Universality of the area product: Solutions with conical singularity

Abstract

It has been observed that the area product of horizons for many black hole solutions is mass independent and satisfy the universality relation A + A − = (8π) 2 N , where N is related to the quantized charges of the solution as angular momentum and electric charge. In this work the same analysis is done for black hole and black ring solutions with conical singularity. We find that the area product is still mass independent and regardless of the horizon topology, the conical characteristic (κ) of the solutions, appears in the universality relation as κA + A − = (8π) 2 N . We also check that the first law of black hole inner mechanics is satisfied for these solutions.

More on the entropy product and dual CFTs

“…The mentioned universality is also observed in the higher dimensional black hole and black ring solutions [19,20]. It has been also shown [29] that in the case of black hole and black ring solutions with conical singularity, the entropy product is mass independent, however the conical characteristic κ of the solutions, appears in the universality relation as κS + S − = (2π) 2 N .…”

“…The conical characteristic, the entropy and temperature of the inner horizon for this solution are [29]…”

“…It has been shown [29] that in the case of solutions with conical singularity, regardless of the horizon topology of the solutions, the conical characteristic κ appears in the entropy product law as κS + S − ∼ N . In this section using the Rot.…”

“…As we mentioned earlier, one may also find the central charge from the thermodynamics of the solution. The entropy and temperature of the inner and outer horizons for the generic (non-extremal) charged rotating C-metric (4.1) are [29] 12) it is straightforward to check that T + S + = T − S − and the entropy product satisfies the universality relation [29] κS…”

“…Thermodynamics of black hole horizons and the entropy product for multi-horizon black holes are also received considerable attentions in the recent years [14]- [29]. It has been observed that the product of horizon entropies for many solutions, is mass independent as S + S − = (2π) 2 N , where N depends only on the quantized charges like angular momentum and electric charge.…”