Higher-dimensional black hole solutions with scalar hair and dilaton field and toroidal horizons and interior solution

Abstract

In this study, we investigate black hole solutions with toroidal horizons in scalar hair and dilaton gravity. First, we obtain the field equations in n-dimensions. Then, we propose different models (ansatz) and find the exact solutions for these types of ansatzs. These solutions are not asymptotically (anti) de Sitter or flat, except in one special case. We also show that the BTZand BTZ-like solutions emerge from some of these solutions as a special case. We also show that when the event horizon radius increases, the temperature will be the same in various dimensions. The only difference is noticeable near the origin (this statement is clear from the figures). For these solutions, we obtained a new version of the Smarr formula. In addition, we show that the presence of the scalar field makes the black holes more stable near the origin, except for the BTZ case. In general, the presence of a scalar field is an important factor in black hole stability investigations. In the critical behavior analysis, we find that there is no evidence to show the existence of P-V criticality. Here, we present a class of interior solutions corresponding to the solution in a scalar hair gravity exterior. The solution obtained in the linear case was regular and well-behaved at the stellar interior.