Quantum kicks near a Cauchy horizon

Juárez-Aubry, Benito A.; Louko, Jorma

Abstract

We analyze a quantum observer who falls geodesically toward the Cauchy horizon of a (1 + 1)-dimensional eternal black hole spacetime with the global structure of the non-extremal Reissner-Nordström solution. The observer interacts with a massless scalar field, using an Unruh-DeWitt detector coupled linearly to the proper time derivative of the field, and by measuring the local energy density of the field. Taking the field to be initially prepared in the Hartle-Hawking-Israel (HHI) state or the Unruh state, we find that both the detector's transition rate and the local energy density generically diverge on approaching the Cauchy horizon, respectively, proportionally to the inverse and the inverse square of the proper time to the horizon, and in the Unruh state the divergences on approaching one of the branches of the Cauchy horizon are independent of the surface gravities. When the outer and inner horizons have equal surface gravities, the divergences disappear altogether in the HHI state and for one of the Cauchy horizon branches in the Unruh state. We conjecture, on grounds of comparison with the Rindler state in 1 + 1 and 3 + 1 Minkowski spacetimes, that similar properties hold in 3 + 1 dimensions for a detector coupled linearly to the quantum field, but with a logarithmic rather than inverse power-law divergence.

Citation

Juárez-Aubry, B. A., & Louko, J. (2022). Quantum kicks near a Cauchy horizon. AVS Quantum Science, 4(1), Article 013201. https://doi.org/10.1116/5.0073373

• Journal Article Type: Article
• Acceptance Date: Jan 11, 2022
• Online Publication Date: Feb 14, 2022
• Publication Date: 2022-03
• Deposit Date: Feb 15, 2022
• Publicly Available Date: Feb 15, 2022
• Journal: AVS Quantum Science
• Print ISSN: 2639-0213
• Electronic ISSN: 2639-0213
• Publisher: American Vacuum Society
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Issue: 1
• Article Number: 013201
• DOI: https://doi.org/10.1116/5.0073373
• Public URL: https://nottingham-repository.worktribe.com/output/7468858
• Publisher URL: https://avs.scitation.org/doi/10.1116/5.0073373