Modern Cosmology -
Part II: From Special to General Relativity
Jacobs University Bremen

Caption: The deficiencies in Newton's theory led Einstein to formulate his General Theory of Relativity, which is based on the Riemann curvature of spacetime.
| 1. Einstein 1905: Special Relativity
speed of light is the same for all inertial observers regardless of the state of motion of the source . Special Relativity has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the classical notion that the duration of the time interval between two events is equal for all observers. |
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| 2. Einstein 1915: GR Einstein's Vision of Gravity General Relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the four-momentum (mass-energy and linear momentum) of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of partial differential equations.
Einstein's theory has important astrophysical implications. It points towards the existence of black holes - regions of space in which space and time are distorted in such a way that nothing, not even light, can escape - as an end-state for massive stars. There is evidence that such stellar black holes as well as more massive varieties of black hole are responsible for the intense radiation emitted by certain types of astronomical objects such as active galactic nuclei or microquasars. The bending of light by gravity can lead to the phenomenon of gravitational lensing, where multiple images of the same distant astronomical object are visible in the sky. General Relativity also predicts the existence of gravitational waves, which have since been measured indirectly; a direct measurement is the aim of projects such as LIGO. In addition, General Relativity is the basis of current cosmological models of a consistently expanding universe. |
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| Exercises II pdf file ............ |
Ex_2 |
| Exercises II - Solutions ............ |
Ex_2 - Sol |
| Exercises II - Light Aberration ............ |
Ex_2 - Aberr | Lecture Notes: Part II pdf-File ...... |
LN: Part II |


Caption: A simulated black hole of ten solar masses as seen from a distance of 600 kilometers with the Milky Way in the background.