Black Holes, The Information Paradox and The Island Formula
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Black holes pose fundamental challenges in theoretical physics. It is believed that its resolutions reveal important features of quantum gravity. One such problem involves the black hole information paradox. From the discovery of Hawking radiation on, for years, physicists have tried find out the precise mechanism by which information of matter, that collapses into a black hole during the formation process, can be retrieved from its Hawking radiation at later times. It is essential to understand how unitarity is preserved in semi-classical or quantum gravity, in order to exclude the possibility of information loss. In this thesis, we dive into black holes and the information paradox. In order to understand black holes and the information paradox, we investigate the fundamental theories of quantum mechanics and general relativity. Hereafter we take a look at important properties of black holes, and the emergence of Hawking radiation. Next, we study the information paradox and especially the Page curve closely, just as proposed solutions to the paradox. We also take a look at the AdS/CFT-duality, from which becomes clear that information is preserved. Finally, we will explore recent advances in the field by Alhmeiri et al. (2019) and Penington et al. (2019). These studies provide a possible explanation to the information problem by a new mechanism for information retrieval, called ”islands”. We arrive at a unitary Page curve via the island formula, a gravitational fine-grained entropy formula for the Hawking radiation. The island formula is derived from the replica trick by including new saddles: the replica wormholes.