Titlebook: General Relativity and Gravitational Waves; Essentials of Theory Sanjeev Dhurandhar,Sanjit Mitra Textbook 2022 The Editor(s) (if applicable

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Overview of Special Relativity,In this chapter we give a short review of Einstein’s special theory of relativity.

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Jean-Luc Brylinski,Steven Zucker the development of the algebra of tensors. We purposely do this in the familiar setting (to the student) of a Euclidean space but with curvilinear coordinates. The advantage is that we can always transform to Cartesian coordinates in which the situation is more simply described. Since the analysis

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https://doi.org/10.1007/978-4-431-30962-8n a tensor—because tensors are coordinate independent quantities. For this purpose, we need to define parallel transport of vectors or in general of tensors. We limit ourselves to Riemannian parallel transport which is relevant to general relativity. It is defined here in a natural way using Cartesi

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https://doi.org/10.1007/978-94-011-6570-9tion. Historically it was the first solution obtained to Einstein’s equations by Karl Schwarzschild in 1916. In full vacuum, this is a black hole solution with an event horizon at .. Since the primary property of the event horizon is its one way character, we discuss the concept of a one-way membran

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https://doi.org/10.1007/978-1-4684-7730-6use of the gravitational field of a massive object, (ii) the perihelion shift in Mercury’s orbit around the Sun—the precession of Mercury’s elliptical orbit, (iii) the gravitational red-shift and the Pound-Rebka experiment and (iv) finally, Shapiro time delay—where light or radar waves experience a

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Complex Numbers in Trigonometric Form, in the theory of general relativity. It is easier to see this in the weak field limit. In the strong field regime there do exist gravitational wave solutions, but we will not consider them here. This is because, astrophysically we expect the waves to be weak, the term “weak” is made more precise la

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https://doi.org/10.1007/0-8176-4449-0in the time or Fourier domain as is required. Then we give a brief description of introductory statistics such as probability, random variables etc. so that the noisy data may be statistically characterised. We then discuss the matched filtering of signals buried in noisy data which must be extracte