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A Toy Penrose Inequality and Its Proof
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
2016 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 48, no 12, 156Article in journal (Refereed) Published
Abstract [en]

We formulate and prove a toy version of the Penrose inequality. The formulation mimics the original Penrose inequality in which the scenario is the following: A shell of null dust collapses in Minkowski space and a marginally trapped surface forms on it. Through a series of arguments relying on established assumptions, an inequality relating the area of this surface to the total energy of the shell is formulated. Then a further reformulation turns the inequality into a statement relating the area and the outer null expansion of a class of surfaces in Minkowski space itself. The inequality has been proven to hold true in many special cases, but there is no proof in general. In the toy version here presented, an analogous inequality in (2+1)-dimensional anti-de Sitter space turns out to hold true.

Place, publisher, year, edition, pages
2016. Vol. 48, no 12, 156
Keyword [en]
Penrose inequality, Black holes, Anti-de Sitter space
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:su:diva-139949DOI: 10.1007/s10714-016-2155-xISI: 000388615400008OAI: oai:DiVA.org:su-139949DiVA: diva2:1076063
Available from: 2017-02-21 Created: 2017-02-21 Last updated: 2017-11-29Bibliographically approved
In thesis
1. Shapes of Spacetimes: Collected tales of black holes
Open this publication in new window or tab >>Shapes of Spacetimes: Collected tales of black holes
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

In theory, the existence of black holes is predicted by general relativity. In reality, there is a general consensus that they exist in space; in particular at the center of many galaxies. The theory of black holes has been around for decades, but there are still interesting questions calling for attention. This doctoral thesis and its four contributions touches upon some of these questions.

One challenging theoretical aspect of black holes lies in their definition, the event horizon. For several reasons, this definition is not satisfactory in many contexts, and alternative horizons based on the concept of trapped surfaces have been suggested to take its place. The question raised in Paper I has to do with the location of such surfaces in a simple model of gravitational collapse, the Oppenheimer-Snyder model.

A different scenario of gravitational collapse, that of a null shell of dust collapsing in flat spacetime, is the starting point of the original formulation of the Penrose inequality. By a reformulation, this inequality can be turned into a purely geometric relation in Minkowski space. In Paper IV we formulate and prove a (2+1)-dimensional version in anti-de Sitter space.

The Penrose inequality sometimes goes under the name of the "isoperimetric inequality for black holes". In Paper III a different kind of isoperimetric inequality is discussed (with less rigour), namely that of the volume contained in a black hole with a given area.

In Paper II, the subject of limits of spacetimes is visualized. Again, (2+1)-dimensional anti-de Sitter space finds its use, as a one parameter family of surfaces, capturing the geometry of charged black hole spacetimes, is embedded in it. Thus different limiting procedures are illustrated.

Finally, interesting models can be constructed by cutting and gluing in spacetimes, but in doing so one needs to take care, in order to obtain a physically realistic model. With this background as motivation, a study of Lorentzian cones is given.

Taken together, all of these contributions make up a collection of interesting aspects of black hole geometry, or, shapes of spacetimes.

Place, publisher, year, edition, pages
Stockholm: Department of Physics, Stockholm University, 2017. 54 p.
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:su:diva-139950 (URN)978-91-7649-706-7 (ISBN)978-91-7649-707-4 (ISBN)
Public defence
2017-04-07, sal FA32, AlbaNova universitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Available from: 2017-03-15 Created: 2017-02-22 Last updated: 2017-03-16Bibliographically approved

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