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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Capozziello, S., Faraoni, V. (2011). Mathematical tools. In: Beyond Einstein Gravity. Fundamental Theories of Physics, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0165-6_2
Download citation
DOI: https://doi.org/10.1007/978-94-007-0165-6_2
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0164-9
Online ISBN: 978-94-007-0165-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)