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Mathematical tools

  • Salvatore Capozziello
  • Valerio Faraoni
Chapter
Part of the Fundamental Theories of Physics book series (FTPH, volume 170)

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.

Keywords

Variational Principle Conformal Transformation Conformal Invariance Mathematical Tool Transformation Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Dipartimento di Scienze FisicheUniversità di Napoli Federico IINapoliItaly
  2. 2.Physics DepartmentBishop’s UniversitySherbrookeCanada

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