Narrow Results

A nontrivial scalar solution, whose source is a massive scalar field with a double-well potential, for a non-rotating Bananas–Teitelboim–Zanelli (BTZ) black hole is obtained with a condition , where μ is the mass of scalar field and the cosmological constant. The stability of solution is also studied. The mass of black hole with a scalar hair is greater than the black hole without hair. The scalar solution proposes a regular horizon which hides the naked singularity.

In this paper, we discuss the generalized Einstein–Maxwell–Dilaton gravity theory with a nonminimal coupling between the Maxwell field and scalar field. Considering different geometric properties of black hole horizon structure, the charged dilaton Lifshitz black hole solutions are presented in 4-dimensional spacetimes. Later, utilizing the Wald Formalism, we derive the thermodynamic first law of black hole and conserved quantities. According to the relationship between the heat capacity and the local stability of black hole, we study the stability of charged Lifshitz black holes and identify the thermodynamic stable region of black holes that meet the criteria.

In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

We consider a general Einstein–scalar–Gauss-Bonnet theory with a coupling function f (ϕ) between the scalar field and the quadratic gravitational Gauss-Bonnet term. We show that the existing no-hair theorems are easily evaded, and therefore black holes may emerge in the context of this theory. Indeed, we demonstrate that, under mild only assumptions for f (ϕ), asymptotic solutions describing either a regular black-hole horizon or an asymptotically-flat solution always emerge. We then show, through numerical integration, that the field equations allow for the smooth connection of these asymptotic solutions, and thus for the construction of a complete, regular black-hole solution with non-trivial scalar hair. We present and discuss the physical characteristics of a large number of such solutions for a plethora of coupling functions f (ϕ). Finally, we investigate whether pure scalar-Gauss-Bonnet black holes may arise in the context of our theory when the Ricci scalar may be altogether ignored.