Table Of ContentPHYSICS RESEARCH AND TECHNOLOGY
A G
DVANCES IN ENERAL
RELATIVITY RESEARCH
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P R T
HYSICS ESEARCH AND ECHNOLOGY
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PHYSICS RESEARCH AND TECHNOLOGY
A G
DVANCES IN ENERAL
RELATIVITY RESEARCH
CAMERON WILLIAMS
EDITOR
New York
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Library of Congress Cataloging-in-Publication Data
Advances in general relativity research / editor, Cameron Williams.
pages cm -- (Physics research and technology)
Includes index.
ISBN: (cid:28)(cid:26)(cid:27)(cid:16)(cid:20)(cid:16)(cid:25)(cid:22)(cid:23)(cid:27)(cid:22)(cid:16)(cid:20)(cid:24)(cid:27)(cid:16)(cid:20) (eBook)
1. General relativity (Physics)--Research. I. Williams, Cameron, 1965- editor. II. Series: Physics research
and technology.
QC173.6.A38 2015
530.11--dc23
2015020601
Published by Nova Science Publishers, Inc. †New York
CONTENTS
Preface vii
Chapter 1 The Classical World and Spinor Formalisms of General Relativity 1
J. G. Cardoso
Chapter 2 Old Math and Renewed Physics: Keys to Understanding Gravity 61
Cynthia Kolb Whitney
Chapter 3 General Relativity from the Aspect of Continuum Mechanics 81
of Space-Time
Yoshinari Minami
Chapter 4 Matter without Energy-Stress Tensor: A Different Approach 111
to General Relativity
Ram Gopal Vishwakarma
Chapter 5 New Approach to Study Gravitational Stability of the Solutions 137
to the Einstein Equations
Janusz Garecki
Chapter 6 Machian Request for Mond Theory 149
Elmo Benedetto and Ignazio Licata
Chapter 7 Essentials of Polynumbers Field Theory 157
D. G. Pavlov and S. S. Kokarev
Chapter 8 Algebra, Geometry and Physics of Hyperland 267
D. G. Pavlov and S. S. Kokarev
Chapter 9 S2 Like Star Orbits Near the Galactic Center in Rn and Yukawa 343
Gravity
Duško Borka, Predrag Jovanović, Vesna Borka Jovanović
and Alexander F. Zakharov
Chapter 10 Geodesic Analysis in Multidimensional Gravity Models 363
S. O. Alexeyev, D. A. Tretyakova and B. N. Latosh
vi Contents
Chapter 11 General Relativity Neither Collapses at Very Small Scale 379
nor at Very Large Scale as Well as Singularity Neither Occurs
at the Big Bang nor at the Black Holes
S. A. Mabkhout
Index 425
PREFACE
This book addresses the latest advances in general relativity research, including the
classical world and spinor formalisms; keys to understanding gravity; the continuum
mechanics of space-time; new evidences on matter without energy-stress tensor; a new
approach to study gravitational stability of the solutions to the Einstein equations; Mond
theory; polynumbers field theory; the algebra, geometry and physics of hyperland; S2-like
star orbits near the galactic center in RN and Yukawa gravity; geodesic analysis in
multidimensional gravity models; and the collapsing of general relativity and the singularity
in the event of the Big Bang and black holes.
A review of some facts concerning classical spacetime geometry is presented in
Chapter 1 together with a description of the most elementary aspects of the two-component
spinor formalisms of Infeld and van der Waerden. Special attention is concentrated upon the
gauge characterization of the basic geometric objects borne by the formalisms. It is pointed
out that spin-affine configurations may be naively defined by carrying out parallel
displacements of null world vectors within the framework of the γ -formalism. The standard
result that assigns a covariant gauge behaviour to the symmetric parts of any admissible spin
coonexions is deduced out of building up a generalized version of spin transformation laws. A
fairly complete algebraic description of curvature splittings is carried out on the basis of the
construction of a set of spinor commutators for each formalism. The pertinent computations
take up the utilization of some covariant differential prescriptions which facilitate specifying
the action of the commutators on arbitrary spin tensors and densities. It turns out that the
implementation of such commutators under certain circumstances gives rise to a system of
wave equations for gravitons and Infeld-van der Waerden photons which possess in either
formalism a gauge-invariance property associated with appropriate spinor-index
configurations. The situation regarding the accomplishment of the couplings between Dirac
fields and electromagnetic curvatures is entertained to a considerable extent.
