The Classical Limit of Teleparallel Gravity

I consider the classical (i.e., non-relativistic) limit of Teleparallel Gravity, a relativistic theory of gravity that is empirically equivalent to General Relativity and features torsional forces. I show that as the speed of light is allowed to become infinite, Teleparallel Gravity reduces to Newtonian Gravity without torsion. I compare these results to the torsion-free context and discuss their implications on the purported underdetermination between Teleparallel Gravity and General Relativity. I conclude by considering alternative approaches to the classical limit developed in the literature

Near-Infrared Stellar Populations in the metal-poor, Dwarf irregular Galaxies Sextans A and Leo A

We present JHK$_{s}$ observations of the metal-poor ([Fe/H] $<$ -1.40) Dwarf-irregular galaxies, Leo A and Sextans A obtained with the WIYN High-Resolution Infrared Camera at Kitt Peak. Their near-IR stellar populations are characterized by using a combination of colour-magnitude diagrams and by identifying long-period variable stars. We detected red giant and asymptotic giant branch stars, consistent with membership of the galaxy's intermediate-age populations (2-8 Gyr old). Matching our data to broadband optical and mid-IR photometry we determine luminosities, temperatures and dust-production rates (DPR) for each star. We identify 32 stars in Leo A and 101 stars in Sextans A with a DPR $>10^{-11}$ $M_\odot \,{\rm yr}^{-1}$, confirming that metal-poor stars can form substantial amounts of dust. We also find tentative evidence for oxygen-rich dust formation at low metallicity, contradicting previous models that suggest oxygen-rich dust production is inhibited in metal-poor environments. The total rates of dust injection into the interstellar medium of Leo A and Sextans A are (8.2 $\pm$ 1.8) $\times 10^{-9}$ $M_\odot \,{\rm yr}^{-1}$ and (6.2 $\pm$ 0.2) $\times 10^{-7}$ $M_\odot \,{\rm yr}^{-1}$, respectively. The majority of this dust is produced by a few very dusty evolved stars, and does not vary strongly with metallicity.Comment: 21 pages, 11 figures, 10 tables; accepted for publication in Ap

Are General Relativity and Teleparallel Gravity Theoretically Equivalent?

Teleparallel gravity shares many qualitative features with general relativity, but differs from it in the following way: whereas in general relativity, gravitation is a manifestation of space-time curvature, in teleparallel gravity, spacetime is (always) flat. Gravitational effects in this theory arise due to spacetime torsion. It is often claimed that teleparallel gravity is an equivalent reformulation of general relativity. In this paper we question that view. We argue that the theories are not equivalent, by the criterion of categorical equivalence and any stronger criterion, and that teleparallel gravity posits strictly more structure than general relativity

Torsion in the Classical Spacetime Context

Teleparallel gravity, an empirically equivalent counterpart to General Relativity, represents the influence of gravity using torsional forces. It raises questions about theory interpretation and underdetermination. To better understand the torsional forces of Teleparallel gravity, we consider a context in which forces are better understood: classical spacetimes. We propose a method of incorporating torsion into the classical spacetime context that yields a classical theory of gravity with a closed temporal metric and spacetime torsion. We then prove a result analogous to the Trautman degeometrization theorem, that every model of Newton-Cartan theory gives rise, non-uniquely, to a model of this theory

Interpreting the Ionization Sequence in Star-Forming Galaxy Emission-Line Spectra

High ionization star forming (SF) galaxies are easily identified with strong emission line techniques such as the BPT diagram, and form an obvious ionization sequence on such diagrams. We use a locally optimally emitting cloud model to fit emission line ratios that constrain the excitation mechanism, spectral energy distribution, abundances and physical conditions along the star-formation ionization sequence. Our analysis takes advantage of the identification of a sample of pure star-forming galaxies, to define the ionization sequence, via mean field independent component analysis. Previous work has suggested that the major parameter controlling the ionization level in SF galaxies is the metallicity. Here we show that the observed SF- sequence could alternatively be interpreted primarily as a sequence in the distribution of the ionizing flux incident on gas spread throughout a galaxy. Metallicity variations remain necessary to model the SF-sequence, however, our best models indicate that galaxies with the highest and lowest observed ionization levels (outside the range -0.37 < log [O III]/H\b{eta} < -0.09) require the variation of an additional physical parameter other than metallicity, which we determine to be the distribution of ionizing flux in the galaxy.Comment: 41 pages, 17 figures, 9 tables, accepted to MNRA

