# General Relativity

In 1915, Einstein published his General Relativity Theory,the result of ten years work to unify Newton's classical mechanics with his own Special Relativity (1905).

\$\$G_{μν} + Λg_{μν} = {8πG}/{c^4}T_{μν}\$\$

where Λ is the infamous "cosmological constant", inserted unnecessarily by Einstein (his self-confessed 'biggest blunder') in order to cause the equation to produce a static universe, the prevailing theory of the time. With the discovery by Lemaître and Hubble of the expansion of the universe, Einstein removed the factor (1931), resulting in the powerful one-line description of the cosmos.

The theory was first tested by Arthur Eddington's observation of the bending of starlight around the Sun, during a solar eclipse in 1919. The positive confirmation was very close to the Einstein's prediction, and more than twice the curvature predicted by Newton's Law of Universal Gravitation, projecting Einstein into fame and mythological status as the creator of the New Physics, replacing Newtonian classical Physics.

### Karl Schwarzschild's Solutions to the Field Equations

The Schwarzschild solution: Exact solutions to the field equations for Einstein's General Relativity.

The Inner Schwarzschild solution: a general solution applicable to any incompressible fluid.

Schwarzschild radius and Schwarzschild black hole, formed by the gravitational collapse, with spherical symmetry, of a body to within the boundary of the Schwarzschild radius.

Schwarzschild radius: \$R_s = {2GM}/{c^2}\$, \$G\$ is the gravitational constant, \$M\$ is the mass, \$c\$ is the speed of light in a vacuum. \$R_s\$ is the boundary between the Schwarzschild interior and exterior solutions, a locus of points in space around the central mass \$M\$, within which everything, including photons, must fall into the central Mass.

### Gravity Waves

One of the predictions of Einstein's General Theory of Relativity is the existence of gravity waves. When a large amount of energy is generated, waves of space-time disturbance should be generated, like ripples in water. These ripples would alternately compress and stretch space as it progresses at the speed of light. In 1993, Russell Hulse and Joseph Taylor were awarded the Nobel Prize for their 1974 discovery of energy loss due to gravitational radiation in a binary pulsar (PSR 1913+16), the first evidence which provided some confirmation of Einstein's prediction.

However, direct evidence would need to wait another 41 years. The amount of distortion would be very small, so an extremely sensitive detection system is needed to detect it. Such a detector was built in the first decade of the 21st century in the US.

#### LIGO

LIGO interferometer prototype, showing the laser and the hub which contains the beam splitting mirror

At the Livingston, Louisiana, a gravitational wave detector was built between 2002 and 2010. The enormous interferometer has arms 4 kilometers long. It is funded (620 million US dollars) by the National Science Foundation (USA), the Max Planck Society (Germany), the UK Science and Technology Facilities Council and the Australian Research Council.

The first phase produced no positive results, and the facility was shut down in 2010 for an overhaul. In September 2015, the detector had a sensitivity four times that of the first phase, and will be enhanced again to its design sensitivity by 2021. The interferometers use a laser and a semi-transparent mirror at an angle of 45°. The light is thereby divided into two perpendicular beams which are then reflected back to reform a single beam. If the two beam parts are synchronised (wave crest matching wave crest), observers know that no spatial distortion has occurred. A gravity wave would distort the space unequally between the two arms of the interferometer, in a beat pattern as the space expands and contracts. Having two detectors so far apart assures the scientists that the phenomenon is not caused by a local effect, such as a seismic event, or, given the sensitivities involved, even a passing truck. The expected distortion is expected to be of the order of \$10^{-21}\$ m, which is a billionth the width of a proton.

The first positive result was announced on 11 February 2016. Two black holes with masses of the order of 30 times the Sun collided 1.3 billion light-years away, and the gravitational ripple it caused was detected in September 2015, 100 years after Einstein predicted gravitational waves!

Technicians adjusting a mirror on the interferometer at LIGO

The LIGO project utilises two sites: the Hanford Observatory (Washington State) and the Livingston Observatory (Louisiana), a separating distance of 3,002 km. Since light travels at 300 thousand km per second, it would take light 100th of a second (10 milliseconds) to travel between the two detectors directly. Triangulation therefore allows the direction of the wave to be determined by the difference in arrival times at the two detectors.

Content © Renewable.Media. All rights reserved. Created : November 25, 2015 Last updated :April 17, 2016

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1928 - 2015

John Nash was an American mathematician whose work in fields like Game Theory was revolutionary. He was awarded the Nobel Prize for Economics in 1994.