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.

Einstein's View of Gravity and the Relativistic Universe
1. Einstein 1905: Special Relativity

Modern Cosmology is based on Einstein's view of gravity which is an extension of Special Relativity developped by Einstein in 1905. Special Relativity (SR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincare and others) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity - that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames) - from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special Relativity incorporates the principle that the
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.

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.

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

Many predictions of General Relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, the gravitational redshift of light, and the gravitational time delay. General relativity's predictions have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

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.

Exercises II
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Exercises II - Solutions
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Exercises II - Light Aberration
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Lecture Notes: Part II
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