An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
Quantum-Gravitational Null Raychaudhuri Equation
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abstract
We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity.
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hep-th 2years
2026 2representative citing papers
Quantum width of spherically symmetric black hole horizons is defined by signal escape timing and calculated in perturbative quantum gravity to often greatly exceed the Planck length, scaling as sqrt(l_P r_s^2 / sigma_perp) for Schwarzschild patches.
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Quantization of Gravity on Null Hypersurfaces
An operator-algebraic quantization of the characteristic initial-value problem yields a candidate on-shell algebra for a gravitational subregion bounded by two null hypersurfaces.
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Quantum Fluctuations of the Black Hole Horizon
Quantum width of spherically symmetric black hole horizons is defined by signal escape timing and calculated in perturbative quantum gravity to often greatly exceed the Planck length, scaling as sqrt(l_P r_s^2 / sigma_perp) for Schwarzschild patches.