Ograničenja kompaktnosti astrofizičkih tijela

master's thesis

• Title (english): Bounds on compactness of astrophysical bodies
• Author: Ema Kompar
• Mentor: Ivica Smolić (mentor)
• Committee member: Ivica Smolić (predsjednik povjerenstva)
• Committee member: Maro Cvitan (član povjerenstva)
• Committee member: Petar Žugec (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2023-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Bilo kakva gravitirajuća materija u ravnotežnom je stanju gravitacijskog stiskanja i internih tlakova. U određenim silovitim procesima, moguće je materiju toliko sabiti da se ona ne može oduprijeti gravitacijskom sažimanju i dolazi do gravitacijskog kolapsa u crnu rupu. Astrofizička tijela mogu se u potpunosti opisati masom, nabojem, angularnim momentom i površinom, te kompaktnost tijela određujemo međusobnim odnosima tih veličina. Razmatranja provodimo u kontekstu opće teorije relativnosti koja omogućuje povezivanje fizikalnih i geometrijskih veličina. Ograničenja općenito proizlaze iz energijskih uvjeta, kozmičke cenzure i uvjeta stvaranja crnih rupa te se iskazuju u obliku nejednakosti. Promotrit ćemo važne rezultate u odnosima mase, naboja, angularnog momenta i površine s raznim uvjetima na prostorvrijeme i početni skup podataka. Pobliže ćemo se baviti dinamičnim crnim rupama sa i bez simetrijskog uvjeta, kao i općenitim rotirajućim osnosimetričnim tijelima. Dodatno, objasnit ćemo pojam geometrijske nejednakosti te za početak opisati izoperimetrijsku nejednakost, kao i neke otvorene probleme.

Abstract (english)

Any kind of gravitating matter is in a state of equilibrium between gravitational contraction and internal pressure. In certain extreme processes, it is possible to compress the matter in such a way that it can no longer resist the gravitational contraction and a gravitational collapse into a black hole occurs. Astrophysical bodies can be completely determined by their mass, charge, angular moment and area, and compactness is established by the relations between those quantities. We are conducting our research in the context of general relativity which enables connections between physical and geometric quantities. Bounds arise from energy conditions, cosmic censorship and conditions on black hole formation and we express them in terms of inequalities. We consider some important results in relations of mass, charge, angular moment and area with various conditions on spacetime and initial dataset. We will closely work on dynamical black holes with and without symmetry assumptions, as well as generic rotating axially symmetric bodies. In addition, we will explain the notion of a geometric inequality and describe firstly the isoperimetric inequality

• Keywords: opća teorija relativnosti; geometrijske nejednakosti; energijski uvjeti; teorem pozitivne energije; Buchdahlova granica; inverzni srednji tok zakrivljenosti
• Keywords (english): general relativity; geometric inequalities; energy conditions; positive energy theorem; Buchdahl bound; inverse mean curvature flow
• Language: croatian
• URN:NBN: urn:nbn:hr:217:256701
• 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: Embargoed access; Embargo expiration date: 2024-11-23
• Created on: 2023-11-23 14:02:15