From this treatment, the traditional material of courses on vector analysis is deduced as a particular case. Cosmology in scalartensor gravity ebook, 2004 worldcat. The scalartensor theory of gravitation ebook, 2003. An introduction to tensors for students of physics and engineering joseph c. It will also cover everything in the advanced quantum field theory. Higgsfield scalar tensor theory of gravity the road to gravitational s. 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. In the present book, much space is devoted to scalar tensor theories.
Gravitational theories nasaipac extragalactic database. Einsteins general theory of relativity is a geometrical theory of spacetime. 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. Vectors, tensors, spinors books dover publications. 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. In this article i give a short introduction to teves theory and focus on its predictions for cosmology as well as some noncosmological studies. 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. The scalar tensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. This is a firstrate book and deserves to be widely read. Assuming only a knowledge of basic calculus, this text presents an elementary and gradual development of tensor theory. You can order books on the applications of tensor analysis, matrix vector analysis, tensor analysis on manifolds, the theory of spinors, and more. A covariant scalartensorvector gravity theory is developed which allows the gravitational constant g, a vector field coupling.
Scalar tensor theories are discussed as encompassing three classical longrange fields, including the electromagnetic field. In theoretical physics, a scalartensor theory is a field theory that includes both a scalar field. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar fields and placing them in context with a. The scalartensor theory of gravitation inspire inspire hep. Appendix a the scalar field from kaluzaklein theory. Cosmology in scalar tensor gravity covers all aspects of cosmology in scalar tensor theories of gravity.
Scalar tensor gravity and its limit to general relativity. Modern physicsbransdicke theory wikibooks, open books for. Phantom evolving wormhole solutions in scalartensor. This feature was actually a key desideratum of dicke and brans. 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 scalar tensor theory was conceived originally by jordan, who startedtoembedafourdimensionalcurvedmanifoldin. 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. Topics covered include the cosmological constant problem. Scalartensor gravity and its limit to general relativity. The scalar product is a tensor of rank 1,1, which we will denote i and call the identity tensor. 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.
The scalartensor theory of gravitation is one of the most popular alternatives to einstein s theory of gravitation. Introduction to tensor calculus for general relativity. At the frontier of spacetime scalartensor theory, bells inequality. 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. 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. Download for offline reading, highlight, bookmark or take notes while you read vector and tensor analysis with applications. This book introduces the subject at a level suitable for both graduate students and researchers. In most linear algebra books the two are reversed the scalar is on the left of the vector. The volume is published in honour of carl brans on the occasion of his 80th birthday.
Offering books by banesh hoffmann, tullio levicivita, ray m. Considerable progress has been made in this exciting area of physics and this book is the first to provide a critical overview of the research. The scalartensor theory of gravitation moved into the limelight in recent years due to developments in string theory, mtheory and. Jun 10, 2014 this is a firstrate book and deserves to be widely read. We also explain the notation and the system of units to be used in this book. 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.
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. Cosmology in scalartensor gravity valerio faraoni springer. It explores scalar fields, placing them in context with a discussion. For example, the bransdicke theory of gravitation uses both a scalar field and a tensor field to mediate the gravitational interaction. This book provides a clear and concise introduction to the theoretical ideas and developments, exploring scalar. 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. An introduction to tensors for students of physics and.
The scalartensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. The scalartensor theory of gravitation the scalartensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. The inner product of force and velocity gives the scalar power being delivered into or being taken out of a system. Tensor analysis and nonlinear tensor functions embraces the basic fields of tensor calculus. The relation between scalartensor theory and fr gravity, and their possible equivalence, has been studied by many authors. In the weakfield approximation, stvg produces a yukawalike modification of the gravitational force due to a point source. 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. 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. Tensors have their applications to riemannian geometry, mechanics, elasticity, theory of relativity. Scalartensor theory of gravitation cambridge monographs on. On the stability of einstein static universe in general. The theory is also often referred to by the acronym mog mo dified g ravity. Scalartensor theory of gravitation cambridge monographs. Tensors, differential forms, and variational principles.
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. The first 238 pages of tensors, differential forms, and variational principles, by david lovelock and hanno rund, are metricfree. So, in order to really apply the tensor theory in physics first we have to give the geometry of physics. The scalartensor theory of gravitation by yasunori fujii. 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. Ascalartheoryof gravity had earlier been attempted by g. Schroeder, an introduction to quantum field theory this is a very clear and comprehensive book, covering everything in this course at the right level. It lays particular stress on the applications of the theory to fluid dynamics. Vector and tensor analysis with applications ebook written by a. Topics covered include the cosmological constant problem, time variability of.
Cosmology in scalartensor gravity ebook by valerio faraoni. 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. 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. It is mathematicalsorrybut it gives the barebones definitions that are needed to do differential geometry. At the frontier of spacetime scalartensor theory, bells. 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. For the newcomer to general relativity we warmly recommend schutz 1985. Tensorvectorscalar gravity teves, 1 developed by jacob bekenstein, is a relativistic generalization of mordehai milgroms modified newtonian dynamics mond paradigm. Thus, late in the history of the universe and today is late, localized gravitational systems are. Modern physicsbransdicke theory wikibooks, open books. Cosmology in scalartensor gravity covers all aspects of cosmology in scalartensor theories of gravity. Cosmology in scalartensor gravity ebook by valerio.
Second, tensor theory, at the most elementary level, requires only linear algebra and some calculus as prerequisites. An introduction to tensors and group theory for physicists. 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. 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. Scalartensor theory news newspapers books scholar jstor december 2018 learn how and when to remove this template message. 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. In this perspective, scalartensor gravitational theory has appeared as one of the most popular candidates. 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. A successful einstein static universe requires to be stable past eternally against both homogeneous and inhomogeneous scalar perturbations. Jan 02, 2003 the scalar tensor theory of gravitation is one of the most popular alternatives to einsteins theory of gravitation. The scalar tensor theory of gravitation by yasunori fujii january 2003. 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. Our notation and presentation is patterned largely after schutz.
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. Cosmology in scalartensor gravity covers all aspects of cosmology in scalar tensor theories of gravity. What are the best books to learn tensors from for the first. Two vectors, u and v can also be combined via an inner product to form a new scalar thus u v example. 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. 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. 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. Scalartensor theories are discussed as encompassing three classical longrange fields, including the electromagnetic field. 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. The scalartensor theory of gravitation cambridge monographs. Effective energymomentum tensors and conformal frames, gravitational waves in scalartensor cosmology, specific scalartensor theories, exact cosmological.
An introduction for mathematicians and physicists by paul renteln. The scalartensor theory of gravitation moved into the limelight in recent years due to developments in string theory, mtheory and brane world constructions. It is a competitor of einsteins theory of general relativity. He showed that a constraint in formulating projectivegeometrycanbeafourdimensionalscalar.
The relation between scalar tensor theory and fr gravity, and their possible equivalence, has been studied by many authors. 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. 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. What are the best books to learn tensors from for the. I really, really love manifolds, tensors, and forms. 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. As it is derived from the action principle, teves respects conservation laws. 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. Brans building upon, among others, the earlier work of pascual jordan. In theoretical physics, the bransdicke theory of gravitation sometimes called the jordanbransdicke theory is a theoretical framework to explain gravitation. The scalartensor theory of gravitation iopscience institute of. 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. 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. 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.
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. 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 scalar tensor theory of gravitation is one of the most popular alternatives to einstein s theory of gravitation. In the present book, much space is devoted to scalartensor theories. In addition, the book forms an introduction to metric differential geometry.
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