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Beyond Einstein GravityMathematical tools

Beyond Einstein Gravity: Mathematical tools [In this chapter we discuss certain mathematical tools which are used extensively in the following chapters. Some of these concepts and methods are part of the standard baggage taught in undergraduate and graduate courses, while others enter the tool-box of more advanced researchers. These mathematical methods are very useful in formulating ETGs and in finding analytical solutions.We begin by studying conformal transformations, which allow for different representations of scalar-tensor and f(R) theories of gravity, in addition to being useful in GR. We continue by discussing variational principles in GR, which are the basis for presenting ETGs in the following chapters. We close the chapter with a discussion of Noether symmetries, which are used elsewhere in this book to obtain analytical solutions.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Beyond Einstein GravityMathematical tools

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Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media B.V. 2011
ISBN
978-94-007-0164-9
Pages
41 –57
DOI
10.1007/978-94-007-0165-6_2
Publisher site
See Chapter on Publisher Site

Abstract

[In this chapter we discuss certain mathematical tools which are used extensively in the following chapters. Some of these concepts and methods are part of the standard baggage taught in undergraduate and graduate courses, while others enter the tool-box of more advanced researchers. These mathematical methods are very useful in formulating ETGs and in finding analytical solutions.We begin by studying conformal transformations, which allow for different representations of scalar-tensor and f(R) theories of gravity, in addition to being useful in GR. We continue by discussing variational principles in GR, which are the basis for presenting ETGs in the following chapters. We close the chapter with a discussion of Noether symmetries, which are used elsewhere in this book to obtain analytical solutions.]

Published: Sep 30, 2010

Keywords: Variational Principle; Conformal Transformation; Conformal Invariance; Mathematical Tool; Transformation Property

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