Analytic critical points of charged Renyi entropies from hyperbolic black holes

Understand

We analytically study phase transitions of holographic charged Renyi entropies in two gravitational systems dual to the $\mathcal{N}=4$ super-Yang-Mills theory at finite density and zero temperature.

• The first system is the Reissner-Nordstrom-AdS$_5$ black hole, which has finite entropy at zero temperature.
• The second system is a charged dilatonic black hole in AdS$_5$, which has zero entropy at zero temperature.
• Hyperbolic black holes are employed to calculate the Renyi entropies with the entangling surface being a sphere.