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Extensions of the Mass Angular Momen...

Sokolowsky, Benjamin David.

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Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity./
Author:	Sokolowsky, Benjamin David.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	68 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
Contained By:	Dissertations Abstracts International81-05B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13885163
ISBN:	9781687983046

Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity.
Sokolowsky, Benjamin David.

Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 68 p.

Source: Dissertations Abstracts International, Volume: 81-05, Section: B.

Thesis (Ph.D.)--State University of New York at Stony Brook, 2019.

This item must not be sold to any third party vendors.

Inequalities between mass, angular momentum, and charge are motivated by the cosmic censorship conjecture in mathematical relativity. In this dissertation we provide several generalizations which expand the class of data sets in which such inequalities are known to hold. First, we expand the mass angular momentum inequality to manifolds with minimal surface boundary. In particular we establish a precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. This result does not require the restrictive assumptions of simple connectivity and completeness, which are undesirable from both a mathematical and physical perspective. Second, we lay out an approach to strengthening the mass angular momentum inequality to the so-called Penrose inequality with angular momentum and charge. Specifically a lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which satisfy the weak energy condition. If, on the horizon, the given data agree to a certain extent with the associated model Kerr-Newman data, then the inequality reduces to the Penrose inequality with angular momentum and charge. In addition, a rigidity statement is also proven whereby equality is achieved if and only if the data set arises from the canonical sliceof a Kerr-Newman spacetime.Finally, we extend a result of Chru\\'{s}ciel concerning the existence of Brill coordinates. These coordinates are generally assumed to exist in proofs of the mass angular momentum inequality; thus we can remove this assumption in many cases. We consider simply connected, axisymmetric initial data sets with finitely many asymptotically flat or asymptotically cylindrical ends. Finally we show the extent to which Brill and similar coordinates are unique. A better understanding of these coordinate systems should aid future efforts at proving the Penrose inequality with angular momentum and charge.

ISBN: 9781687983046Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Geometric Inequalities

Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity.
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245 1 0 $a Extensions of the Mass Angular Momentum Inequality in Mathematical Relativity.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 68 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
500 $a Advisor: Khuri, Marcus;Anderson, Michael.
502 $a Thesis (Ph.D.)--State University of New York at Stony Brook, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a Inequalities between mass, angular momentum, and charge are motivated by the cosmic censorship conjecture in mathematical relativity. In this dissertation we provide several generalizations which expand the class of data sets in which such inequalities are known to hold. First, we expand the mass angular momentum inequality to manifolds with minimal surface boundary. In particular we establish a precise mass lower bound for an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and minimal surface boundary, in terms of angular momentum and charge. This result does not require the restrictive assumptions of simple connectivity and completeness, which are undesirable from both a mathematical and physical perspective. Second, we lay out an approach to strengthening the mass angular momentum inequality to the so-called Penrose inequality with angular momentum and charge. Specifically a lower bound for the ADM mass is established in terms of angular momentum, charge, and horizon area in the context of maximal, axisymmetric initial data for the Einstein-Maxwell equations which satisfy the weak energy condition. If, on the horizon, the given data agree to a certain extent with the associated model Kerr-Newman data, then the inequality reduces to the Penrose inequality with angular momentum and charge. In addition, a rigidity statement is also proven whereby equality is achieved if and only if the data set arises from the canonical sliceof a Kerr-Newman spacetime.Finally, we extend a result of Chru\\'{s}ciel concerning the existence of Brill coordinates. These coordinates are generally assumed to exist in proofs of the mass angular momentum inequality; thus we can remove this assumption in many cases. We consider simply connected, axisymmetric initial data sets with finitely many asymptotically flat or asymptotically cylindrical ends. Finally we show the extent to which Brill and similar coordinates are unique. A better understanding of these coordinate systems should aid future efforts at proving the Penrose inequality with angular momentum and charge.
590 $a School code: 0771.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical physics. $3 2144760
653 $a Geometric Inequalities
653 $a Geometry
653 $a Relativity
690 $a 0405
690 $a 0753
710 2 $a State University of New York at Stony Brook. $b Mathematics. $3 2096807
773 0 $t Dissertations Abstracts International $g 81-05B.
790 $a 0771
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13885163