New family of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi></mml:math> metrics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn></mml:math> gauged supergravity
Masato Nozawa, Takashi Torii
Abstract
We present a new family of charged $C$ metrics in $\mathcal{N}=2$ gauged supergravity in four dimensions. The double Wick rotation of the $C$ metric allows us to bring our solution into a different family of the $C$ metrics previously found by L\"u and V\'azquez-Poritz. In the case of zero acceleration limit, our solution with vanishing charges reduces to the scalar haired black holes in anti--de Sitter space with regular horizons. Nevertheless, it turns out that each family of neutral solutions fails to veil the curvature singularity by the event horizon, showing that neither of them represents the accelerated black holes with a scalar hair. Physical solutions without visible curvature singularities are obtained only in the case of nonvanishing charges. Causal structures of the solution are spelled out in detail. We also present conditions under which the solution preserves supersymmetry.