In this master’s thesis, we present the fundamental concepts of general relativity with an emphasis on the use of the Schwarzschild metric. The topic is addressed at a level and scope suitable for physics teachers to acquire a deeper understanding of these concepts, which could be used in class when students have questions concerning the concepts of relativity theory and astronomy. In the first part, we present the basics of special relativity, explaining concepts of time dilation, length contraction, Minkowski space, or flat fourdimensional spacetime, and total energy. Afterwards we discuss the fundamental concepts of general relativity: equivalence principle, spacetime curvature, metric tensor, geodesic, and a phenomenological description of Einstein’s field equations. In the central part of the thesis, we focus on the presentation and derivation of the Schwarzschild metric, which is an exact solution to Einstein’s gravitational field equations for a static, spherically symmetric mass, such as stars and planets. It describes the geometry of curved spacetime in the vicinity of a spherically symmetric mass. Furthermore, we present the operation of the GPS satellite navigation system, where, due to the time dilation effect in Earth’s gravitational field, we apply the Schwarzschild metric to correct the GPS signal. We also use the Schwarzschild metric to derive three classical tests of general relativity: gravitational redshift, light deflection by a spherically symmetric mass (such as a star), and Mercury’s perihelion precession. These phenomena are qualitatively described as well. In connection with light deflection in a gravitational field, we briefly introduce gravitational lensing and describe a NASA mission in which the Sun is proposed to be used as a gravitational lens for observing exoplanets.
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