Area(or Entropy) Product Formula for a Regular Black Hole

Abstract

We compute the area(or entropy) product formula for a regular black hole derived by Ayón-Beato and García in 1998\cite{abg}. By explicit and exact calculation, it is shown that the entropy product formula of two physical horizons strictly \emph{depends} upon the ADM mass parameter that means it is \emph{not} an universal(mass-independent) quantity. But a slightly more complicated function of event horizon area and Cauchy horizon area is indeed a \emph{mass-independent} quantity. We also compute other thermodynamic properties of the said black hole. We further study the stability of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses second order phase transition. The pictorial diagram of the phase transition is given.

11 pages, 7 figures, GRG version

References in corpus (2)

• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory

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