The information paradox: A pedagogical introduction (0909.1038v2)

Abstract: The black hole information paradox is a very poorly understood problem. It is often believed that Hawking's argument is not precisely formulated, and a more careful accounting of naturally occurring quantum corrections will allow the radiation process to become unitary. We show that such is not the case, by proving that small corrections to the leading order Hawking computation cannot remove the entanglement between the radiation and the hole. We formulate Hawking's argument as a theorem': assumingtraditional' physics at the horizon and usual assumptions of locality we will be forced into mixed states or remnants. We also argue that one cannot explain away the problem by invoking AdS/CFT duality. We conclude with recent results on the quantum physics of black holes which show the the interior of black holes have a `fuzzball' structure. This nontrivial structure of microstates resolves the information paradox, and gives a qualitative picture of how classical intuition can break down in black hole physics.

• The paper’s main contribution is demonstrating that small quantum corrections to Hawking radiation are insufficient to resolve the black hole information paradox.
• It employs entropy computations and locality assumptions to show that entanglement between radiation and black hole states inevitably leads to mixed states or remnants.
• The work challenges traditional horizon models, promoting the fuzzball paradigm as a transformative framework for understanding quantum gravity and information recovery.

Overview of "The information paradox: A pedagogical introduction"

The paper by Samir D. Mathur concentrates on a precise formulation of the black hole information paradox, fundamentally challenging many preconceived notions in black hole physics. The paradox originates from Stephen Hawking's argument that the thermal nature of black hole radiation precludes any information from leaking out, seemingly resulting in an information loss when the black hole evaporates completely. Specifically, Mathur contends that small quantum corrections to Hawking's original thermique radiation cannot nullify the entanglement between the radiation and the black hole. This entanglement leads to a profound contradiction if we assume conventional locality and "traditional" horizon conditions, ultimately culminating in either mixed states or remnants.

Theoretical Framework and Methodology

The paper delineates the intricacies of the paradox through discussions with regards to early principles that engage with general relativity extended into curved spacetime. Mathur systematically elaborates on `solar system physics,' where spacetime curvatures typical to our solar system do not necessitate concerns about quantum gravitational details. This framework underlays the assumptions and niceness conditions used to explore locality at the horizon, bifurcating into specific conditions such as the negligible intrinsic and extrinsic curvatures in spacelike slices that evolve smoothly.

Core Argument and Numerical Insights

At its core, Mathur presents Hawking's argument as a theorem, elucidating how small quantum corrections cannot preempt the inevitable entanglement between Hawking radiation quanta and the black hole's asymptotic states. The paper uses entropy computations and locality assumptions to mathematically establish that such entanglements grow over time, inexorably forcing mixed states or remnants unless large-scale (order unity) changes occur. Mathur leverages the space of small corrections to position that only significant perturbations to the Hawking model reduce this entwined relationship, implying deep-seated changes in our understanding of quantum gravity to surpass perennial paradoxes.

Strong Claims and Theoretical Implications

Mathur emphasizes that addressing the information paradox requires abandoning traditional conceptions of black hole horizons, proposing instead a "fuzzball" paradigm. He suggests that each microstate is fundamentally distinct with no horizon or singularity, portraying classical intuition as misleading. Importantly, the assertion refutes that AdS/CFT duality offers a simplistic escape from the information paradox, arguing that it cannot in isolation circumvent the nontrivial challenge posed by Hawking's theorem.

Future Scope and Speculation

The implications resonate beyond theoretical formulations, gesturing towards transformative insights in quantum gravity and black hole physics. Future research might explore the robust establishment of non-locality influences within black hole physics, alongside significant reinterpretations of spacetime stretching. Considering the nascent conceptualization of fuzzballs, extensive validations in string theory could pave new trajectories in understanding information recovery in quantum mechanics, thereby resolving the Hawking paradox with practical clarity.

Mathur’s methodical pedagogy reaffirms that unraveling black hole dynamics requires overarching revisions to standard physics—propelling a profound shift as future explorations reconceptualize quantum information within gravity's ambit.