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2016
The fundamental holographic principle is first proposed, then demonstrated in its validity and viability through a thought experiment and then finally derived. The Heisenberg uncertainty relations are shown to follow from this fundamental relation. The quantum blackhole entropy is then demonstrated using this holographic uncertainty relation along with the application of the Landauer’s principle for the thermodynamic erasure of a bit yielding a formula with a logarithmic correction. The blackhole entropy is found to be half the value normally delivered by any other method. So, it is proposed that there is a real relevant physical horizon at the twice the Schwarzschild radius dubbed the holographic information geometric horizon.
A detailed review is made on the classical concepts of General Relativity that allow us to heuristically infer a first formulation of the so-called Holographic Principle. With the study of rotating black holes and their properties related to the area of the Event Horizon, the Hawking Area Theorem is formally stated. We also review of the concept of Entropy to establish the theoretical framework that justifies the connection between the horizon area and entropy through Information Theory on what is known as the Bekenstein Entropy. Including black holes in the laws of thermodynamics imply a generalization of the Second Law. This postulated generalized law has as a consequence a limit in the entropy of the Universe. Finally, under a weak interaction and spherical symmetry considerations it is found a that the entropy of a system is bounded from above by one-fourth of the area (in natural units) of the minimum sphere containing the system.
On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (In 3 Volumes)
Black Hole Entropy: Certain Quantum Features2002 •
arXiv (Cornell University)
Does Information Rule the Quantum Black Hole2007 •
Using the Landauer's principle of information erasure, we show that the statement "the Schwarzschild black hole is a maximal entropy object" implies that its entropy is given by mass-squared. We also obtain the quantized black hole mass spectra and entropy by using the fact that the information is composed of bit or trit. The black hole entropy has a sub-leading contribution proportional to the logarithm of area in addition to the usual areal term without an artificial cutoff. Comparing the results with the analysis of Hod \cite{Hod}, we argue that the Schwarzschild black hole erases information in unit of trit. We also argue that the minimum of a black hole mass is $\sqrt{\log 3/(8\pi)}M_P$.
2015 •
In this paper, we calculate the modification to the thermodynamics of a Schwarzschild black hole in higher dimensions because of Generalized Uncertainty Principle (GUP). We use the fact that the leading order corrections to the entropy of a black hole has to be logarithmic in nature to restrict the form of GUP. We observe that in six dimensions, the usual GUP produces the correct form for the leading order corrections to the entropy of a black hole. However, in five and seven dimensions a linear GUP, which is obtained by a combination of DSR with the usual GUP, is needed to produce the correct form of the corrections to the entropy of a black hole. Finally, we demonstrate that in five dimensions, a new form of GUP containing quadratic and cubic powers of the momentum also produces the correct form for the leading order corrections to the entropy of a black hole.
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