The relation between scalartensor theory and fr gravity, and their possible equivalence, has been studied by many authors. On the stability of einstein static universe in general. Keiichi maeda a pedagogical overview of the theoretical ideas behind the cosmological constant problem, in particular the scalar tensor theory, which is one of the most popular alternative theories of gravitation. Phantom evolving wormhole solutions in scalartensor. It is an example of a scalartensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor. With an introduction to tensors and group theory for physicists, physicist nadir jeevanjee has produced a masterly book that will help other physicists understand those subjects tensors and groups as mathematicians understand them from the first pages, jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight.
It is an example of a scalartensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity. The scalartensor theory of gravitation iopscience institute of. The scalar tensor theory of gravitation moved into the limelight in recent years due to developments in string theory, m theory and brane world constructions. The scalartensor theory of gravitation ebook, 2003. We also explain the notation and the system of units to be used in this book. In the bransdicke theory, in addition to the metric, which is a rank two tensor field, there is a scalar field, which has the physical effect of changing the effective gravitational constant from place to place. The inner product of force and velocity gives the scalar power being delivered into or being taken out of a system. Scalartensor theory of gravitation cambridge monographs on. Thus, late in the history of the universe and today is late, localized gravitational systems are.
A relativistic theory called tensor vector scalar teves has been proposed by bekenstein building on earlier work of sanders which has a mond limit for nonrelativistic systems. The authors begin with a definition of vectors and a discussion of algebraic operations on vectors. Ascalartheoryof gravity had earlier been attempted by g. We study a modification of the plebanski action, which generically corresponds to a bimetric theory of gravity, and identify a subclass which is equivalent to. To my knowledge the scalartensor theory of gravitation by y fujii and k maeda is the first book to develop a modern view on this topic and is one of the latest titles in the wellpresented cambridge monographs on mathematical physics series. Thus in the variable mass theory vmt, see table 1, a scalartensor theory devised to test the necessity for the strong equivalence principle, the expansion of the universe forces evolution of toward a particular value at which diverges. The authors make a very strong, and successful, attempt to motivate the key tensor calculus concepts, in particular christoffel symbols, the riemann curvature tensor and scalar densities.
Gravitational theories nasaipac extragalactic database. Topics covered include the cosmological constant problem, time variability of. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalar tensor theory, also known as jordanbransdicke theory. At the frontier of spacetime scalartensor theory, bells inequality. From this treatment, the traditional material of courses on vector analysis is deduced as a particular case.
The scalartensor theory of gravitation is one of the most popular alternatives to einstein s theory of gravitation. Modern physicsbransdicke theory wikibooks, open books. Brans, who also contributes personally, is a creative and independent researcher and one of the founders of the scalartensor theory, also known as jordanbransdicke theory. The scalartensor theory of gravitation moved into the limelight in recent years due to developments in string theory, mtheory and. Scalar tensor theories are discussed as encompassing three classical longrange fields, including the electromagnetic field. American mathematical monthly despite its success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of mathematical and physical problems, tensor analysis has always had a rather restricted level of use, with an emphasis on notation and the manipulation of indices.
The scalartensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. As it is derived from the action principle, teves respects conservation laws. Download for offline reading, highlight, bookmark or take notes while you read vector and tensor analysis with applications. Scalartensorvector gravity stvg is a modified theory of gravity developed by john moffat, a researcher at the perimeter institute for theoretical physics in waterloo, ontario. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a discussion of bransdicke theory.
In the present book, much space is devoted to scalartensor theories. In theoretical physics, a scalartensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction. The stress at a point of an elastic solid is an example of a tensor which depends on two directions one normal to the area and other that of the force on it. You can order books on the applications of tensor analysis, matrix vector analysis, tensor analysis on manifolds, the theory of spinors, and more. Second, tensor theory, at the most elementary level, requires only linear algebra and some calculus as prerequisites. Bowen, and other respected authors, our publishing program on vectors, tensors, and spinors includes a wealth of lowpriced texts. Assuming only a knowledge of basic calculus, this text presents an elementary and gradual development of tensor theory. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar. It is a competitor of einsteins theory of general relativity. It is mathematicalsorrybut it gives the barebones definitions that are needed to do differential geometry. Offering books by banesh hoffmann, tullio levicivita, ray m. In most linear algebra books the two are reversed the scalar is on the left of the vector. Cosmology in scalar tensor gravity covers all aspects of cosmology in scalar tensor theories of gravity.
