arXiv subjects

Benjamin Ett

Publications and source records attributed to Benjamin Ett.

5 recordsLinked to original sources

arXiv2025

Sensemaking in Sound from a Free-Response Final Exam for 6th Grade Physics

This article investigates the sensemaking demonstrated in 6th grade students' written responses to a single question free-response final exam for physics asking them to recount everything they learned over the course of the academic year. International exams such as the PISA and TIMSS show that students continue to have persistent difficulties with their comprehension, and appreciation, of science. Sensemaking and development of a deeper understanding of concepts is of fundamental importance when teaching science, but little progress has been made over the ensuing decades. The research questions are: What sensemaking of physics is communicated through a single question free-response exam? In particular, what topics are preferred by students and how are the semiotic resources of written and visual representations utilized to express sensemaking? With specific attention given to the topic of sound we observe two levels of comprehension, defined as Basic and Advanced, related to Bloom's Taxonomy, and we see evidence that previously low-performing students are capable of sensemaking at the Advanced level, thereby lending support to recent research calling for an increase in the level of complexity employed in primary and lower secondary science curricula. In addition to the sensemaking analysis, we discuss how these results are facilitated by the single-question free-response format which has been completely unexplored in the research literature and has the potential to be a valuable asset for research on or using assessment, as well as for teacher self-assessment.

physics.ed-ph↗

arXiv2013

Sum Rule for the ADM Mass and Tensions in Planar AdS Spacetimes

An asymptotically planar AdS spacetimes is characterized by its ADM mass and tensions. We define an additional ADM charge Q associated with the scaling Killing vector of AdS, show that Q is given by a certain sum over the ADM mass and tensions and that Q vanishes on solutions to the Einstein equation with negative cosmological constant. The sum rule for the mass and tensions thus established corresponds in an AdS/CFT context to the vanishing of the trace of the boundary stress tensor. We also show that an analogous sum rule holds for local planar sources of stress-energy sources in AdS. In a simple model consisting of a static, plane symmetric source we find that the perturbative stress-energy tensor must be tracefree.

hep-th↗

arXiv2013

Gravitational Tension and Thermodynamics of Planar AdS Spacetimes

We derive new thermodynamic relations for asymptotically planar AdS black hole and soliton solutions. In addition to the ADM mass, these spacetimes are characterized by gravitational tensions in each of the planar spatial directions. We show that with planar AdS asymptotics, the sum of the ADM mass and tensions necessarily vanishes, as one would expect from the AdS /CFT correspondence. Each Killing vector of such a spacetime leads to a Smarr formula relating the ADM mass and tensions, the black hole horizon and soliton bubble areas, and a set of thermodynamic volumes that arise due to the non-vanishing cosmological constant. These Smarr relations display an interesting symmetry between black holes and bubbles, being invariant under the simultaneous interchange of the mass and black hole horizon area with the tension and soliton bubble area. This property may indicate a symmetry between the confining and deconfined phases of the dual gauge theory.

hep-th↗

arXiv2011

Kerr-Schild Ansatz in Lovelock Gravity

We analyze the field equations of Lovelock gravity for the Kerr-Schild metric ansatz, $g_{ab}=\bar g_{ab} +λk_ak_b$, with background metric $\bar g_{ab}$, background null vector $k^a$ and free parameter $λ$. Focusing initially on the Gauss-Bonnet case, we find a simple extension of the Einstein gravity results only in theories having a unique constant curvature vacuum. The field equations then reduce to a single equation at order $λ^2$. More general Gauss-Bonnet theories having two distinct vacua yield a pair of equations, at orders $λ$ and $λ^2$ that are not obviously compatible. Our results for higher order Lovelock theories are less complete, but lead us to expect a similar conclusion. Namely, the field equations for Kerr-Schild metrics will reduce to a single equation of order $λ^p$ for unique vacuum theories of order $p$ in the curvature, while non-unique vacuum theories give rise to a set of potentially incompatible equations at orders $λ^n$ with $1\le n \le p$. An examination of known static black hole solutions also supports this conclusion.

hep-th↗

arXiv2010

An Extended Kerr-Schild Ansatz

We present an analysis of the vacuum Einstein equations for a recently proposed extension of the Kerr-Schild ansatz that includes a spacelike vector field as well as the usual Kerr-Schild null vector. We show that many, although not all, of the simplifications that occur in the Kerr-Schild case continue to hold for the extended ansatz. In particular, we find a simple set of sufficient conditions on the vectors such that the vacuum field equations truncate beyond quadratic order in an expansion around a general vacuum background solution. We extend our analysis to the electrovac case with a related ansatz for the gauge field.

hep-th↗