ENTANGLEMENT AND CHAOS WITH HOLOGRAPHIC PRINCIPLE IN ROTATING AND CHARGED BLACK HOLES

• Main Author: Luthfan Prihadi, Hadyan
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/81907
• Institution: Institut Teknologi Bandung

Extreme regions in the universe, which have a strong gravitational field like near black holes or in the early Universe, are good places to look for the signatures of quantum effects in the theory of gravity. One of the unique aspects of a quantum theory is the presence of entanglement which does not have any classical equiv- alent. In regions near the horizon of a black hole solution with wormhole geometry, the signature of quantum effects through entanglement can be seen as correlations between regions outside and inside the horizon. In the classical point of view, both regions are causally disconnected, which means that there can be no correlation between regions outside and inside the horizon. This shows that a wormhole, as a classical bridge that connects points in space and time, plays a role in creating quantum correlation through entanglement between two regions that are causally separated. In this dissertation, such entanglement measure is calculated using the entanglement entropy and it works for various static or rotating black hole solutions. Entanglement in wormholes can be quantified using entanglement entropy, which is a measure of how much entanglement is present in a quantum system. The entropy of entanglement for various black holes, ranging from static single horizon, and multi-horizon, to rotating black holes, are calculated by the general form of entanglement entropy formula for a continuous quantum system. Using the replica trick, entanglement entropy can be calculated and gives rise to the Bekenstein-Hawking entropy which scales as the surface area of the horizon. The entropy proportional to the surface area with one dimension lower than the volume indicates that the black hole system is holographic. Using the holographic principle and the AdS/CFT correspondence, the black hole system can be modeled as a quantum system in the boundary with one dimension lower than that of the black hole itself. In this work, the disruption of the entanglement structure of a wormhole geometry given only a small perturbation is also studied. It means that a black hole system is very sensitive to the change of initial condition, in other words, a black hole is a chaotic quantum system. The rate of the chaos of a system, or the Lyapunov exponent, is calculated for rotating and charged black hole solutions in the Einstein-Maxwell dilaton-axion (EMDA) theory, which have extra charges called the dilaton and axion. In this work, it is shown that the Lyapunov exponent can exceed the maximum bound suggested earlier. Such a violation is not present in the standard black hole as the solution to the Einstein field equation (or even Einstein-Maxwell). This result gives us significant physical insight into the study of a chaotic feature in some quantum systems, especially the ones that correspond to an extreme region near a black hole.