# Chad A. MiddletonColorado Mesa University | CMU · Physical and Environmental Sciences

Chad A. Middleton

Doctor of Philosophy

## About

16

Publications

887

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129

Citations

Introduction

Additional affiliations

August 2006 - present

## Publications

Publications (16)

We examine the time evolution of the \(D=d+4\) dimensional Einstein field equations subjected to a flat Robertson-Walker metric where the 3D and higher-dimensional scale factors are allowed to evolve at different rates. We find the exact solution to these equations for a single fluid component, which yields two limiting regimes offering the 3D scal...

We present a theoretical and experimental analysis of the elliptical-like
orbits of a marble rolling on a warped spandex fabric. We arrive at an
expression describing the angular separation between successive apocenters, or
equivalently successive pericenters, in both the small and large slope regimes.
We find that a minimal angular separation of a...

Embedding diagrams prove to be quite useful when learning general relativity as they offer a way of visualizing spacetime curvature through warped two dimensional (2D) surfaces. In this manuscript, we present a different 2D construct that also serves as a useful conceptual tool for gaining insight into gravitation:
orbital dynamics—namely, the cyli...

We present a theoretical and experimental analysis of circular-like orbits
made by a marble rolling on a warped spandex fabric. We show that the mass of
the fabric interior to the orbital path influences the motion of the marble in
a nontrivial way, and can even dominate the orbital characteristics. We also
compare a Kepler-like expression for such...

We examine the time evolution of the five-dimensional Einstein field
equations subjected to a flat, anisotropic Robertson-Walker metric, where the
3D and higher-dimensional scale factors are allowed to dynamically evolve at
different rates. By adopting equations of state relating the 3D and
higher-dimensional pressures to the density, we obtain an...

Consider two separate tracks of equal horizontal displacements and equal initial and final heights. One track remains at this initial height while the other angles down, levels out, and then angles back up in order to regain its original height. Question: If two identical balls are set rolling with equal initial speeds, which ball completes the tra...

We examine the effect on cosmological evolution of adding a Gauss-Bonnet term to the standard Einstein-Hilbert action for a (1 + 3) + d dimensional Friedman-Robertson- Walker (FRW) metric. By assuming that the additional dimensions compactify as a power law as the usual 3 spatial dimensions expand, we solve the resulting dynamical equations and fin...

We examine the effect on cosmological evolution of adding a Gauss–Bonnet term to the standard Einstein–Hilbert action for
a (1 + 3) + d dimensional Friedman–Robertson–Walker (FRW) metric. By assuming that the additional dimensions compactify as a power law
as the usual 3 spatial dimensions expand, we solve the resulting dynamical equations and find...

We study an extension of the gravity dual to a perfect fluid model found by Janik and Peschanski. By relaxing one of the constraints, namely invariance under reflection in the longitudinal direction, we introduce a metric ansatz which includes off-diagonal terms. We also include an R-charge following Bak and Janik. We solve the Maxwell–Einstein equ...

We study an extension of the gravity dual to a perfect fluid model found by Janik and Peschanski. By relaxing one of the constraints, namely invariance under reflection in the longitudinal direction, we introduce a metric ansatz which includes off-diagonal terms. We also include an R-charge following Bak and Janik. We solve the Maxwell-Einstein equ...

We examine the effect on cosmological evolution of adding a string motivated Gauss-Bonnet term to the traditional Einstein-Hilbert action for a (1 + 3) + d dimensional Friedman-Robertson- Walker (FRW) metric. By assuming that the additional dimensions compactify as the usual 3 spatial dimensions expand, we find that the Gauss Bonnet terms give pert...

Imagine by crude illustration that our universe is a slice of bread, one particular slice from a larger loaf. This odd imagining is not too far removed from how some cosmologists have begun to picture the Universe.

We address the vDVZ discontinuity of the 5D DGP model which consists of a 3-brane residing in a flat, infinite-volume bulk. Following a suggestion by Gabadadze [hep-th/0403161], we implement a constrained perturbative expansion parametrized by brane gauge parameters. We explore the parameter space and show that the DGP solution exhibiting the vDVZ...

In this thesis, we discuss various aspects of the Dvali-Gabadadze-Porrati (DGP) model in D-dimensions. Firstly, we generalize the DGP model, which consists of a delta-function type 3-brane embedded in an infinite volume bulk-space, by allowing the 3-brane to have a finite thickness into the bulk-space. We calculate the graviton propagator in the ha...

We discuss the Schwarzschild solution in the Dvali-Gabadadze-Porrati (DGP)
model. We obtain a perturbative expansion and find the explicit form of the
lowest-order contribution. By keeping off-diagonal terms in the metric, we
arrive at a perturbative expansion which is valid both far from and near the
Schwarzschild radius. We calculate the lowest-o...

We study branes residing in infinite volume space and of finite extent in the transverse directions. We calculate the graviton propagator in the harmonic gauge both inside and outside the brane and discuss its dependence on the thickness of the brane. Our treatment includes the full tensor structure of the propagator. We obtain two infinite towers...