Gauge Invariant Hamiltonian Evolution across Black Hole Horizons in AAdS Spacetimes Demonstrated

Understanding what happens to information as it crosses a black hole’s event horizon remains a fundamental challenge in theoretical physics, and Anurag Kaushal, Naveen S. Prabhakar, and Spenta R. Wadia from the International Centre for Theoretical Sciences-Tata Institute of Fundamental Research now present a significant advance in addressing this problem. Their work establishes a clear framework for describing the evolution of quantum fields, specifically scalar fields, as they traverse the horizon of a black hole within a specific spacetime geometry. The team develops a mathematically rigorous Hamiltonian formulation that allows them to track the field’s behaviour using a gauge-invariant approach, effectively providing a unitary description of horizon-crossing excitations and resolving long-standing questions about information preservation. This achievement not only clarifies the dynamics within black holes but also yields a novel method for reconstructing observable signals of horizon crossing in a corresponding boundary theory, offering potential avenues for connecting theoretical predictions with future observations.

A gauge invariant Hamiltonian evolution across the black hole horizon in asymptotically AdS spacetimes. This work investigates the quantum dynamics of a scalar field in the background of a black hole within a specific spacetime geometry, employing a Hamiltonian formulation of general relativity and a particular slicing of spacetime.

The research explores how quantum fields behave when crossing the event horizon of a black hole, a region where classical physics breaks down. By utilising a gauge invariant Hamiltonian approach, the team accurately describes the field’s evolution, avoiding ambiguities that can arise in other formulations. This method provides a consistent treatment of quantum effects near the black hole horizon, offering insights into the interplay between gravity and quantum mechanics. This gauge is expressed using a smooth coordinate system that cuts across the horizon and smoothly connects to standard coordinates far from the black hole.

The quantum scalar field expands in terms of solutions to the Klein-Gordon equation, valid throughout spacetime. The mathematical operators appearing in this expansion reside in the theories describing the boundaries of the spacetime and remain unchanged under small changes in the geometry. This construction naturally leads to the entangled Hartle-Hawking state, and a well-defined formula for the time-dependent Hamiltonian represents a key result.

AdS/CFT Probes Quantum Gravity’s Black Holes

This research establishes a framework for understanding the quantum behaviour of scalar fields in the vicinity of a two-sided black hole, building upon Hawking’s original work on black hole thermodynamics and entropy. The team successfully constructed a well-defined Hamiltonian that governs the evolution of a probe scalar field along maximal slices of the black hole spacetime, demonstrating a unitary description of how excitations cross the event horizon. This achievement resolves a long-standing challenge in describing quantum dynamics in these extreme gravitational environments. Furthermore, the researchers developed a bulk reconstruction formula, allowing them to relate properties of the scalar field within the black hole to corresponding observables in a boundary theory, effectively bridging the gap between gravitational and quantum descriptions.

Calculations of scalar field correlation functions reveal a time reflection symmetry and demonstrate that these functions approach a non-zero constant as the time separation between measurement points increases, offering insights into the long-range correlations near the black hole. The authors acknowledge that their analysis relies on specific coordinate systems and approximations inherent in the chosen mathematical framework. They also note that extending this approach to more complex scenarios, such as incorporating interactions between fields or considering rotating black holes, represents a natural direction for future investigation. This work provides a solid foundation for exploring the intricate interplay between quantum mechanics and gravity in the presence of black holes and opens avenues for further research into the fundamental nature of spacetime.

Black Hole Quantum Dynamics and Unitary Evolution

This research establishes a framework for understanding the quantum behaviour of scalar fields in the vicinity of a two-sided black hole, building upon Hawking’s original work on black hole thermodynamics and entropy. The team successfully constructed a well-defined Hamiltonian that governs the evolution of a probe scalar field along maximal slices of the black hole spacetime, demonstrating a unitary description of how excitations cross the event horizon. This achievement resolves a long-standing challenge in describing quantum dynamics in these extreme gravitational environments. Furthermore, the researchers developed a bulk reconstruction formula, allowing them to relate properties of the scalar field within the black hole to corresponding observables in a boundary theory, effectively bridging the gap between gravitational and quantum descriptions.

Calculations of scalar field correlation functions reveal a time reflection symmetry and demonstrate that these functions approach a non-zero constant as the time separation between measurement points increases, offering insights into the long-range correlations near the black hole. The authors acknowledge that their analysis relies on specific coordinate systems and approximations inherent in the chosen mathematical framework. They also note that extending this approach to more complex scenarios, such as incorporating interactions between fields or considering rotating black holes, represents a natural direction for future investigation. This work provides a solid foundation for exploring the intricate interplay between quantum mechanics and gravity in the presence of black holes and opens avenues for further research into the fundamental nature of spacetime.