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36807 results in Cambridge Textbooks

Page 639 of 1841

  • Chapter 4 - Principles of Special Relativity

  • from Part I - Space and Time in Newtonian Physics and Special Relativity
  • James B. Hartle, University of California, Santa Barbara
  • Book:
    Gravity
    Published online:
    03 September 2021
    Print publication:
    24 June 2021, pp 47-76

  • Summary

    Einstein’s 1905 special theory of relativity requires a profound revision of the Newtonian ideas of space and time that were reviewed in the previous chapter. In special relativity, the Newtonian ideas of Euclidean space and a separate absolute time are subsumed into a single four-dimensional union of space and time, called spacetime. This chapter reviews the basic principles of special relativity, starting from the non-Euclidean geometry of its spacetime. Einstein’s 1905 successful modification of Newtonian mechanics, which we call special relativity, assumed that the velocity of light had the same value, c, in all inertial frames, which requires a reexamination, and ultimately the abandonment, of the Newtonian idea of absolute time. Instead, he found a new connection between inertial frames that is consistent with the same value of the velocity of light in all of them. The defining assumption of special relativity is a geometry for four-dimensional spacetime.

  • Chapter 12 - Gravitational Collapse and Black Holes

  • from Part II - The Curved Spacetimes of General Relativity
  • James B. Hartle, University of California, Santa Barbara
  • Book:
    Gravity
    Published online:
    03 September 2021
    Print publication:
    24 June 2021, pp 255-280

  • Summary

    In this chapter, we concentrate on a particular endpoint of stellar evolution – the state of ongoing gravitational collapse leading to a black hole. This possibility must exist in nature because there is a maximum amount of nonrotating matter that can be supported against gravitational collapse by Fermi pressure or nuclear forces. This mass is in the neighbourhood of two solar masses. (The exact value is uncertain because our knowledge of the properties of matter above nuclear densities is uncertain.) There are many stars more massive than this upper limit, so it is likely that some must wind up in a state of ongoing collapse. This chapter also explores the properties of this state.

Page 639 of 1841