Chaos and thermal effects in black hole interactions

Project Information

BlackHoleChaos

Grant agreement ID: 101105116

DOI

10.3030/101105116

Project closed

EC signature date 14 July 2023

Start date 1 August 2023

End date 31 July 2025

Funded under

• Marie Skłodowska-Curie Actions (MSCA)

Total cost

No data

EU contribution

€ 153 486,72

Coordinated by

EREVNITIKO PANEPISTIMIAKO INSTITOUTO THEORITIKIS KAI YPOLOGISTIKIS FYSIKIS
Greece

Periodic Reporting for period 1 - BlackHoleChaos (Chaos and thermal effects in black hole interactions)

Reporting period: 2023-08-01 to 2025-07-31

Summary of the context and overall objectives of the project

The convergence of chaos, thermal physics, and quantum information in the context of black hole dynamics poses one of the most fundamental and technically rich challenges in theoretical physics. Black holes represent unique laboratories where these domains are not only coexistent but deeply entangled: they exhibit classical chaotic behavior in their near-horizon dynamics, quantum thermal emission through Hawking radiation, and obey a Bekenstein-Hawking entropy law proportional to horizon area—suggesting an underlying statistical origin. Unraveling the microscopic mechanisms that give rise to these macroscopic phenomena is essential for resolving foundational questions at the intersection of general relativity, quantum field theory in curved spacetime, and quantum statistical mechanics.

This project aims to make progress on this front by developing a perturbative, S-matrix-based framework for the quantitative analysis of chaotic and thermal effects in black hole physics, using perturbative string theory as a UV-complete setting for gravitational interactions. In this approach, black holes are modeled as ensembles or superpositions of highly excited string states (HES) or coherent string states (CSS), whose scattering amplitudes encode rich dynamical information about entropy production, quantum decoherence, and information scrambling. By computing string-level decay and absorption processes, analyzing the spectral statistics of the associated amplitudes, and probing the emergence of universal thermal signatures, the project seeks to identify the microscopic signatures of black hole thermodynamics and to quantify the role of quantum chaos in horizon-scale dynamics. The broader objective is to advance toward a microscopically controlled understanding of black hole interactions, with implications for quantum gravity, gravitational wave phenomenology, and the unitarity problem in black hole evaporation.

By anchoring these questions in a rigorous and computable framework, the project aspires to contribute to the long-term objective of a quantum-mechanical, unitary, and thermodynamically consistent description of black holes, grounded in the principles of string theory and holography, and guided by the phenomenological input of emerging gravitational wave astronomy.

The specific objectives of the project are:

a) To formulate a quantum gravity description of black hole interactions, focusing on the generation of chaos and thermal effects from first principles.

b) To resolve key technical challenges related to S-matrix unitarity and the incorporation of external states characterized by entropy, horizon, and angular momentum.

c) To investigate how chaotic behavior influences the structure of the black hole horizon, with implications for holography and quantum information flow.

d) To identify and analyze observable signatures of chaos and thermalization in gravitational and electromagnetic wave emissions (GWs and EMWs), particularly in processes involving highly excited and entropic states.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

This project focused on constructing a rigorous theoretical framework to analyze chaotic dynamics and thermalization mechanisms within perturbative string theory, with a specific emphasis on highly excited string states (HES) and coherent string states (CSS) as controlled microscopic models of black hole (BH) microstates. The overarching objective was to identify string-theoretic signatures of black hole-like behavior, such as chaotic decay, thermal emission, and information scrambling, through precise Scattering matrix computations and spectral analysis. The research was structured into four complementary work packages, each of which yielded significant theoretical advancements and peer-reviewed publications.


a) Computation of Scattering Amplitudes for Arbitrary Excited String States

The first component of the project aimed to develop efficient computational techniques for evaluating tree-level four-point scattering amplitudes involving arbitrarily excited string states in bosonic and superstring theories. These amplitudes are fundamental for probing the dynamical properties of HES/CSS and serve as a starting point for quantifying chaos and thermal features in string interactions.

