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Tools for the Study of Dynamical Spacetimes


Zhang, Fan (2014) Tools for the Study of Dynamical Spacetimes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9WD3XHF.


This thesis covers a range of topics in numerical and analytical relativity, centered around introducing tools and methodologies for the study of dynamical spacetimes. The scope of the studies is limited to classical (as opposed to quantum) vacuum spacetimes described by Einstein's general theory of relativity. The numerical works presented here are carried out within the Spectral Einstein Code (SpEC) infrastructure, while analytical calculations extensively utilize Wolfram's Mathematica program.

We begin by examining highly dynamical spacetimes such as binary black hole mergers, which can be investigated using numerical simulations. However, there are difficulties in interpreting the output of such simulations. One difficulty stems from the lack of a canonical coordinate system (henceforth referred to as gauge freedom) and tetrad, against which quantities such as Newman-Penrose Psi_4 (usually interpreted as the gravitational wave part of curvature) should be measured. We tackle this problem in Chapter 2 by introducing a set of geometrically motivated coordinates that are independent of the simulation gauge choice, as well as a quasi-Kinnersley tetrad, also invariant under gauge changes in addition to being optimally suited to the task of gravitational wave extraction.

Another difficulty arises from the need to condense the overwhelming amount of data generated by the numerical simulations. In order to extract physical information in a succinct and transparent manner, one may define a version of gravitational field lines and field strength using spatial projections of the Weyl curvature tensor. Introduction, investigation and utilization of these quantities will constitute the main content in Chapters 3 through 6.

For the last two chapters, we turn to the analytical study of a simpler dynamical spacetime, namely a perturbed Kerr black hole. We will introduce in Chapter 7 a new analytical approximation to the quasi-normal mode (QNM) frequencies, and relate various properties of these modes to wave packets traveling on unstable photon orbits around the black hole. In Chapter 8, we study a bifurcation in the QNM spectrum as the spin of the black hole a approaches extremality.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:bifurcation of mode spectrum, quasi-normal modes, quasi-Kinnersley tetrad, tendex and vortex, gauge invariance
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Scheel, Mark (advisor)
  • Chen, Yanbei (advisor)
Group:Astronomy Department
Thesis Committee:
  • Chen, Yanbei (chair)
  • Scheel, Mark
  • Szilagyi, Bela
  • Weinstein, Alan Jay
Defense Date:17 June 2013
Non-Caltech Author Email:fanzfanzh25 (AT)
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
Record Number:CaltechTHESIS:06192013-175010723
Persistent URL:
Related URLs:
URLURL TypeDescription
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7904
Deposited By: Fan Zhang
Deposited On:29 Jul 2013 17:48
Last Modified:26 Oct 2021 18:31

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