Entropy of black holes: quantum aspects

master's thesis

• Title (croatian): Entropija crnih rupa: kvantni aspekti
• Author: Axel Hrelja
• Mentor: Tajron Jurić (mentor)
• Mentor: Ivica Smolić (komentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Tajron Jurić (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Petar Žugec (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2023-12-18, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

The goal of this thesis was to research and analyze the literature that deals with quantum aspects of black hole entropy, with a heavy emphasis on quantum corrections. In the first chapter, we generalize ’Hooft’s brick wall method to higher-dimensional black holes, and we apply those results to the Schwarzschild and Reissner-Nordström black holes. In the second chapter, we look at the entanglement between the degrees of freedom inside and outside a black hole, while considering the horizon as the entanglement surface and interpreting the obtained entropy as the entropy of the black hole. We present two methods that simplify the calculations of the entanglement entropy: the replica trick, where we turn the task of calculating the entanglement entropy to calculating the partition function on a replicated manifold, and the heat kernel method, where we calculate the entropy by taking the trace of the so-called
heat kernel. In the third chapter, we consider the one-loop renormalization of the gravitational action, and using the Pauli-Villars regulator, we show that it leads to the renormalization of the Bekenstein-Hawking entropy. In the final chapter, we conclude with a discussion on the applicability of these methods to lower-dimensional black holes.

Abstract (croatian)

Cilj ovog diplomskog rada je bio istražiti i analizirati literaturu koja se bavi kvantnim aspektima entropije crnih rupa, s naglaskom na kvantnim korekcijama. U prvom poglavlju generaliziramo ’t Hooftovu brick wall metodu na više dimenzionalne crne rupe, i te rezultate primjenjujemo na Schwarzschildovu te Reissner-Nordströmovu crnu rupu. U drugom poglavlju promatramo ispreplitanje stupnjeva slobode unutra i izvan crne rupe, tretirajući njen horizont kao ispreplitajuću plohu te interpretirajući dobivenu entropiju kao entropiju crne rupe. Predstavljamo dvije metode koje olakšavaju računanje isprepletene entropije: replica trick u kojem smo zadatak računanja isprepletene entropije sveli na računanje particijske funkcije na repliciranoj mnogostrukosti i heat kernel metodu gdje računamo entropiju putem traga tzv. heat kernela. U trećem poglavlju promatramo jednopetljenu renormalizaciju gravitacijske akcije putem Pauli-Villarsovog regulatora, te pokazujemo da to vodi na renormalizaciju Bekenstein-Hawkingove entropije. U zadnjem poglavlju zaključujemo raspravom o mogućnosti primjene ovih metoda na crnim rupama nižih dimenzija.

• Keywords: general theory of relativity; quantum mechanics; statistical mechanics; black holes; black hole thermodynamics; entropy; quantum field theory on curved spacetimes
• Keywords (english): opća teorija relativnosti; kvantna mehanika; statistička mehanika; crne rupe; termodinamika crnih rupa; entropija; kvantna teorija polja na zakrivljenim prostorima
• Language: croatian
• URN:NBN: urn:nbn:hr:217:124586
• Study programme: Title: The University Integrated Undergraduate and Graduate Programme in Physics; Research Physics; specializations in: Research Physics; Course: Research Physics; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: sveučilišni magistar fizike (sveučilišni magistar fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2024-02-06 10:06:54