Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed

Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity

It is well-known that Birkhoff's theorem is no longer valid in theories with more than four dimensions. Thus, in these theories the effective 4-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for the description of the spacetime outside of a spherical star, contrary to general relativity in 4D. We investigate the exterior spacetime of a spherically symmetric star in the context of Kaluza-Klein gravity. We take a well-known family of static spherically symmetric solutions of the Einstein equations in an empty five-dimensional universe, and analyze possible stellar exteriors that are conformal to the metric induced on four-dimensional hypersurfaces orthogonal to the extra dimension. All these exteriors are continuously matched with the interior of the star. Then, without making any assumptions about the interior solution, we prove the following statement: the condition that in the weak-field limit we recover the usual Newtonian physics singles out an unique exterior. This exterior is "similar" to Scharzschild vacuum in the sense that it has no effect on gravitational interactions. However, it is more realistic because instead of being absolutely empty, it is consistent with the existence of quantum zero-point fields. We also examine the question of how would the deviation from the Schwarzschild vacuum exterior affect the parameters of a neutron star. In the context of a model star of uniform density, we show that the general relativity upper limit M/R < 4/9 is significantly increased as we go away from the Schwarzschild vacuum exterior. We find that, in principle, the compactness limit of a star can be larger than 1/2, without being a black hole. The generality of our approach is also discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors

A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source, but also an {\it arbitrary} constant. In this work, we show that the constants appearing in the "temporal Schwarzschild", "spatial Schwarzschild" and "Reissner-Nordstr{\"o}m-like" exteriors are not arbitrary but are completely determined by star's parameters, like the equation of state and the gravitational potential. Consequently, in the braneworld scenario the gravitational field outside of a star is no longer determined by the total mass alone, but also depends on the details of the internal structure of the source. We show that the general relativistic upper bound on the gravitational potential $M/R < 4/9$, for perfect fluid stars, is significantly increased in these exteriors. Namely, $M/R < 1/2$, $M/R < 2/3$ and $M/R < 1$ for the temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordstr{\"o}m-like exteriors, respectively. Regarding the surface gravitational redshift, we find that the general relativistic Schwarzschild exterior as well as the braneworld spatial Schwarzschild exterior lead to the same upper bound, viz., $Z < 2$. However, when the external spacetime is the temporal Schwarzschild metric or the Reissner-Nordstr{\"o}m-like exterior there is no such constraint: $Z < \infty$. This infinite difference in the limiting value of $Z$ is because for these exteriors the effective pressure at the surface is negative. The results of our work are potentially observable and can be used to test the theory.Comment: 19 pages, 3 figures and caption

Brane classical and quantum cosmology from an effective action

Motivated by the Randall-Sundrum brane-world scenario, we discuss the classical and quantum dynamics of a (d+1)-dimensional boundary wall between a pair of (d+2)-dimensional topological Schwarzschild-AdS black holes. We assume there are quite general -- but not completely arbitrary -- matter fields living on the boundary ``brane universe'' and its geometry is that of an Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The effective action governing the model in the mini-superspace approximation is derived. We find that the presence of black hole horizons in the bulk gives rise to a complex action for certain classically allowed brane configurations, but that the imaginary contribution plays no role in the equations of motion. Classical and instanton brane trajectories are examined in general and for special cases, and we find a subset of configuration space that is not allowed at the classical or semi-classical level; these correspond to spacelike branes carrying tachyonic matter. The Hamiltonization and Dirac quantization of the model is then performed for the general case; the latter involves the manipulation of the Hamiltonian constraint before it is transformed into an operator that annihilates physical state vectors. The ensuing covariant Wheeler-DeWitt equation is examined at the semi-classical level, and we consider the possible localization of the brane universe's wavefunction away from the cosmological singularity. This is easier to achieve for branes with low density and/or spherical spatial sections.Comment: Shortened to match version accepted by Phys. Rev. D (unabridged text found in version 2), 42 pages, 9 figures, Rextex

Leibniz algebroid associated with a Nambu-Poisson structure

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let

The Influence of Situated and Experiential Music Education in Teacher-Practitioner Formation: An Autoethnography

This study explores how my musical background, teaching and performance skills, understandings, and knowledge acquired from both formal and informal influence has shaped myself as musician, teacher and researcher. The study reveals various learning cultures and social networks that frame my multiple professional identities that have themselves developed from my understandings of being a performer, an educator and researcher. This study explores three aspects to my being: personal identity, professional identity and my perception of the impact this has on my students through my teaching and performing. An autoethnographical method is used to investigate my background that is initially formed by the different modes of music education I received. The study reveals significant influences and formative experiences that impact knowledge and skill accumulation, shaping what informs my own practice as a musician, teacher and researcher. It reveals ongoing exploration, reflection and personal negotiations in maintaining ones’ development of performance and personal creative processes, whilst functioning as a facilitator and educator to others. This study offers insights into how cultural backgrounds, social contexts, teachers and peers influence others

Dialogic Communication in the One-to-One Improvisation Lesson: A Qualitative Study

This qualitative study investigates the dialogic interactions between teacher and student that enhance learning and teaching within the one-to-one music improvisation lesson. This study analyses the ways teachers elicit student actions, thoughts and processes that develop student skills, critical and creative thinking processes necessary for improvisational development. Interactions and interplay between six Australian conservatoire improvisation students and their teachers were investigated. Data reveal dialogic interactions that span instruction, conversation, inquiry and enablement of student knowledge and skills that constitute a complex socio-cultural tapestry of discursive threads. Teacher-student interactions that activate desired creative student activity engage meta-cognitive processes and the cultivation of creative habits of mind that allow improvisational skill to flourish. Teachers engage in dialogic interaction and shape interactional behaviour, asserting a learning culture that makes explicit and visible the acquiring of skills and knowledge. Implications for skilled teaching that can effectively craft the at times improvisatory and ephemeral nature of teacher-student interactions are suggested

Stress and Coping During Simulated EVAs and Habitat Living

Planning for long duration exploration missions (LDEM) involves both the effectiveness of the extravehicular operations, in particular as it is related to the functioning and comfort of the space suits, and how the crew functions together in accomplishing the objectives of the mission. The University of North Dakota Department of Space Studies has developed a multi-modular Inflatable Lunar/Mars Analog Habitat (ILMAH) and is testing iterations of their NDX-2AT space suit. Five 12-14 day missions, each consisting of 3-4 individuals (Total 13; 11 men, two women) were carried out. Team members independently completed a Daily Rating Form (DRF) each day of the mission; the measure assessed space suit functioning during a simulated exploration EVA, psychological factors of mood, positive events and stressful situations experienced, and strategy/decision making processes. The EVAs proceeded in a smooth manner and ratings indicated that the space suit performed well in enabling the team members to carry out the simulated exploration tasks effectively. There were few incidents of tension or arguments with a teammate; ratings of mood state indicated that positive mood predominated over negative mood throughout the mission. Adaptive coping methods were reported as appropriate for the particular stressor experienced; problem-focused coping, for example, discussing task concerns with a teammate, emotion-focused coping methods, relaxation, meditation, humor; and meaning-focused coping, keeping the goal in sight. The specific behavioral and cognitive coping methods participants used to deal with the stressors experienced were highly effective in promoting optimal personal and team performance. Training in the use of particular coping strategies and the flexibility to use different coping methods depending on the specific stressors experienced appears helpful in preparing astronauts for the many demands and challenges of living and working together on LDEM. This training should also be helpful for dealing with the psychological recovery period following an EVA