Abstract
Gravitational waves are a hot topic today. It is now possible to directly detect gravitational waves from astrophysical sources, and we expect an impressive amount of completely new data in the next 10–20 years. The aim of this chapter is to provide an introductory overview on the topic. Contrary to the other chapters of the book, the discussion is not at a purely theoretical level, and some sections are devoted to observations and experimental facilities.
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- 1.
One has to remove the effect due to the relative acceleration between us and the pulsar caused by the differential rotation of the Galaxy.
- 2.
\(h_{\mu \nu }\) transforms as a tensor under Lorentz transformations. If the transformation is \(x^\mu \rightarrow x'^\mu = \varLambda ^\mu _\nu x^\nu \), we have
$$\begin{aligned} g_{\mu \nu } = \eta _{\mu \nu } + h_{\mu \nu } \rightarrow g'_{\mu \nu } = \varLambda _\mu ^\alpha \varLambda _\nu ^\beta \left( \eta _{\alpha \beta } + h_{\alpha \beta }\right) = \eta _{\mu \nu } + \varLambda _\mu ^\alpha \varLambda _\nu ^\beta h_{\alpha \beta } \, , \end{aligned}$$(12.21)and we see that \(h'_{\mu \nu } = \varLambda _\mu ^\alpha \varLambda _\nu ^\beta h_{\alpha \beta }\).
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Bambi, C. (2018). Gravitational Waves. In: Introduction to General Relativity. Undergraduate Lecture Notes in Physics. Springer, Singapore. https://doi.org/10.1007/978-981-13-1090-4_12
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