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Geometric Obstructions on Gravity

- Y. X. Martins, Rodney Josu'e Biezuner
- Mathematics, Physics
- 24 December 2019

These are notes for a short course and some talks gave at Departament of Mathematics and at Departament of Physics of Federal University of Minas Gerais, based on the author's paper arXiv:1808.09249.… Expand

Constraints between equations of state and mass-radius relations in general clusters of stellar systems

- Y. X. Martins, D. S. P. Teixeira, L. F. A. Campos, R. J. Biezuner
- Physics, Mathematics
- 28 August 2018

In this article we prove three obstruction results on the existence of equations of state in clusters of stellar systems fulfilling mass-radius relationships and some additional bound (on the mass,… Expand

On Maximal, Universal and Complete Extensions of Yang-Mills-Type Theories

- Y. X. Martins, L. F. A. Campos, Rodney Josu'e Biezuner
- Mathematics, Physics
- 14 July 2020

In this paper we continue the program on the classification of extensions of the Standard Model of Particle Physics started in arXiv:2007.01660. We propose four complementary questions to be… Expand

On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories

- Y. X. Martins, L. F. A. Campos, R. J. Biezuner
- Mathematics, Physics
- 2 July 2020

In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theories. For us, a YMT theory differs from the classical Yang-Mills theories by allowing an arbitrary… Expand

Topological and geometric obstructions on Einstein–Hilbert–Palatini theories

- Y. X. Martins, R. J. Biezuner
- Mathematics, Physics
- 28 August 2018

Abstract In this article we introduce A -valued Einstein–Hilbert–Palatini functional ( A -EHP) over a n -manifold M , where A is an arbitrary graded algebra, as a generalization of the functional… Expand

O ct 2 01 9 Geometric Regularity Results on B kα , β-Manifolds , I : Affine Connections

In this paper we consider the existence problem of affine connections on C-manifolds M whose coefficients are as regular as one needs. We show that if M admits a suitable subatlas, meaning a B… Expand

Existence of B kα , β-Structures on C k-Manifolds

In this paper we introduce B α,β-manifolds as generalizations of the notion of smooth manifolds with G-structure or with k-bounded geometry. These are C-manifolds whose transition functions φji = φj… Expand

Existence and Classification of Pseudo-Asymptotic Solutions for Tolman-Oppenheimer-Volkoff Systems

- Y. X. Martins, L. F. A. Campos, D. S. P. Teixeira, R. J. Biezuner
- Mathematics, Physics
- 7 September 2018

The Tolman--Oppenheimer--Volkoff (TOV) equations are a partially uncoupled system of nonlinear and non-autonomous ordinary differential equations which describe the structure of isotropic spherically… Expand

An Axiomatization Proposal and a Global Existence Theorem for Strong Emergence Between Parameterized Lagrangian Field Theories

- Y. X. Martins, Rodney Josu'e Biezuner
- Mathematics, Physics
- 15 September 2020

In this paper we propose an axiomatization for the notion of strong emergence phenomenon between field theories depending on additional parameters, which we call parameterized field theories. We… Expand

Towards An Approach to Hilbert's Sixth Problem: A Brief Review

- Y. X. Martins, R. J. Biezuner
- Mathematics
- 30 July 2020

In 1900 David Hilbert published his famous list of 23 problems. The sixth of them-the axiomatization of Physics-remains partially unsolved. In this work we will give a gentle introduction and a brief… Expand

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