國立虎尾科技大學 |

Linear Stability of Schwarzschild Spacetime.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Linear Stability of Schwarzschild Spacetime./
Author:	Keller, Jordan.
Description:	1 online resource (86 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
Contained By:	Dissertation Abstracts International78-09B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369717259

Linear Stability of Schwarzschild Spacetime.
Keller, Jordan.

Linear Stability of Schwarzschild Spacetime. - 1 online resource (86 pages)

Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In this work, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, remain uniformly bounded and decay to a linearized Kerr metric on the exterior region. Our method employs Hodge decomposition to split the solution into closed and co-closed portions, respectively identified with even-parity and odd-parity solutions in the physics literature. For both portions, we derive Regge-Wheeler type equations for decoupled, gauge-invariant quantities at the level of perturbed connection coefficients. A general framework for the analysis of Regge-Wheeler type equations is presented, identifying sufficient conditions for decay estimates. With the choice of an appropriate gauge in each of the two portions, such decay estimates on these decoupled quantities are used to establish decay of the linearized metric coefficients, completing the proof of linear stability. The initial value problem is formulated on Cauchy data sets, complementing the work of Dafermos-Holzegel-Rodnianski [6], where the linear stability of Schwarzschild is established for characteristic initial data sets.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369717259Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Linear Stability of Schwarzschild Spacetime.
LDR:02556ntm a2200337Ki 4500 001 909757
005 20180426091045.5
006 m o u
007 cr mn||||a|a||
008 190606s2017 xx obm 000 0 eng d
020 $a 9781369717259
035 $a (MiAaPQ)AAI10269586
035 $a (MiAaPQ)columbia:13879
035 $a AAI10269586
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Keller, Jordan. $3 1180694
245 1 0 $a Linear Stability of Schwarzschild Spacetime.
264 0 $c 2017
300 $a 1 online resource (86 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-09(E), Section: B.
500 $a Adviser: Mu-Tao Wang.
502 $a Thesis (Ph.D.) $c Columbia University $d 2017.
504 $a Includes bibliographical references
520 $a In this work, we study the theory of linearized gravity and prove the linear stability of Schwarzschild black holes as solutions of the vacuum Einstein equations. In particular, we prove that solutions to the linearized vacuum Einstein equations centered at a Schwarzschild metric, with suitably regular initial data, remain uniformly bounded and decay to a linearized Kerr metric on the exterior region. Our method employs Hodge decomposition to split the solution into closed and co-closed portions, respectively identified with even-parity and odd-parity solutions in the physics literature. For both portions, we derive Regge-Wheeler type equations for decoupled, gauge-invariant quantities at the level of perturbed connection coefficients. A general framework for the analysis of Regge-Wheeler type equations is presented, identifying sufficient conditions for decay estimates. With the choice of an appropriate gauge in each of the two portions, such decay estimates on these decoupled quantities are used to establish decay of the linearized metric coefficients, completing the proof of linear stability. The initial value problem is formulated on Cauchy data sets, complementing the work of Dafermos-Holzegel-Rodnianski [6], where the linear stability of Schwarzschild is established for characteristic initial data sets.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Columbia University. $b Mathematics. $3 1179054
773 0 $t Dissertation Abstracts International $g 78-09B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10269586 $z click for full text (PQDT)