Black holes with spindles at the horizon
Suvendu Giri
Abstract
A bstract We construct AdS 4 × Σ and AdS 2 × Σ × $$ {\Sigma}_{\mathfrak{g}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> solutions in F(4) gauged supergravity in six dimensions, where Σ is a two dimensional manifold of non-constant curvature with conical singularities at its two poles, called a spindle, and $$ {\Sigma}_{\mathfrak{g}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> is a constant curvature Riemann surface of genus $$ \mathfrak{g} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> . We find that the first solution realizes a “topologically topological twist”, while the second class of solutions gives rise to an “anti twist”. We compute the holographic free energy of the AdS 4 × Σ solution and find that it matches the entropy computed by extremizing an entropy functional that is constructed by gluing gravitational blocks. For the AdS 2 × Σ × $$ {\Sigma}_{\mathfrak{g}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> solution, we find that the Bekenstein-Hawking entropy is reproduced by extremizing an appropriately defined entropy functional, which leads us to conjecture that this solution is dual to a three dimensional SCFT on a spindle. A class of the AdS 2 × Σ × $$ {\Sigma}_{\mathfrak{g}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>g</mml:mi> </mml:msub> </mml:math> solutions can be embedded in four dimensional T 3 gauged supergravity, which is a subtruncation of the six dimensional theory.