Author: Sarthak Talukdar (view email), Center for High Energy Physics, Indian Institute of Science, Bengaluru, 560012, India
The black hole information paradox was a very poorly understood problem for so long. The idea that the “semi-classical calculation by Hawking could not be trusted below the Planck scale because quantum gravity effects would introduce corrections to that calculation” gave people hope that it may solve the paradox, but Mathur showed that these small corrections are NOT the solution to the paradox.
In this paper, we will start with the general idea of the Information paradox. Then, we will show, with calculations by Mathur, that small quantum gravity corrections cannot solve the problem. We will give an example of a toy model and solve it by mapping it to 1-dimensional Ising model. Finally, we will also prove the Hawking theorem, which gives some possible ways to look further into the paradox.
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 Samir D. Mathur, The Information Paradox and the infall problem [arXiv:hep-th/1012.2101]
 Samir D. Mathur, The Information Paradox: A pedagogical introduction
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 D. N. Page, Phys. Rev Lett. 71, 1291 (1993), [arXiv:gr-qc/9305007]