Spacetimes with Torsion

How should we understand gravitational influence? In traditional formulations of Newtonian Gravity, gravitational influence is understood through forces; massive bodies attract one another through gravitational force. Our current best theory of gravity, General Relativity (GR), presents a different understanding of gravitational influence. GR is thought to have taught us that gravitational influence should be properly understood as a manifestation of spacetime curvature. This lesson, however, is complicated by the existence of a gravitational theory that is empirically equivalent to General Relativity and represents gravitational influence again through forces: Teleparallel Gravity (TPG). In contrast to Newtonian Gravity, the forces of TPG feature torsion (or, twisting). TPG raises both questions regarding underdetermination and more fundamental conceptual questions: Which theory, General Relativity or Teleparallel Gravity, describes our world? And how should we understand the torsional forces posited by Teleparallel Gravity?The first question mentioned above has been the subject of philosophical study (see, e.g., Knox 2011). Addressing the second question mentioned above will be the main goal of this dissertation. Since we are familiar with how forces operate in the non-relativistic context, Chapter 1 begins by formulating a novel non-relativistic theory of gravity that features torsional forces. To build this theory, we discuss how to incorporate torsion in the non-relativistic context and what we would expect of such a theory. We state and prove a theorem that establishes the relation between models of Newton-Cartan theory and torsional models.With a non-relativistic, torsional theory in hand, in Chapter 2, I turn to consider the non-relativistic limit of Teleparallel Gravity. I show how to take the classical limit using the tetrad formalism of Teleparallel gravity. I prove that Teleparallel gravity reduces not to the previously outlined non-relativistic, torsional theory but, rather, to standard Newtonian Gravity.In Chapter 3, I discuss and contextualize these results. I first present the similarities between my results and those derived in the torsion-free context. Malament (1986) shows that taking the classical limit of General Relativity results in Newton-Cartan theory, a theory that is spatially flat. In other words, taking the classical limit “squeezes out” the spatial curvature of General Relativity. I discuss how my results similarly show that taking the classical limit of TPG “squeezes out” the torsion.Next, I consider recent efforts by physicists to develop classical, torsional theories of gravity. It is commonly claimed in this literature that one cannot have both non-vanishing torsion and a closed temporal metric. Having formulated a classical theory with both non-vanishing torsion and a closed temporal metric, I reflect on why this claim is made and where the argument went awry.Finally, I discuss projects that use other methods of relating relativistic theories to classical, torsional ones. Some argue that torsional gravity is the correct framework to describe the non-relativistic limit of General Relativity while others claim it is the non-relativistic limit of Teleparallel Gravity. I show how we might understand these projects so that their claims are not inconsistent with one another or with the results presented here

Beyond Classification and Prediction: The Promise of Physics-Informed Machine Learning in Astronomy and Cosmology

Though the use of machine learning (ML) is ubiquitous in astrophysics and cosmology, many still see the opacity of ML algorithms as a major issue to their scientific utility. One way of addressing this opacity is through an emerging trend in ML research of "teaching" ML algorithms physical laws and domain-specific knowledge. "Physics-informed machine learning" (PIML), as this methodology is called, promises to produce better predictions and yield more interpretable algorithms. It does so by using physical principles in the training process and/or by using physical principles to guide the development of the neural network architecture. In this chapter, I investigate two uses of PIML in astronomy/cosmology, each a representative example of the two PIML methods. In both cases, PIML provides improvements in terms of the predictions and efficiency of ML algorithms. However, I argue that only in the second case does PIML offer any improvement in terms of the interpretability of the algorithms

Using Focus Groups to Explore the Underrepresentation of Female-Identified Undergraduate Students in Philosophy

This paper is part of a larger project designed to examine and ameliorate the underrepresentation of female-identified students in the philosophy department at Elon University. The larger project involved a variety of research methods, including statistical analysis of extant registration and grade distribution data from our department as well as the administration of multiple surveys. Here, we provide a description and analysis of one aspect of our research: focus groups. We ran three focus groups of female-identified undergraduate students: one group consisted of students who had taken more than one philosophy class, one consisted of students who had taken only one philosophy class, and one consisted of students who had taken no philosophy classes. After analyzing the results of the focus groups, we find evidence that: (1) one philosophy class alone did not cultivate a growth mindset among female-identified students of philosophy, (2) professors have the potential to ameliorate (or reinforce) students’ (mis)perceptions of philosophy; and (3) students who have not taken philosophy are likely to see their manner of thinking as being at odds with that required by philosophy. We conclude by articulating a series of questions worthy of further study