AdS black holes in two-dimensional dilaton gravity and holography
Date
2025-11
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Benemérita Universidad Autónoma de Puebla
Abstract
“The gauge/gravity correspondence allows the study of strongly coupled field theories by relating quantum systems in thermal equilibrium with black holes whose temperature matches that of the system. This thesis presents two families of analytical AdS2 black hole solutions in a two-dimensional dilaton gravity model with two coupled scalar fields, useful for exploring the physics, thermodynamics, and possible generalizations to higher dimensions. The AdS2 geometry, symmetric under SO(2,1), connects with the conformal invariance of the boundary theory and with models such as Sachdev-Ye-Kitaev, which are relevant in quantum chaos. The causal structure is analyzed using Eddington-Finkelstein and Kruskal coordinates, constructing Penrose diagrams that show internal and external horizons. Thermodynamics is developed using the Euclidean path integral approach, applying Hamilton-Jacobi to eliminate divergences and obtain a renormalized action that allows calculating energy, Hawking temperature, and satisfying the first law. In addition, the effective theory at the boundary is studied, and results are compared with previous dilatonic models, showing consistency, holographic properties, and relevance for black hole physics and quantum gravity.
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