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Updated: Jun 7, 2025

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Quantum Inequalities for Quantum Black Holes.

Antonia M Frassino1,2,3, Robie A Hennigar2, Juan F Pedraza4

  • 1Departamento de Física y Matemáticas, <a href="https://ror.org/04pmn0e78">Universidad de Alcalá</a>, Campus Universitario, Alcalá de Henares, 28805 Madrid, Spain.

Physical Review Letters
|November 15, 2024
PubMed
Summary

We developed new spacetime inequalities for quantum black holes that work in all dimensions and orders of backreaction. These findings support the existence of cosmic censorship and suggest a maximum entropy state for quantum black holes.

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Area of Science:

  • Theoretical physics
  • Quantum gravity
  • Black hole thermodynamics

Background:

  • Semiclassical gravity describes quantum effects in black holes.
  • Existing quantum Penrose inequalities are limited, failing in 3D beyond perturbative calculations.
  • Understanding black hole behavior requires accounting for all orders of backreaction.

Purpose of the Study:

  • To formulate new spacetime inequalities for quantum-corrected black holes.
  • To propose refined quantum Penrose and reverse isoperimetric inequalities for 3D anti-de Sitter black holes.
  • To investigate implications for cosmic censorship and black hole entropy.

Main Methods:

  • Formulating spacetime inequalities in semiclassical gravity.
  • Applying these inequalities to all orders of backreaction.
  • Analyzing three-dimensional asymptotically anti-de Sitter quantum black holes.

Main Results:

  • Developed quantum Penrose and reverse isoperimetric inequalities valid in 3D for all orders of backreaction.
  • Demonstrated that the quantum Penrose inequality holds beyond the perturbative regime in 3D.
  • Showed that the quantum reverse isoperimetric inequality implies a maximum entropy state for quantum black holes.

Conclusions:

  • The proposed quantum Penrose inequality supports the existence of cosmic censorship in nonperturbative semiclassical gravity.
  • The quantum reverse isoperimetric inequality suggests a limit on quantum black hole entropy for a fixed volume.
  • These inequalities provide a new framework for studying quantum black holes.