Supersymmetric $AdS_6$ black holes from matter coupled $F(4)$ gauged supergravity

Abstract

In matter coupled $F(4)$ gauged supergravity in six dimensions, we study supersymmetric $AdS_6$ black holes with various horizon geometries. We find new $AdS_2\,\times\,Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}$ horizons with $\mathfrak{g}_1>1$ and $\mathfrak{g}_2>1$, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically $AdS_6$ boundary and the $AdS_2\,\times\,Σ_{\mathfrak{g}_1}\timesΣ_{\mathfrak{g}_2}$ horizon. We also find black holes with horizons of Kähler four-cycles in Calabi-Yau fourfolds and Cayley four-cycles in $Spin(7)$ manifolds.

Figures (3)

• Figure 1: Positivity range of $(b_1,b_2)$ for the $H^2\,\times\,H^2$, $H^2\,\times\,S^2$, $S^2\,\times\,H^2$ and $S^2\,\times\,S^2$ backgrounds, from the top-left and clockwise. In the $H^2\,\times\,H^2$ plot, the black dot at $(b_1,b_2)\,=\,(0,0)$ corresponds to the $AdS_2$ solution in \ref{['ads2ads2']}.
• Figure 2: Numerical black hole solutions with $m\,=\,1/2$ and $g_1\,=\,3m$. For the magnetic charges, $(b_1,b_2)$, we have $(-0.1,-0.1)$, purple, $(-0.01,-0.01)$, red, and $(-0.001,-0.001)$, orange.
• Figure 3: Numerical black hole solutions with $m\,=\,1/2$ and $g\,=\,3m$. We have $b=-0.1$ for purple, $b=-0.3$ for red, and $b=-0.5$ for orange.