional Lie groups classification [16], have been widely used to generate cosmological and black hole solutions [17][18][19][20][21][22][23]. An interesting approach to find classical and quantum cosmological solutions on these homogeneous space-times has been using the Lie symmetries [20], and the symmetries of the supermetrics [24].…”

“…and the field strength tensor of type (23). Then, given the effective action ( 6), the Lagrangian reads…”

Phase transitions of neutral planar hairy AdS black holes

“…Since the latter has a compact spatial direction, there is a negative Casimir energy contribution similar to the one in [4]. The contribution of the scalar to the mass of hairy black holes and hairy solitons, and their relation to the boundary conditions of the scalar field, were discussed in [29][30][31][32][33][34][35][36] (see also [37][38][39][40][41][42] for various applications in AdS and flat spacetimes), though they typically rely in numerical methods. In [43], by making use of the Hamiltonian formalism, it was shown that when the conformal symmetry is broken at the boundary there is an extra contribution to the mass of hairy black holes that makes the first law of thermodynamics well posed, explaining some of the previous results.…”

“…The contribution of the counterterm depending on the scalar field (2.21) is 34) while the sum of the other terms in the action gives…”