Analytic Hyperbolic Geometry And Albert Einstein's Special Theory Of Relativity

This book uses analogies with classical results to study Einstein's special theory of relativity and its hyperbolic geometry, introducing gyrovectors as equivalence classes that add according to the gyroparallelogram law. It develops relativistic gyrotrigonometry to study stellar aberration and presents the relativistic center of mass of an isolated system of noninteracting particles, suggesting a mechanism for the formation of dark matter in the universe.

Format: Hardback
Length: 776 pages
Publication date: 25 March 2022
Publisher: World Scientific Publishing Co Pte Ltd

This book offers a compelling approach to studying Einstein's special theory of relativity and its underlying hyperbolic geometry, where analogies with classical results serve as valuable tools. The core premise of analogy as a study strategy is to make the unfamiliar familiar. Accordingly, this book introduces the concept of vectors into analytic hyperbolic geometry, where they are referred to as gyrovectors. Gyrovectors behave similarly to vectors, as they are equivalence classes that add according to the gyroparallelogram law, just as vectors are equivalence classes that add according to the parallelogram law. In the language of this book, a gyro is prefixed to a classical term to denote its hyperbolic geometry counterpart. For instance, the book develops and applies relativistic gyrotrigonometry to study the phenomenon of stellar aberration in astronomy. Furthermore, the book presents, for the first time, the relativistic center of mass of an isolated system of noninteracting particles that coincided at some initial time t = 0. It turns out that the invariant mass of the relativistic center of mass of an expanding system, such as galaxies, exceeds the sum of the masses of its constituent particles. This excess of mass suggests a viable mechanism for the formation of dark matter in the universe, which has not been detected but is necessary to gravitationally bind each galaxy in the universe. The discovery of the relativistic center of mass in this book thus reaffirms the significance of studying Einstein's special theory of relativity in terms of its underlying hyperbolic geometry.

ISBN-13: 9789811244100
Edition number: Second Edition