An introduction to tensors and group theory for physicists. What are the best books to learn tensors from for the. The scalar tensor theory was conceived originally by jordan, who startedtoembedafourdimensionalcurvedmanifoldin. Jan 02, 2003 the scalar tensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. Cosmology in scalartensor gravity ebook, 2004 worldcat. An introduction to tensors for students of physics and. The scalar product is a tensor of rank 1,1, which we will denote i and call the identity tensor. Two vectors, u and v can also be combined via an inner product to form a new scalar thus u v example.
Introduction to tensor calculus for general relativity. At the frontier of spacetime scalartensor theory, bells. Higgsfield scalar tensor theory of gravity the road to gravitational s. Cosmology in scalartensor gravity covers all aspects of cosmology in scalartensor theories of gravity. Modern physicsbransdicke theory wikibooks, open books for. This book introduces the subject at a level suitable for both graduate students and researchers. It is an example of a scalar tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity. Cosmology in scalartensor gravity ebook by valerio faraoni. The scalartensor theory of gravitation cambridge monographs. We begin this chapter with an overview in section 1 of how the scalartensor theory was conceived, how it has evolved, and also what issues we are going to discuss from the point of view of such cosmological subjects as the cosmological constant and. In theoretical physics, a scalartensor theory is a field theory that includes both a scalar field. The scalartensor theory of gravitation inspire inspire hep. In this article i give a short introduction to teves theory and focus on its predictions for cosmology as well as some noncosmological studies.
In the present book, much space is devoted to scalar tensor theories. It will also cover everything in the advanced quantum field theory. Scalartensor theories are discussed as encompassing three classical longrange fields, including the electromagnetic field. The largest part of the relevant literature is devoted to the study of the equivalence between purely metric fr gravity and a specific type of scalartensor theory, bransdicke theory. The scalartensor theory of gravitation the scalartensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. Scalar tensor gravity 1 introduction 2 bransdicke theory 3 bransdicke cosmology in the jordan frame 4 the limit to general relativity 5 relation to kaluzaklein theory 6 bransdicke theory from lyras geometry 7 scalar tensor theories. He showed that a constraint in formulating projectivegeometrycanbeafourdimensionalscalar.
Topics covered include the cosmological constant problem. In addition, the book forms an introduction to metric differential geometry. Cosmology in scalartensor gravity covers all aspects of cosmology in scalar tensor theories of gravity. The well stablish physics, in general, deals with spacetime like newtonian physics, and the theory of spacetime is geometry. The first 238 pages of tensors, differential forms, and variational principles, by david lovelock and hanno rund, are metricfree. Schroeder, an introduction to quantum field theory this is a very clear and comprehensive book, covering everything in this course at the right level. Our notation will not distinguish a 2,0 tensor t from a 2,1 tensor t, although a notational distinction could be made by placing marrows and ntildes over the symbol, or by appropriate use of dummy indices wald 1984.
An introduction to tensors for students of physics and engineering joseph c. Einsteins general theory of relativity is a geometrical theory of spacetime. Effective energymomentum tensors and conformal frames, gravitational waves in scalartensor cosmology, specific scalartensor theories, exact cosmological. Scalartensor theory news newspapers books scholar jstor december 2018 learn how and when to remove this template message. The relation between scalar tensor theory and fr gravity, and their possible equivalence, has been studied by many authors. For the newcomer to general relativity we warmly recommend schutz 1985.
This feature was actually a key desideratum of dicke and brans. Cosmology in scalartensor gravity valerio faraoni springer. Aug 28, 2012 eminently readable, it covers the elements of vector and tensor analysis, with applications of the theory to specific physics and engineering problems. Scalar tensor gravity and its limit to general relativity. It lays particular stress on the applications of the theory to fluid dynamics. In the weakfield approximation, stvg produces a yukawalike modification of the gravitational force due to a point source. We begin this chapter with an overview in section 1 of how the scalartensor theory was conceived, how it has evolved, and also what issues we are going to discuss from the point of view of such cosmological subjects as the cosmological constant and timevariability of coupling constants. In order to shed additional light on the restrictive assumptions made by dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalar tensor theory are constructed free of approximations in the form of integral laws. To my knowledge the scalar tensor theory of gravitation by y fujii and k maeda is the first book to develop a modern view on this topic and is one of the latest titles in the wellpresented cambridge monographs on mathematical physics series. What are the best books to learn tensors from for the first.
