The Astrophysics Spectator

The basic layout of the site is as survey paths, which can be found under the Surveys link at the top of this and most other pages on this site. Each survey begins with a basic overview of the subject. Part of this overview include simulators of astrophysical phenomena that allow the reader to experiment with the phenomena. The later pages in a survey present the subject in greater and more mathematical depth. A path ends with research pages that describe current research projects and results in astrophysics.

The links at the top of each page are Home, which is the current home page of this site, Commentary, which is an index of short essays on topics loosely related to astrophysics, Surveys, which is the index of survey paths, Research, which is the index of research pages and the page leading to recent news items, Background, which is the index page for all background information on astrophysics, including survey pages, simulator pages, tables, bibliographic references, and lists of web resources, Previously, which is an index of previous home pages, and Site Info, which describes the site and its author, and gives contact information.

On the home page is found an addition link. This is the Store link, which leads to reviews of worthwhile books on astronomy and other relates subjects. Links on these pages enable the reader to buy these books from Amazon.com, which helps to financially sustain this web site.

On Wednesday of every fortnight, a new issue of The Astrophysics Spectator is published that comprises a new home page, a new commentary, whatever news the author notices, and background, research, and simulator pages added to the survey paths. The home page acts as an index to the newly added pages. This site also has an RSS channel, whose link is given at the bottom of the right-hand column of this page.

October 5, 2005

General relativity is our modern theory of gravity, displacing Newtonian gravity in the second decade of the twentieth century. In this issue of The Astrophysics Spectator, I add the first two pages of the “General Relativity” survey path, which will in time discuss all aspects of general relativity that are relevant to astrophysics. In time the “Gravitational Radiation” path will be incorporated into this new path.

When Albert Einstein developed special relativity, completing the classical theory of electromagnetism, he destroyed Newton's theory of gravity. In Newtonian gravity, the gravitational field changes instantly when the mass generating the field is changed. For instance, if a mass at rest is set into motion, its gravitational field is instantaneously set in motion throughout all space. This directly contradicts special relativity, which requires changes in a field to propagate at no more than the speed of light. In electrodynamics, when a charged particle at rest is set into motion, its electric field is not immediately changed; instead the electric field at a given point remains unchanged until an electromagnetic signal, propagating at the speed of light and containing information about the electron's changed velocity, reaches that point. General relativity was developed to give the theory of gravity this same consistency with special relativity as the theory of electrodynamics.

The foundation of general relativity is the equivalence principle. This principle states that acceleration within a gravitation field, as happens when we stand on Earth's surface, is indistinguishable from constant acceleration in a rocket well way from any gravitational fields. Immediate consequences of this principle are that gravity can Doppler shift the frequency of light, it can force light to travel on a curved path, and it caused time to travel more slowly in the deeper parts of a gravitational potential.

The equivalence principle motivated Einstein to approach the theory of gravity in a novel way. Instead of placing the effect of gravity into a set of force terms, as is done in electromagnetism, he chose to place the effect into the space-time variables themselves through the mathematics developed to describe curved surfaces. This approach gave Einstein a simple method of incorporating the effects of gravity into every equation of physics without damaging the equivalence principle.

While general relativity was the first theory of gravity to incorporate special relativity, it is not the only theory of gravity that is consistent with special relativity. In principle, there are an infinite number of such theories. Because Einstein's theory was developed first, is mathematically simple, and is consistent with all current tests, we use general relativity exclusively in astrophysics in problems where Newtonian gravity is inaccurate.

The effects of general relativity appear in only a handful of problems. We see the effects of gravity on light, particularly the bending of light by stars and galaxies. We apply general relativity to compact objects such as neutron stars, and we suspect that very massive compact objects obey the black hole solution of general relativity. We see the effects of space-time curvature in the most distant regions of the universe. We see the spiraling together of binary neutron stars from the gravitational radiating of energy, and we hope to detect this gravitational radiation as it passes by Earth.

Publication Notice. The next issue of The Astrophysics Spectator is slated for October 19.

Background

Origin of General Relativity. General relativity is the modern theory of gravity that supplanted Newtonian gravity after the development of special relativity. Unlike in Newtonian gravity, in which changes to the gravitational field propagate instantaneously, changes to the gravitational field in general relativity propagate through space at the speed of light. General relativity is based on the equivalence principle, which asserts that gravitational acceleration is identical to acceleration by a rocket in special relativity. This principle, which inspired Einstein to place the effects of gravity into the definitions of space and time, only provides partial guidance in developing a theory of gravity. We are left to our own prejudices in writing a complete theory. General relativity, which is the only modern theory of gravity used in astrophysics, is just one of many possible theories. (continue)

General Relativity in Astrophysics. General relativity appears in only a handful of places in astrophysics. We see the effects of general relativity in the gravitational redshift of light, in the bending of light as it passes by the Sun , a distant star, or a galaxy, and in the drift of Mercury's perihelion. We also see general relativity in the generation of gravitational waves, in black holes, and in the expansion of the universe. Some of these effects provide us with tests of general relativity, but others are submerged from plain view by a host of other physical processes. (continue)