Myrzakul, Aizhan2023-12-292023-12-292023-11-10Myrzakul, A. (2023). Black Hole/Moving Mirror correspondence in (1+1)-dimensions. Nazarbayev University, School of Engineering and Digital Scienceshttp://nur.nu.edu.kz/handle/123456789/7577The Hawking effect predicts that black holes can emit particles and energy when quantum mechanical effects are taken into account in quantum atmosphere around the black hole. However, certain models of black holes emit infinite energy and infinite particles that are contradictory to both classical and quantum theories' laws. These and other black hole evaporation problems along with the need to get experimental verification have underscored the need for analog and toy models that can solve the issues without losing the essential physical properties of the black hole radiation processes. The significance of studying moving mirrors is that they are accelerated boundaries that create energy, particles, and entropy similar to black holes. In fact, moving mirrors, which are simplified (1+1)-dimensional versions of the dynamical Casimir effect, act as toy models for black hole evaporation, in some cases, with an exact correspondence to the amount of particle production. Moreover, the dynamical Casimir effect has been measured in the laboratory within the framework of moving mirror model providing experimental observations and insight into the effect, whereas Hawking radiation from black holes effectively can not be measured because the effect is too small. The general and physically relevant connections of moving mirrors to black hole physics is a prime focus of this thesis. Here black holes and some cosmological models are approximated by (1+1)-dimensional moving mirrors. The detailed and complete investigation of all existing moving mirror models, their classifications and specific characters are the main objectives. This extensive study allows one to distinguish the moving mirror solutions that most physically describe black hole evaporation. They have proven capability to solve specific issues related to Hawking radiation. A new model related to the Schwarzschild black hole that solves the issue of finite energy with respect to Hawking radiation is developed. Also, it is established that Callan-Giddings-Harvey-Strominger (CGHS) black hole model has a correspondence to the exponentially accelerated moving mirror in coordinate time for the particle production. In addition, the mirror radiation power and radiation reaction force, that have recently been derived, have been applied to the specific moving mirror model of the CGHS correspondence. As a result, it is shown that Larmor power and self-force for the mirror describe quantum radiation. Furthermore, two distinct methods of deriving the stress tensor for the quantum radiation of the moving mirror are analyzed and a comparison analysis is made. Finally, while extensively studying all the known moving mirror solutions and trying to compile collective results, some new results have been found, including some trajectories in null and spacetime coordinates, particle count for the mirrors that have finite particle production, fluxes for some mirrors in certain coordinates that have interesting physical effect, and etc. All existing moving mirror solutions are studied by classification into several types based on their dynamics. Then, each mirror is extensively reviewed from four perspectives: dynamics, flux & energy, particles, and entropy. These methodologies enable one to obtain a complete set of solutions, understand their behavior, and unveil particular implications and physical features of the moving mirror model as a whole.enAttribution-NonCommercial-NoDerivs 3.0 United StatesType of access: Open accessmoving mirrorsblack holesrelativistic quantum informationPhD thesis