Chapter 2 develops a new approach to the central subject matter of GRT: the
phenomenon of gravity. It pursues a concept of gravity as a statistical residue from
electromagnetic interactions between members in a population of overall charge-neutral
atoms. Such interactions are similar to interactions between neutral current elements: some
are attractive, and some are repulsive. More than century ago, J. M. Ampère studied forces
between macroscopic current elements, and characterized them mathematically in great detail.
His theory has never been falsified experimentally, although it has been eclipsed theoretically,
by a different theory, about different subject matter: Maxwell’s theory of electromagnetic
viii Cameron Williams
fields and their actions on charged particles. In modern times, Ampère’s experiments have
been successfully repeated and extended so, even though his theory has been largely
sidelined, it remains viable in all experiments, and awaits a revival. Thus, it is here enlisted
for the study of the gravity problem. The statistical aspects of the study come from the
modern Statistical Mechanics of classical gasses, quantum photons, and elementary material
particles. There are also computational aspects to the study, and they too reach into history:
Plato’s ideal regular polyhedra help solve a big statistical sampling problem.
A General Relativity Research based on the mechanical structure of space is suggested in
Chapter 3. On the supposition that a space as vacuum has a physical fine structure like
continuum, it enables us to apply a continuum mechanics to the so-called “vacuum” of space.
A space is an infinite continuum and its structure is determined by Riemannian geometry.
Assuming that space is an infinite continuum, the pressure field derived from the geometrical
structure of space is newly obtained by applying both continuum mechanics and General
Relativity to space. A fundamental concept of space-time is described that focuses on
theoretically innate properties of space including strain and curvature in this chapter.
GR supersedes the Newton’s vision of gravity as a force with the spacetime curvature,
whose source is attributed to the matter, represented either by the energy-stress tensor Tik or
by a singularity (in the absence of Tik). Nevertheless, there exist various solutions of Einstein's
equations, in the absence of Tik, which are curved but singularity-free. This casts doubt over
the conventional wisdom on the source of curvature in GR.
On another count, GR has to take refuge in the speculative dark components which
constitute more than 95 percent of the contents of Tik but do not have any direct observational
support. In Chapter 4, it would be interesting to note that all the cosmological observations
can be explained successfully in the framework of Milne model, without requiring the dark
components. This may seem like an extraordinary coincidence, as the Milne model is not
believed to represent the real Universe in the absence of Tik!
These two issues, taken together, signal towards a subtler way of incorporating the source
of gravitation in the theory than the conventional ones and indicate that a geometric theory of
gravitation should not have any bearing on the energy-stress tensor. In this view, the new
discovery - that the energy-momenta-angular momenta of the gravitational and the material
fields are built-in ingredients of the geometry of spacetime and the energy-stress tensor Tik is
a redundant part of Einstein's equations - would be worthy of note. Baffling as it may seem,
however provides a novel paradigm in GR which holds promise for understanding many
unresolved problems of GR in a unified manner. Moreover, the new paradigm explains
observations at all scales without requiring dark matter, dark energy and inflation.
It is shown that the new paradigm emanates from the equivalence and Mach principles.
New evidences are discovered to support the new paradigm. Interestingly, the new paradigm
shows that the speed of light emerges from the inertia of the Universe.
In the framework of general relativity one has very hard problem with gravitational
energy density, not satisfactorily solved up to now. It is a consequence of the Einstein
Equivalence Principle. To avoid the problem the authors have introduced in past the
canonical superenergy tensors. It turned out that these tensors give a very good tool to local,
and in special cases also to global, analysis of the gravitational field in general relativity. In
Chapter 5, the authors propose a new application of the canonical superenergy tensors.
Namely, the authors propose to use these tensors to study local gravitational stability of the
solutions to the Einstein equations. Our proposition follows the procedure of finding the
