Quantum Corrections to near extremal black hole entropy and higher curvature terms.
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Date
2026
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Universidad de Concepción
Abstract
Esta tesis investiga las correcciones cuánticas a un loop a la entropía de agujeros negros cercanos a la extremalidad en gravedad de Einstein-Gauss-Bonnet (EGB) acoplada a un campo de Maxwell en cinco dimensiones. Se estudia una solución puramente eléctrica que admite un límite extremal. En este límite, la termodinámica clásica predice una gran degeneración del estado fundamental. El análisis se centra en el régimen cercano a la extremalidad, donde al disminuir la temperatura la emisión de un cuanto de Hawking puede producir variaciones apreciables en el estado térmico, lo que plantea interrogantes conceptuales sobre la validez de la descripción semiclásica. Para abordar estos problemas, se emplea el formalismo de la integral de camino euclidiana y se calcula la función de partición en la aproximación semiclásica. El análisis se realiza expandiendo la acción hasta segundo orden en la métrica y el campo de gauge alrededor de la geometría cerca del horizonte, la cual desarrolla una estructura AdS2 × S3 en el límite extremal. En este marco, las correcciones cuánticas quedan codificadas en el espectro de un operador generalizado de Lichnerowicz que gobierna las fluctuaciones de la métrica y del campo de gauge. Una característica clave de este operador es la presencia de modos cero en el límite extremal, los cuales conducen a divergencias en la función de partición a un loop. Se muestra que, en el régimen cercano a la extremalidad, estos modos dejan de ser modos cero y adquieren autovalores proporcionales a la temperatura, dando lugar a correcciones logarítmicas a la entropía. Los resultados proporcionan una realización concreta de cómo los efectos cuánticos modifican la descripción semiclásica de agujeros negros en teorías de gravedad con curvatura superior, y develan la estructura de la densidad de estados en el régimen cercano a la extremalidad.
This thesis investigates the one-loop quantum corrections to the entropy of nearextremal black holes in five-dimensional Einstein-Gauss-Bonnet (EGB) gravity coupled to a Maxwell field. A purely electric solution admitting an extremal limit is considered. In this limit, classical thermodynamics predicts a large groundstate degeneracy. The analysis focuses on the near-extremal regime, where, as the temperature decreases, the emission of a Hawking quantum can induce appreciable changes in the thermal state, raising conceptual questions about the validity of the semiclassical description To address these issues, the Euclidean path integral formalism is employed to compute the partition function in the semiclassical approximation. The analysis is performed by expanding the action to quadratic order in the metric and the gauge field around the near-horizon geometry, which develops an AdS2 × S3 structure in the extremnal limit. In this framework, quantum corrections are encoded in the spectrum of a generalized Lichnerowicz operator governing fluctuations of the metric and the gauge field. A key feature of this operator is the presence of zero modes in the extremal limit, which lead to divergences in the one loop partition function. It is shown that, in the near-extremal regime, these modes are lifted and acquire eigenvalues proportional to the temperature, giving rise to logarithmic corrections to the entropy. The results provide a concrete realization of how quantum effects modify the semiclassical description of black holes in higher-curvature gravity, and shed light on the structure of the near-extremal density of states.
This thesis investigates the one-loop quantum corrections to the entropy of nearextremal black holes in five-dimensional Einstein-Gauss-Bonnet (EGB) gravity coupled to a Maxwell field. A purely electric solution admitting an extremal limit is considered. In this limit, classical thermodynamics predicts a large groundstate degeneracy. The analysis focuses on the near-extremal regime, where, as the temperature decreases, the emission of a Hawking quantum can induce appreciable changes in the thermal state, raising conceptual questions about the validity of the semiclassical description To address these issues, the Euclidean path integral formalism is employed to compute the partition function in the semiclassical approximation. The analysis is performed by expanding the action to quadratic order in the metric and the gauge field around the near-horizon geometry, which develops an AdS2 × S3 structure in the extremnal limit. In this framework, quantum corrections are encoded in the spectrum of a generalized Lichnerowicz operator governing fluctuations of the metric and the gauge field. A key feature of this operator is the presence of zero modes in the extremal limit, which lead to divergences in the one loop partition function. It is shown that, in the near-extremal regime, these modes are lifted and acquire eigenvalues proportional to the temperature, giving rise to logarithmic corrections to the entropy. The results provide a concrete realization of how quantum effects modify the semiclassical description of black holes in higher-curvature gravity, and shed light on the structure of the near-extremal density of states.
Description
Tesis presentada para optar al grado de Magíster en Ciencias con mención en Física.
Keywords
Black holes (Astronomy), Entropy, Gravity