Gravitational Physics Exploring the Structure of Space and Time (1999) / Chapter Skim
Currently Skimming:
2 Ideas and Phenomena of General Relativity
2 Ideas and Phenomena of General Relativity
Pages 24-31
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 24... ...
But in relativity a stationary clock above Earth's surface runs fast compared to a clock at the surface by 1 part in ten thousand billion for each kilometer in height. That tiny difference is the result of the curvature of spacetime produced by the mass of Earth a small effect indeed, but large enough that the Global Positioning System would fail in a few minutes 24
|
From page 25... ...
Apart from the obvious military uses, the GPS is finding applications in airplane navigation, wilderness recreation, sailing, and interstate trucking. Even Hollywood has met the GPS, pitting James Bond in "Tomorrow Never Dies" against an evil genius able to insert deliberate errors into the system and send British ships into harm's way.
|
From page 26... ...
It is a correct approximation to Einstein's theory when spacetime curvature is small and the velocities of masses are much smaller than the velocity of light. The first general relativistic corrections beyond Newtonian theory (called "post-Newtonian")
|
From page 27... ...
In turn, gravitational waves can be detected through the motion of masses produced as the ripple in spacetime curvature passes by. The weak coupling of mass to spacetime curvature means that an extraordinarily energetic, strong-gravity event, such as the coalescence of two massive stars, is required to produce gravitational waves copious enough to be detected by gravitational wave receivers now under construction.
|
From page 28... ...
Black holes exhibit many properties of ordinary objects: they have mass and spin and can have electric charge; they can oscillate, change shape, show tides, and emit gravitational radiation; they can exhibit electric polarizability, resistivity, eddy currents, and threaded magnetic fields; they can act as generators and engines for the most energetic phenomena in the universe. Yet all this richness of physics is described cleanly by the Einstein equation coupled to ordinary matter.
|
From page 29... ...
The simplest FRW models come in two varieties: models in which space is closed like the surface of a sphere, and models in which space is unlimited or open. The closed models end in a finite time in a "big crunch," whereas the open models expand forever.
|
From page 30... ...
Einstein's classical theory predicts the formation of a singularity in the interior of a massive body whose gravity collapses it to a sufficiently compact volume. A singularity is a region of the universe where a classical description breaks down because it predicts infinite spacetime curvatures or densities of matter.
|
From page 31... ...
called the Planck length: ~(hG / 34~/2 10-33 The corresponding Planck energy is about ten thousand trillion times greater than the energy reached by the world's largest accelerators. Yet these energies, with their accompanying enormous curvatures, occurred at the big bang and occur in the final stages of gravitational collapse.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.