This book presents a rigorous and unified treatment of generalized continuum theory and its applications to gravitation, electromagnetism, and cosmology. The text emphasizes the role of covariance and conservation laws in generalized continua, exploring symmetries, gauge invariance, and the variational principles that underpin gravitation and electromagnetism. Concepts such as torsion, curvature, and Riemann-Cartan manifolds are treated in depth, providing the foundation for modeling complex spacetime structures and the behavior of fields within them.
Building on these mathematical foundations, the book applies continuum physics to cosmology and relative gravitation. It examines geodesics and autoparallels, the Einstein and Einstein-Cartan spacetimes, and the interplay between gravitational and electromagnetic fields. Advanced models incorporate torsion, isotropy, and generalized volume forms to address contemporary questions, including dark matter, dark energy, and the accelerating expansion of the universe.
By bridging abstract continuum theory with cosmological applications, the book provides insight into both the local and large-scale dynamics of spacetime, including FLRW metrics, Schwarzschild and de Sitter spacetimes, and torsion-influenced cosmologies. Designed for researchers and advanced students in theoretical physics and cosmology, it offers a rigorous, integrative perspective on the mathematical structures that shape our understanding of the universe.
Contents:
- Preface
- About the Author
- Generalized Continuum: Mathematical Background:
- General Introduction
- Elements of Geometry for Spacetime Models
- Covariance: Form Invariance of Equations on Generalized Continua
- General Covariance: Conservation Laws on Generalized Continua
- Applications of Generalized Continuum to Spacetime Models: Relative Gravitation and Cosmology:
- Einstein Spacetime: Relative Gravitation
- Einstein-Cartan Spacetimes: Gravitation and Electromagnetism
- Continuum Spacetime Models for Cosmology
- Some Concluding Remarks
- Annexes
- Annexes
- Bibliography
- Index
Readership: Researchers and graduate students studying continuum physics, theoretical physics, cosmology and gravitation.