An introduction for mathematicians and physicists by paul renteln. The scalar tensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. So, in order to really apply the tensor theory in physics first we have to give the geometry of physics. In this paper, we study the stability of einstein static universes in general scalartensor theory with nonminimal derivative coupling by analyzing scalar and tensor perturbations. Jun 10, 2014 this is a firstrate book and deserves to be widely read. In this perspective, scalartensor gravitational theory has appeared as one of the most popular candidates. Scalartensor theory of gravitation cambridge monographs. In theoretical physics, a scalar tensor theory is a field theory that includes both a scalar field and a tensor field to represent a certain interaction. In theoretical physics, the bransdicke theory of gravitation sometimes called the jordanbransdicke theory is a theoretical framework to explain gravitation. The scalar tensor theory of gravitation by yasunori fujii january 2003. A covariant scalartensorvector gravity theory is developed which allows the gravitational constant g, a vector field coupling. Scalartensor gravity and its limit to general relativity.
For example, the bransdicke theory of gravitation uses both a scalar field and a tensor field to mediate the gravitational interaction. Tensors, differential forms, and variational principles. It explores scalar fields, placing them in context with a discussion. Appendix a the scalar field from kaluzaklein theory.
I really, really love manifolds, tensors, and forms. Scalartensorvector gravity theory, also known as modified gravity mog, is based on an action principle and postulates the existence of a vector field, while elevating the three constants of the theory to scalar fields. The volume is published in honour of carl brans on the occasion of his 80th birthday. Keiichi maeda a pedagogical overview of the theoretical ideas behind the cosmological constant problem, in particular the scalartensor theory, which is one of the most popular alternative theories of. Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of relativity. Brans building upon, among others, the earlier work of pascual jordan.
With an introduction to tensors and group theory for physicists, physicist nadir jeevanjee has produced a masterly book that will help other physicists understand those subjects tensors and groups as mathematicians understand them from the first pages, jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern. Scalartensor gravity 1 introduction 2 bransdicke theory 3 bransdicke cosmology in the jordan frame 4 the limit to general relativity 5 relation to kaluzaklein theory 6 bransdicke theory from lyras geometry 7. The scalartensor theory of gravitation by yasunori fujii. Kolecki national aeronautics and space administration glenn research center cleveland, ohio 445 tensor analysis is the type of subject that can make even the best of students shudder. The theory is also often referred to by the acronym mog mo dified g ravity. Adding to the answers already given, pressure is mostly treated as a scalar, however there are cases outside of general relativity where the pressure, like the energy density, has to appear as components of a tensor, in order to maintain the c. Tensorvectorscalar gravity teves, 1 developed by jacob bekenstein, is a relativistic generalization of mordehai milgroms modified newtonian dynamics mond paradigm.
Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of. The list of the fundamental ideas sketched in section 2 includes the kaluzaklein kk theory, string theory, brane theory as the latest outgrowth of string theory, and a conjecture on. This is a firstrate book and deserves to be widely read. In 1955, jordan proposed a complete gravitational theory based on the idea that g the gravitational constant in gr plays the role of a gravitational scalar field in accordance with diracs argument in such a way that the gravitational.
Tensor analysis and nonlinear tensor functions embraces the basic fields of tensor calculus. Vector and tensor analysis with applications ebook written by a. A relativistic theory called tensorvectorscalar teves has been proposed by bekenstein building on earlier work of sanders which has a mond limit for nonrelativistic systems. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a. In order to shed additional light on the restrictive assumptions made by dicke concerning the coupling of the scalar field with matter, the ponderomotive laws of a scalartensor theory are constructed free of approximations in the. The scalar tensor theory of gravitation is one of the most popular alternatives to einstein s theory of gravitation. Our notation and presentation is patterned largely after schutz. Cosmology in scalartensor gravity ebook by valerio. The scalartensor theory of gravitation moved into the limelight in recent years due to developments in string theory, mtheory and brane world constructions.
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