| Summary: | It has been shown by explicit and exact calculation that the geometric product formula i.e., area (or entropy) product formula of outer horizon (<inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi mathvariant="script">H</mi> </mrow> <mo>+</mo> </msup> </semantics> </math> </inline-formula>) and inner horizon (<inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi mathvariant="script">H</mi> </mrow> <mo>−</mo> </msup> </semantics> </math> </inline-formula>) for charged accelerating black hole (BH) should neither be mass-independent nor quantized. This implies that the area (or entropy ) product is mass-independent conjecture has been broken down for charged accelerating BH. This also further implies that the mass-independent feature of the area product of <inline-formula> <math display="inline"> <semantics> <msup> <mrow> <mi mathvariant="script">H</mi> </mrow> <mo>±</mo> </msup> </semantics> </math> </inline-formula> is not a generic feature at all. We also compute the Cosmic-Censorship-Inequality for this BH. Moreover, we compute the specific heat for this BH to determine the local thermodynamic stability. Under certain criterion, the BH shows the second order phase transition. Furthermore, we compute logarithmic corrections to the entropy for the said BH due to small statistical fluctuations around the thermal equilibrium.
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