Dissertation
Black holes & radiative degrees of freedom of Thomas-Whitehead Gravity
University of Iowa
Doctor of Philosophy (PhD), University of Iowa
Summer 2024
DOI: 10.25820/etd.007611
Abstract
Thomas-Whitehead Gravity is a d-dimensional projectively invariant model of gravity. This model incorporates additional fields $\mathcal{D}_{ab}$ and $\Pi^a{}_{bc}$ with the metric $g_{ab}.$ These additional field are connection components of a $(\rd+1)$ dimensional manifold, the Thomas Cone, associated with the d dimensional spacetime manifold with metric $g_{ab}.$
TW gravity will be briefly motivated. The coadjoint orbit action of the Kac-Moody and Virasoro semi-direct product algebra obtains the WZNW action and a modified Polyakov action incorporating a field D, the diffeomorphism field. The pure Kac-Moody coadjoint element corresponds to the Yang-Mills gauge potential in higher dimensions and the pure Virasoro coadjoint element corresponds to the diffeomorphism field, a component of the Thomas-Whitehead connection (The connection on a volume bundle of the projective equivalence class of affine connections for a manifold M.) The diffeomorphism field is understood as a component of the connection describing projective geometry. TW gravity incorporates projective and metric geometry as a theory of gravitation.
We'll examine the diffeomorphism field $\mathcal{D}_{ab}$ in a Minkowski space background with $\Pi$ constructed from a compatible connection. $\mathcal{D}_{ab}$ is decomposed into its irreducible representations, and studied as separate radiating degrees of freedom. There are tensor, vector, and scalar radiating solutions. Geodesic deviation from these 0th order in $h_{ab}$ fluctuations is trivial. However, as a source to 1st order in $h_{ab}$ through the metric field equations, non trivial geodesic deviation is computed. Antenna patterns for a LIGO like interferometer's response to this deviation will be presented. we'll examine the (Anti) De Sitter solutions to the theory, where the cosmological constant is related to the trace of $\mathcal{D}_{ab}$. The familiar stationary black hole spacetimes are solutions to TW gravity where their cosmological constant is determined by the trace of $\mathcal{D}_{ab}.$ The ongoing effort to understand the Tangherlini singular contribution to the Einstein equations and the contributions of the $\mathcal{D}_{ab}$ field to the temperature and entropy of spherically symmetric black holes will be discussed.
Details
- Title: Subtitle
- Black holes & radiative degrees of freedom of Thomas-Whitehead Gravity
- Creators
- Tyler Christian Grover
- Contributors
- Vincent G.J. Rodgers (Advisor)Palle E Jorgensen (Committee Member)Wayne N Polyzou (Committee Member)Kory M Stiffler (Committee Member)
- Resource Type
- Dissertation
- Degree Awarded
- Doctor of Philosophy (PhD), University of Iowa
- Degree in
- Physics
- Date degree season
- Summer 2024
- Publisher
- University of Iowa
- DOI
- 10.25820/etd.007611
- Number of pages
- xi, 118 pages
- Copyright
- Copyright 2024 Tyler Christian Grover
- Language
- English
- Date submitted
- 07/18/2024
- Description illustrations
- illustrations, graphs, table
- Description bibliographic
- Includes bibliographical references (pages 114-118).
- Public Abstract (ETD)
- Einstein’s theory of General Relativity describes gravitation and its feature through the curvature of spacetime where objects in free fall are just following their geodetic specified by their initial data. The observed dynamics in spacetime should be invariant of choice of parameterization. We can ask then “What connections are equivalent in that they cast the same geodesics as unparameterized curves?” The answer is “Those which are related by a projective transformation.” Thomas Whitehead projective gravity is a theory of gravity that describes gravitation in the context of projectively equivalent connections. Two indepen- dent field arise in the Thomas Whitehead projective connection, the fundamental projective invariant Π and the Diffeomorphism field D. The D field have an origin in string theory from the coadjoint orbits of the Virasoro algebra. TW gravity can be viewed as a natural promotion of a lower dimensional theory of gravity from string theory to higher dimensions. TW gravity is being investigated as a geometric source for dark matter and dark energy. The qualification as a geometric source is to distinguish the origin of dark matter and energy coming from a theory of gravity than from a contribution to the standard model. Examples of Dark matter are found in the radiative degrees of freedom of the diffeomorphism field where the fields approximated in a Minkowski background possess a mass. By examining simple vacuum solutions to TW gravity we find (A)dS Schwarzschild black hole solutions where the trace of the diffeomorphism field provides a source for dark energy.
- Academic Unit
- Physics and Astronomy
- Record Identifier
- 9984698250102771
Metrics
1 Record Views