Critical phenomena of regular black holes in anti-de Sitter space-time

Understand

In General Relativity coupled to a non-linear electromagnetic field, together with a negative cosmological constant, we obtain the general static spherical symmetric black hole solution with magnetic charges, which is asymptotic to anti-de Sitter (AdS) space-times.

• In particular, for a degenerate case the solution becomes a Hayward-AdS black hole, which is regular everywhere in the full space-time.
• The existence of such a regular black hole solution preserves the weak energy condition while the strong energy condition is violated.
• We then derive the first law and the Smarr formula of the black hole solution.