Black Hole Secrets Unravel As Entanglement Entropy Reveals Hidden Periodic Patterns

Researchers are increasingly focused on resolving the black hole information paradox, and a new study proposes a novel approach using timelike entanglement entropy to probe Hawking radiation. Yahya Ladghami from Mohammed I University, Francisco S. N. Lobo from the University of Lisboa, and Taoufik Ouali et al. define timelike correlations within black hole spacetimes, revealing a series of timelike Page times where entanglement entropy matches the Bekenstein-Hawking entropy. Their analysis, applied to diverse black hole solutions including Schwarzschild and Kerr metrics, demonstrates periodic behaviour in timelike entanglement, sensitive to key black hole parameters such as charge and rotation. Significantly, this framework recovers information solely within the Hawking radiation, offering a potential pathway to preserve unitarity and horizon smoothness without invoking concepts like islands or firewalls, and establishing timelike entanglement as a powerful tool for investigating gravitational dynamics.

By employing analytical continuation of black hole spacetimes to Euclidean signature, researchers defined timelike correlations revealing a sequence of timelike Page times, moments at which the entanglement entropy reaches the Bekenstein-Hawking entropy.

Application of this framework to Schwarzschild, Reissner-Nordström, static higher-dimensional and braneworld solutions, four-dimensional Kerr, and higher-dimensional rotating Myers, Perry black holes demonstrates that timelike entanglement behaves periodically or quasi-periodically. Recurrence times within this behaviour are sensitive to surface gravity, charge, rotation, and the dimensionality of spacetime.
Extremal and near-extremal black holes exhibit effectively frozen thermal oscillations with persistent rotational modulation, directly reflecting their near-horizon geometries. This work establishes a framework that encodes information entirely within the Hawking radiation, thereby preserving unitarity and avoiding the need for horizon smoothness violations.

The research details a robust and physically transparent mechanism for information recovery, offering a versatile tool for exploring quantum gravitational dynamics across diverse black hole spacetimes. This study reveals that timelike entanglement exhibits a characteristic behaviour, with the entanglement entropy initially increasing, reaching a maximum, and then decreasing as the black hole evaporates.

This late-time decrease confirms that information initially encoded in the quantum state is gradually recovered in the emitted radiation, upholding quantum mechanical unitarity. Unlike approaches relying on islands or firewalls, this new method does not require modifications to the event horizon or the introduction of exotic spacetime regions to account for information preservation.

The findings establish timelike entanglement as a novel probe of the information paradox, providing a means to explore gravitational dynamics across a wide range of black hole solutions. Researchers observed that recurrence times in the timelike entanglement are demonstrably sensitive to key black hole parameters, including surface gravity, electric charge, rotational velocity, and the number of spatial dimensions. These results offer a new perspective on the interplay between gravity, quantum mechanics, and thermodynamics in the extreme environment of black holes.

Analytic continuation and timelike entanglement in diverse black hole spacetimes

Timelike entanglement entropy serves as a novel probe of the black hole information paradox within this research. The study analytically continued black hole spacetimes to Euclidean signature to define timelike correlations, revealing a sequence of timelike Page times where entanglement entropy equals the Bekenstein-Hawking entropy.

This analytical continuation facilitated the investigation of temporal quantum correlations within Hawking radiation, shifting the focus from spatial entanglement to correlations between radiation states emitted at different times. Researchers applied this framework to Schwarzschild, Reissner-Nordström, static higher-dimensional, and braneworld black holes, alongside four-dimensional Kerr and higher-dimensional rotating Myers, Perry black holes.

By examining these diverse spacetimes, the work demonstrated that timelike entanglement exhibits periodic or quasi-periodic behaviour, with recurrence times proving sensitive to surface area, charge, rotation, and spacetime dimensionality. Extremal and near-extremal black holes were found to display effectively frozen thermal oscillations with persistent rotational modulation, reflecting their unique near-horizon geometries.

The methodology innovatively encodes information entirely within the Hawking radiation, circumventing the need for spatial partitions like those used in the island formula. This was achieved by evaluating timelike entanglement entropy through a Wick rotation, resulting in a complex-valued pseudoentropy that generalizes the von Neumann entropy.

The resulting pseudoentropy provides a measure of quantum correlations between distinct quantum states separated in time, offering a new perspective on information recovery. This approach preserves unitarity and avoids violations of horizon smoothness, establishing timelike entanglement as a robust mechanism for exploring gravitational dynamics across a wide range of black hole spacetimes.

Timelike entanglement entropy and periodic recurrence in diverse black hole spacetimes

Timelike entanglement entropy reveals a sequence of timelike Page times where the entanglement entropy equals the Bekenstein-Hawking entropy. This research defines timelike correlations derived from analytically continuing black hole spacetimes to Euclidean signature, establishing a novel probe of the black hole information paradox.

Applying this framework to Schwarzschild, Reissner-Nordström, static higher-dimensional, and braneworld solutions, alongside four-dimensional Kerr and higher-dimensional rotating Myers, Perry black holes, demonstrates periodic or quasi-periodic behavior in timelike entanglement. Recurrence times exhibited sensitivity to surface gravity, charge, rotation, and spacetime dimensionality, providing detailed insights into black hole dynamics.

Extremal and near-extremal black holes displayed effectively frozen thermal oscillations with persistent rotational modulation, reflecting the unique characteristics of their near-horizon geometries. The observed behavior indicates that information is encoded entirely within the Hawking radiation, preserving unitarity and avoiding violations of horizon smoothness.

This work establishes timelike entanglement as a robust and physically transparent mechanism for information recovery, offering a versatile tool for exploring quantum gravitational dynamics. The study details how the recurrence times of timelike entanglement are directly influenced by fundamental black hole properties.

Variations in surface gravity, charge, rotation, and the number of spacetime dimensions all contribute to measurable shifts in the periodicity of the entanglement. Furthermore, the persistent rotational modulation observed in near-extremal black holes provides a unique signature of their near-horizon structure, offering a new avenue for observational studies. This framework offers a distinct approach to resolving the information paradox, differing from conventional methods based on islands or firewalls by maintaining unitarity without requiring modifications to the event horizon.

Periodic Entanglement Dynamics Resolve the Black Hole Information Paradox

Timelike entanglement entropy offers a new method for examining the black hole information paradox. Analytical continuation of black hole spacetimes to Euclidean signature enabled the definition of timelike correlations revealing a series of timelike Page times where entanglement entropy equals the Bekenstein-Hawking entropy.

Application of this framework to Schwarzschild, Reissner-Nordström, higher-dimensional static, braneworld, Kerr, and Myers-Perry black holes demonstrated periodic or quasi-periodic behaviour in timelike entanglement. Recurrence times are sensitive to surface gravity, charge, rotation, and spacetime dimensionality, with near-extremal black holes exhibiting frozen thermal oscillations alongside persistent rotational modulation.

This approach encodes information entirely within the Hawking radiation, upholding unitarity and avoiding horizon violations unlike proposals involving islands or firewalls. The findings establish timelike entanglement as a robust mechanism for information recovery and a versatile tool for investigating gravitational dynamics across diverse black hole spacetimes.

The research acknowledges that a true extremal limit does not exist, with the 5D case corresponding to ultra-spinning black holes and finite horizon angular velocity. This results in diverging thermal recurrences while rotational modulation continues. Future research could extend this analysis, potentially exploring the implications of these findings for understanding the fundamental nature of quantum gravity and black hole evaporation.