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Radiation Entropy in asymptotically AdS Black Holes within f(Q) Gravity

Yipeng Liu, Wei Xu, Baocheng Zhang

TL;DR

This work investigates radiation entropy and information recovery for asymptotically AdS black holes in $f(Q)$ gravity using the island rule. The authors show that the generalized (area) term in the entropy is rescaled by $f_Q$, tying the radiation entropy to the specific $f(Q)$ model, while the semiclassical contribution remains standard; in eternal settings the entropy becomes time-independent but diverges with the cutoff, highlighting limits of the $s$-wave approximation, whereas in collapsing scenarios a finite, logarithmically corrected radiation entropy emerges, consistent with quantum-gravity expectations. The Page time likewise depends on $f(Q)$, indicating that the underlying gravitational theory leaves an imprint on the information recovery process. Overall, the results provide a theoretical pathway to constrain $f(Q)$ gravity through entanglement and information-theoretic considerations in black hole spacetimes.

Abstract

We employ the island rule to study the radiation entropy in the background of asymptotically AdS black holes within f(Q) gravity. Through an analysis based on the Euclidean action, we find that within this framework the area term of the generalized entropy must be modified, leading to a corrected island rule. Using this rule to compute the radiation entropy in the eternal case shows that, although the result is time-independent, it diverges as the cutoff surface moves outward, indicating the breakdown of the s-wave approximation. For a collapsing black hole, the radiation entropy is dominated by the area term, with a logarithmic correction proportional to the area, which is consistent with the predictions of quantum gravity theories. Furthermore, both the radiation entropy and the Page time are ultimately influenced by the choice of the f(Q) model, implying that information about the underlying gravitational model is encoded in the final radiation entropy.

Radiation Entropy in asymptotically AdS Black Holes within f(Q) Gravity

TL;DR

This work investigates radiation entropy and information recovery for asymptotically AdS black holes in gravity using the island rule. The authors show that the generalized (area) term in the entropy is rescaled by , tying the radiation entropy to the specific model, while the semiclassical contribution remains standard; in eternal settings the entropy becomes time-independent but diverges with the cutoff, highlighting limits of the -wave approximation, whereas in collapsing scenarios a finite, logarithmically corrected radiation entropy emerges, consistent with quantum-gravity expectations. The Page time likewise depends on , indicating that the underlying gravitational theory leaves an imprint on the information recovery process. Overall, the results provide a theoretical pathway to constrain gravity through entanglement and information-theoretic considerations in black hole spacetimes.

Abstract

We employ the island rule to study the radiation entropy in the background of asymptotically AdS black holes within f(Q) gravity. Through an analysis based on the Euclidean action, we find that within this framework the area term of the generalized entropy must be modified, leading to a corrected island rule. Using this rule to compute the radiation entropy in the eternal case shows that, although the result is time-independent, it diverges as the cutoff surface moves outward, indicating the breakdown of the s-wave approximation. For a collapsing black hole, the radiation entropy is dominated by the area term, with a logarithmic correction proportional to the area, which is consistent with the predictions of quantum gravity theories. Furthermore, both the radiation entropy and the Page time are ultimately influenced by the choice of the f(Q) model, implying that information about the underlying gravitational model is encoded in the final radiation entropy.
Paper Structure (11 sections, 48 equations, 3 figures)

This paper contains 11 sections, 48 equations, 3 figures.

Table of Contents

  1. Introduction
  2. General Entropy in $f(\mathbb{Q})$ Gravity
  3. Elements
  4. Black holes
  5. Generalized Entropy
  6. Entropy of the Hawking radiation
  7. Island Rule
  8. Eternal Scenarios
  9. Collapsing Scenarios
  10. Page Time
  11. Conclusion

Figures (3)

  • Figure 1: The island configuration in an eternal AdS black hole, where $X$ denotes the quantum extremal surface. The left and right regions in the figure are symmetric.
  • Figure 2: The vacuum fluctuations near the island and the cutoff surface, and only the right-half spacetime structure of the eternal black hole is illustrated here.
  • Figure 3: A black hole formed by the collapse of an AdS vacuum, with its right exterior region coupled to a thermal bath that collects the Hawking radiation.