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Absolute space is eliminated from the body of mechanics by gauging translations and rotations in the Lagrangian of a classical system. The procedure implies the addition of compensating terms to the kinetic energy, in such a way that the…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even…
The present paper continues the work of the authors [arXiv:1306.6887 [gr-qc]]. Here, we study generally covariant metric-torsion theories of gravity presented more concretely, setting that their Lagrangians are \emph{manifestly} generally…
In this work, a geometric discretization of the Navier-Stokes equations is sought by treating momentum as a covector-valued volume-form. The novelty of this approach is that we treat conservation of momentum as a tensor equation and…
I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to…
In this paper, we investigate the fluid/gravity correspondence in the framework of massive Einstein gravity. Treating the gravitational mass terms as an effective energy-momentum tensor and utilizing the Petrov-like boundary condition on a…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
We consider modified theories of gravity with a direct coupling between matter and geometry, denoted by an arbitrary function in terms of the Ricci scalar. Due to such a coupling, the matter stress tensor is no longer conserved and there is…
The proposal for a new formulation of the Navier-Stokes equations is based on a Helmholtz-Hodge decomposition where all the terms corresponding to the physical phenomena are written as the sum of a divergence-free term and another curl-free…
New microscopic geodesics with local balances of kinetic and metric four-potentials can maintain the non-local mass mechanism of continuous matterspace due to positive energies of kinetic micro-oscillations. The monistic pan-unity of the…
Quantum Geometrodynamics with intrinsic time development and momentric variables is presented. An underlying SU(3) group structure at each spatial point regulates the theory. The intrinsic time behavior of the theory is analyzed, together…
We study the modifications on the metric of an isolated self-gravitating bosonic superconducting cosmic string in a scalar-tensor gravity in the weak-field approximation. These modifications are induced by an arbitrary coupling of a…
It is shown how the variable density model (VDM) that governs the Rayleigh-Taylor instability (RTI) for the miscible mixing of two incompressible fluids can be transformed into a diffusive version of the inhomogeneous, incompressible…
The invariant projections of the energy-momentum tensors of Lagrangian densities for tensor fields over differentiable manifolds with contravariant and covariant affine connections and metrics [$(\bar{L}_n,g)$-spaces] are found by the use…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
The Covariant Canonical Gauge theory of Gravity (CCGG) is a gauge field formulation of gravity which a priori includes non-metricity and torsion. It extends the Lagrangian of Einstein's theory of general relativity by terms at least…
In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature $R$ and the Lagrangian…
We develop a variationally consistent mesoscopic extension of Cosserat elasticity motivated by the breakdown of compatibility in classical formulations. By admitting compatibility-breaking perturbations, the classical theory ceases to…
We develop different synthetic notions of Ricci flow in the setting of time-dependent metric measure spaces based on ideas from optimal transport. They are formulated in terms of dynamic convexity and local concavity of the entropy along…