Other Physics Commons^™

The Trouble Of Energy: Theoretical Foundations Of Loop Quantum Gravity, Hallie Gift

Senior Honors Theses

While general relativity and quantum mechanics have proved to be successful theories with elegant explanations of special cases, an underlying theory is needed to harmonize their copious discrepancies. Popular theories to reconcile the two are broadly termed “quantum gravity,” which refers to theories that introduce a discretized component of gravity either by directly suggesting gravitational quanta or attempting to discretize spacetime geometry. Loop quantum gravity falls under the latter category; it respects the background independence intrinsic to general relativity while attempting to provide an explanation of underlying quantum behavior via Planck-scale-level geometrical discretization. This thesis aims to provide a primer …

Geometric Algebra For Field Theory In Curved Spacetime, Kevin Rhine

All Graduate Reports and Creative Projects, Fall 2023 to Present

Physics seeks to understand the universe by uncovering the fundamental laws that govern matter, energy, space, and time. At its heart lies the challenge of unification: finding a mathematical framework that consistently describes these interactions across all scales, from the subatomic to the cosmological.

This thesis explores geometric algebra, a mathematical language that unifies algebra and geometry, as a tool for advancing this understanding. By extending this framework to curved spacetimes, where gravity influences the structure of space and time, we investigate its ability to describe physical phenomena such as electromagnetism and general relativity. A notable contribution includes the geometric …

Stability Of A Regular Black Holes Thin-Shell Wormhole In Reissner-Nordstrom - De Sitter Space-Time, A. Eid

Applications and Applied Mathematics: An International Journal (AAM)

The dynamics regular black holes thin shell wormhole with a phantom energy equation of state in Reissner-Nordstrom - De sitter space-time is studied using the Darmois-Israel formalism. A mechanical stability analysis is carried out by using the standard perturbation method. The stable and unstable static solution depends on the suitable value of parameters.

An Extremum Principle For Charged Black Holes, Shaker Von Price Funkhouser

Physics

There is a well known static condition that characterizes how two or more charged black holes stay in place: this condition is |qi |=mi , where a black hole (labeled by i) has electric charge qi and mass mi . For nearly half a century, this static condition has eluded a simple physical interpretation, without appealing to forces. I provide the first proof that the static condition, |qi |=mi , corresponds to an extremum of the black holes’ total energy. My approach uses geometry and calculus in the context of general relativity. For the non-specialist, this work draws upon one’s …

Λcdm Cosmology + Chaotic Inflation, Peter A. Farago

Theses and Dissertations

ΛCDM cosmology is described in terms of general relativity and the Robertson-Walker metric. The evolution of the observable universe, currently dominated by dark energy (Λ) and cold dark matter (CDM), is presented in terms of its thermal history. CDM is extended to include an inflation epoch that accelerates the early expansion rate to near exponential levels. It is shown that inflation solves several problems in CDM and produces perturbations in the metric that lead to the observed anisotropies in the Cosmic Microwave Background and the formation of large scale cosmological structures. Various theories of inflation are explored. Predictions of inflation …

Aspects Of General Relativity In 1+1 Dimensions, Richard D. Mellinger Jr

Physics

What would be the properties of a universe with only one spatial dimension and one time dimension? General relativity in 1+1 dimensions is unique since the two curvature terms in the Einstein field equations cancel. This makes the Einstein field equations algebraic rather than differential equations. This special feature can make 1+1 dimensionality attractive as an instructional tool to simplify the mathematics that many beginners find opaque. We explore the implications and features of the Einstein field equations in 1+1 dimensions and find they provide a surprisingly rich and interesting model. We then study an alternate theory and its implications …