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- Sergiu I. Vacaru
- 1997

An introduction into the theory of locally anisotropic spaces (modelled as vector bundles provided with compatible nonlinear and distinguished linear connections and metric structures and containing as particular cases different types of Kaluza–Klein and/or extensions of Lagrange and Finsler spaces ) is presented. The conditions for consistent propagation… (More)

1 We develop the method of anholonomic frames with associated nonlinear connection (in brief, N–connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton spaces) can be modelled on the metric–affine spaces. There are formulated the criteria when such generalized Finsler metrics are… (More)

- Sergiu I. Vacaru
- 2000

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic non–equilibrium thermodynamics with local anisotropy. This lead to a unified formulation… (More)

- Sergiu I. Vacaru
- 2001

A new method of construction of integral varieties of Einstein equations in three dimensional (3D) and 4D gravity is presented whereby, under corresponding redefinition of physical values with respect to anholonomic frames of reference with associated nonlinear connections, the structure of gravity field equations is substantially simplified. It is shown… (More)

We apply a new general method of anholonomic frames with associated nonlinear connection structure to construct new classes of exact solutions of Einstein–Dirac equations in five dimensional (5D) gravity. Such solutions are parametrized by off–diagonal metrics in coordinate (holonomic) bases, or, equivalently, by diagonal metrics given with respect to some… (More)

- Sergiu I. Vacaru, Nadejda A. Vicol
- Int. J. Math. Mathematical Sciences
- 2004

We present an introduction to the geometry of higher order vector and co–vector bundles (including higher order generalizations of the Finsler geometry and Kaluza– Klein gravity) and review the basic results on Clifford and spinor structures on spaces with generic local anisotropy modeled by anholonomic frames with associated nonlinear connection… (More)

- Sergiu I. Vacaru
- 2000

Our approach views the thermodynamics and kinetics in general relativity and extended gravitational theories (with generic local anisotropy) from the perspective of the theory of stochastic differential equations on curved spaces. Nonequilibrium and irreversible processes in black hole thermodynamics are considered. The paper summarizes the author’s… (More)

- Katerina Chatziioannou, Sergiu I. Vacaru, +6 authors Demetrios A. Pliakis
- 2013

We consider the spacetime of a perfect fluid described by the Einstein-Euler equations. We assume given spatial growth for the fluid and spacetime initial data and estimate the temporal evolution of the spatial growth rates through the wave equations derived for the fluid and spacetime data.

- Sergiu I. Vacaru, Daylan Esmer Göksel
- 2003

The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off–diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of the Einstein equations describing ”black… (More)