Key achievements include:

1) Systematic classification of vertex operator structures for general excited levels.
2) Generalization of the Veneziano and Shapiro-Virasoro amplitudes to arbitrary excitation modes.
3) Implementation of recursive and generating function techniques to facilitate amplitude computation.

b) Quantification of Quantum Chaos via Spectral Form Factors

The second objective was to investigate quantum chaotic behavior in the decay dynamics of HES. In particular, the project focused on the computation of spectral form factors (SFFs) and scattering form factors (ScFFs) for two- and three-body decay processes, interpreting the results through the lens of Random Matrix Theory (RMT). HES were treated as ensembles of microstates representing gravitational configurations with entropy, and their decay channels were analyzed to test for universal chaotic signatures.

Main contributions include:

1) Derivation of decay amplitudes in specific kinematic regimes with clear resonance structures.
2) Proposal and validation of a new numerical scheme for evaluating SFFs in closed string backgrounds.
3) Demonstration of non-trivial agreement with RMT predictions for level correlations and late-time behavior.


c) Thermal Behaviour in String Absorption and Emission

The third phase examined thermalization mechanisms in the context of string absorption and emission processes, with a focus on establishing an explicit link between statistical behavior and microscopic scattering amplitudes. By applying the optical theorem to the amplitudes constructed in phase (1), we studied how HES absorb and re-emit string states across a range of energies.

Key findings:

1) Identification of a universal absorption profile for excited string states in the classical limit.
2) Emergence of thermal emission spectra analogous to Hawking radiation, derived from first principles.
3) Microscopic justification for thermodynamic behavior in string-theoretic models of black holes.


d) Applications to Gravitational Radiation and Black Hole Evaporation

The final stage explored phenomenological applications, particularly the potential signatures of chaos and thermal effects in gravitational wave (GW) and electromagnetic wave (EMW) emissions from high-energy string interactions. Using the scattering amplitudes and form factors derived previously, we analyzed multi-particle production processes and their correlation structures, identifying analogues of black hole evaporation and potential observables in gravitational radiation.

Outcomes:

1) Construction of a string-theoretic form factor with properties mimicking black hole greybody factors.
2) Preliminary results indicating chaotic imprints in multiparticle radiation spectra, with implications for GW signal analysis.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

This project has delivered a systematically developed suite of analytical and computational tools for probing chaotic dynamics and thermalization mechanisms in perturbative string theory. By establishing a concrete framework grounded in the explicit computation of scattering amplitudes involving highly excited and coherent string states, and by deploying advanced spectral diagnostics such as the spectral and scattering form factors, the project has illuminated the complex interplay between microscopic string dynamics and macroscopic thermodynamical behavior. The successful synthesis of S-matrix analysis, quantum chaos theory, and thermodynamic observables within the string-theoretic formalism opens novel pathways for addressing longstanding problems in high-energy theoretical physics.

In particular, the developed techniques offer a promising avenue for exploring the microscopic origin of black hole entropy, the quantum mechanical basis of Hawking radiation, and the structure of information scrambling in systems with gravitational analogues. The results provide compelling evidence that perturbative string theory, when applied to suitable high-energy regimes, can reproduce key features of black hole thermodynamics—suggesting that a deeper statistical description of black hole microstates is achievable within this framework. Furthermore, the project lays the groundwork for future investigations into the unitarity of black hole evaporation, the emergence of spacetime geometry from entanglement and scattering data, and the characterization of entropic bounds and quantum chaos thresholds in string-theoretic models.

Taken together, these contributions represent a significant step toward a quantitative, first-principles understanding of quantum gravitational phenomena, and reinforce the role of string theory as a leading framework for the unification of gravity with quantum mechanics. The methodologies developed are broadly applicable and are expected to inform future efforts aimed at confronting string-theoretic predictions with observational data, particularly in the context of gravitational wave signatures, horizon-scale physics, and quantum aspects of black hole dynamics.