Black Hole Paradoxes: A Unified Framework for Information Loss

Dissertation, University of Geneva (2024)
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The black hole information loss paradox is a catch-all term for a family of puzzles related to black hole evaporation. For almost 50 years, the quest to elucidate the implications of black hole evaporation has not only sustained momentum, but has also become increasingly populated with proposals that seem to generate more questions than they purport to answer. Scholars often neglect to acknowledge ongoing discussions within black hole thermodynamics and statistical mechanics when analyzing the paradox, including the interpretation of Bekenstein-Hawking entropy, which is far from settled. To remedy the dialectical gridlock, I have formulated an overarching, unified framework, which I call ``Black Hole Paradoxes'', that integrates the debates and taxonomizes the relevant `camps' or philosophical positions. I demonstrate that black hole evaporation within Hawking's semi-classical framework insinuates how late-time Hawking radiation is an entangled global system, a contradiction in terms. The relevant forms of information loss are associated with a decrease in maximal Boltzmann entropy and an increase in global von Neumann entropy respectively, which engender what I've branded the ``paradox of phantom entanglement''. Prospective solutions are then tasked with demonstrating how late-time Hawking radiation is either exclusively an entangled subsystem, in which a black hole remnant lingers as an information safehouse, or exclusively an unentangled global system, in which information is evacuated to the exterior. The disagreement between safehouse and evacuation solutions boils down to the statistical interpretation of thermodynamic black hole entropy, i.e., Bekenstein-Hawking entropy. Safehouse solutions attribute Bekenstein-Hawking entropy to a minority of black hole degrees of freedom, those that are associated with the horizon. Evacuation solutions, in contrast, attribute Bekenstein-Hawking entropy to all black hole degrees of freedom. I argue that the interpretation of Bekenstein-Hawking entropy is the litmus test to vet the overpopulated proposal space. So long as any proposal rejecting Hawking's original calculation independently derives black hole evaporation, globally conserves degrees of freedom and entanglement, preserves a version of semi-classical gravity at sub-Planckian scales, and describes black hole thermodynamics in statistical terms, then it counts as a genuine solution to the paradox.



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Saakshi Dulani
Johns Hopkins University

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