Supersymmetric \(\mathrm{AdS}_{6}\) black holes from matter coupled \(F(4)\) gauged supergravity

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Abstract: In matter coupled

F (4)

gauged supergravity in six dimensions, we study supersymmetric

A d S_{6}

black holes with various horizon geometries. We find new

A d S_{2}, i m e s, S i g m a_{m a t h f r a k g_{1}} i m e s S i g m a_{m a t h f r a k g_{2}}

horizons with

m a t h f r a k g_{1} > 1

and

m a t h f r a k g_{2} > 1

, and present the black hole solution numerically. The full black hole is an interpolating geometry between the asymptotically

A d S_{6}

boundary and the

A d S_{2}, i m e s, S i g m a_{m a t h f r a k g_{1}} i m e s S i g m a_{m a t h f r a k g_{2}}

horizon. We also find black holes with horizons of K"ahler four-cycles in Calabi-Yau fourfolds and Cayley four-cycles in

S p i n (7)

manifolds.

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