Abstract
We present a consolidated manual of Euclidean gravity approaches for finding the logarithmic corrections to the entropy of the full Kerr-Newman family of black holes in both extremal and nonextremal limits. Seeley-DeWitt coeffcients for the quadratic fluctuations of a concern gravity theory appear to be the key ingredients in this manual. Following the manual, we calculate the first three Seeley-DeWitt coefficients and logarithmic corrections to the entropy of extremal and nonextremal black holes in a generalized Einstein-Maxwell theory minimally coupled to additional massless scalar, vector, spin-$1/2$ Dirac and spin-$3/2$ Rarita-Schwinger fields. We finally employ the Seeley-DeWitt data to reproduce the logarithmic entropy corrections for extremal black holes in all $\mathcal{N}\ensuremath{\ge}2$ Einstein-Maxwell supergravity via an alternative local supersymmetrization method.
Highlights
In any quantum gravity model, including string theory, it has been found that the leading quantum correction to the Bekenstein-Hawking entropy formula of black holes carrying large charges [1] is proportional to the logarithm of horizon area, called the logarithmic correction [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]
Where a special treatment [71] is used to extract out the particular black hole partition function by eliminating the thermal gas contribution of all particles present in the theory. This treatment effectively leads to the logarithmic corrections for a particular choice of integration range of the heat kernel time s and writes the following Clocal formula for nonextremal black holes d4x det ga4ðxÞ; full geometry ð19Þ
This section generalizes the d 1⁄4 4 minimally coupled Einstein-Maxwell theory (EMT) further by coupling any arbitrary numbers of massless fields, which leads to a set of generalized SeeleyDeWitt coefficient and logarithmic correction formulas for all the extremal and nonextremal Kerr-Newman family of black holes
Summary
In any quantum gravity model, including string theory, it has been found that the leading quantum correction to the Bekenstein-Hawking entropy formula of black holes carrying large charges [1] is proportional to the logarithm of horizon area, called the logarithmic correction [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. The minimally coupled massless fields will give rise to additional contributions to the pure EMT results (both Seeley-DeWitt coefficients and logarithmic entropy corrections), and our primary goal in this paper is to evaluate all these contributions. We calculate the first three Seeley-DeWitt coefficients for the fluctuations of the d 1⁄4 4 minimally coupled EMT and employ them in obtaining logarithmic entropy corrections for both the extremal and nonextremal Kerr-Newman family of black holes. We locally supersymmetrize the generalized a4ðxÞ formula (93) and derive logarithmic entropy corrections for the extremal Kerr-Newman, Kerr and ReissnerNordström black holes in N ≥ 2; d 1⁄4 4 Einstein-Maxwell supergravity theories In Appendix C, we briefly present the cumbersome trace calculations for the Einstein-Maxwell sector
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