Quantum Gravity and String Theory

   

On Noncommutative Spacetimes and Corrections to the Kerr-Newman Black Hole Entropy Due to Quantization of Area, Mass and Entropy

Authors: Carlos Castro

Recently we have argued [1] that the noncommutativity of the spacetime coordinates is the answer to the question : Why is area, mass, entropy quantized ? Furthermore, it casts light into a deep interplay among black hole entropy, discrete calculus, number theory, theory of partitions, random matrix theory, fuzzy spheres, ..... We extend our previous construction of Schwarzschild black holes and derive the corrections to the Kerr-Newman temperature and black hole entropy, to all orders, from the discrete mass transitions taken place among different mass states. The mass spectrum for Kerr, Kerr-Newman, and Reissner-Nordstrom black holes is explicitly obtained which reduces to the Schwarzschild case when the angular momentum and charge is set to zero. One of the most salient features in the expansion of the $modified$ temperature $ {cal T } = T + c_1{ T over N } + c_2 { T over N^2 } + ldots $ is that it spells a correspondence between the loop expansion in QFT in powers of $ hbar$, after setting $ hbar leftrightarrow ( 1/ N)$. $ N $ is the principal quantum number labeling the spectrum of mass states and which is given by $ N = l_3 ( l_3 + 2 ) - l_2 ( l_2 + 1) + l_1^2$, with $ l_3 ge l_2 ge | l_1|$ being the quantum numbers associated with the hyper-spherical harmonics of the three-sphere $ S^3$. These results can be extended to higher dimensions. To finalize, we should add that the deviation from a full thermal spectrum and the corrections to the Hawking temperature might be relevant to the solution of the Black Hole Information paradox.

Comments: 19 Pages.

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Submission history

[v1] 2024-08-16 09:17:30

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