چگالش پوز-اينشتين در نزديكي افق رويداد و صفحات هولوگرافيك

چكيده انگليسي :

Bose Einstein Condensation on Stretched Horizon and Holographic Screen Zahra Raissi z raissi@ph iut ac ir Date of Submission Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Behrouz Mirza b Mirza@cc iut ac ir Abstract In this thesis at first we study Verlinde s approach to gravity which interprets gravitationalinteraction as a kind of entropic force Then propose a model for the quantum bits of space time onstretched horizon and holographic screens A recent work by Verlinde has proposed a qualitatively new approach to gravity which joins theholographic and thermodynamic ideas The essence of the approach is based on two principles first is theholographic principle through which space is emergent The holographic principle supposes that space isonly a kind of container of information The information is stored on holographic screens which separatepoints Also the screens are equipotential surfaces The second principle suggests that when the bodymoves relatively the screen it exerts an entropic force similar to the one that appears in osmosis or whenbig colloid molecules are surrounded by thermal environment of smaller particles Thus according to theVerlinde approach gravity is not a fundamental interaction like other three but a kind of entropic force Whatever fantastic these ideas look like they allowed to derive both the Newton law of gravity and theEinstein equations Motivated by this new interpretation of gravity we study equipotential surfaces theUnruh Verlinde temperature energy acceleration and The physics of black holes attracted wide attention as an arena for study of statistical concepts likeentropy In this context the idea of a stretched horizon arose as a useful tool for thinking about blackholes Therefore we consider a system with relativistic and non interacting Bose particles located in astatic space time with horizon like Rindler Schwartzschild and general form of spherically symmetricstatic space times We merely know that the system is confined in a box with one dimension less thanspace It is well known that theory of the grand canonical ensemble is sufficient to find all of thethermodynamical variables At first we need to evaluate the density of state in the background of a curvedspace time It is shown that the gas on the stretched horizon is in a Bose Einstein condensed state with theHawking temperature if the particle number of the system be equal to the number of quantum bits ofspace times Originally we assuming that total number of particles are proportional to the area of the box In the following we evaluate another statistical quantity like entropy One of excellent result is theentropy area relationship of the stretched horizon In this way we may obtain the Bekenstein Hawkingentropy as well as its corrections which are somewhat universal in theories of quantum gravity such asstring theory and loop quantum gravity Also we evaluate that a boson gas on a holographic screen withthe same number of particles and at Unruh Verlinde temperature is also in a condensed state Far from thehorizon the Unruh temperature is much lower than the condensation temperature This analysis implies apossible physical model for quantum bits of space time on holographic screen It should be noted that thisresults is also valid for Kerr space time Keywords Thermodynamics Black Holes Condensation Stretched horizon Holographic screen

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چگالش پوز-اينشتين در نزديكي افق رويداد و صفحات هولوگرافيك

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