chapter 24.1 general relativity & 24.2 spacetime and gravity & tests of general relativity & time in general relativity & 24.5 black holes

black hole formation

• When a very massive star collapses at the end of its life, however, not even the mutual repulsion between densely packed neutrons can support the core against its own weight.

• If the remaining mass of the star’s core is more than about three times that of the Sun (M_Sun), our theories predict that no known force can stop it from collapsing forever!

• Gravity simply overwhelms all other forces and crushes the core until it occupies an infinitely small volume.

equivalence principle

• falling freely in a gravitational field or floating in space is equal

• zero gravity is called the equivalence principle

• explains how local effects of gravity can be completely compensated by the right acceleration

• fundamental fact of nature according to Einstein

locating an event in space and time

• any event in the universe, can be pinpointed using the three dimensions of space (left-right, up-down, forward-backward) and one dimension of time

overview of Einstein’s general theory and spacetime

• the presence of matter curves or warps the fabric of spacetime

  • this curving of spacetime is identified with gravity

• when something else enters such a region of distorted spacetime, its path will be different from what it would have been in the absence of the matter

• the amount of distortion in spacetime depends on the mass of material that is invovled and on how concentrated and compact it is

• stars produce measurable distortions in spacetime

• distortion of spacetime is greater near surfaces of compact, massive objects (white dwarf or neutron star for example)

light’s pathway through spacetime

• light always follows the shortest path through spacetime

• but the mass associated with large concentrations of matter distorts spacetime, and the shortest, most direct paths are no longer straight lines, but curves

Einstein’s theory of general relativity

• mass determines the curvature of spacetime and that curvature, in turn, controls how objects move

• when the distorting mass is small, the predictions of general relativity must agree with those resulting from Newton’s law of universal gravitation

• spacetime is more curved in regions where the gravitational field is strong

  • thus we would expect light passing very near the Sun to appear to follow a curved path

  • Einstein calculated that starlight grazing the Sun’s surface should be deflected by an angle of 1.75 arcsecs

general relativity predictions about the behaviour of space and time

• the stronger the gravity, the slower the pace of time

  • when light emerges from a region of strong gravity where time slows down, the light experiences a change in its frequency and wavelength

  • eaves become less frequent with the presence of stronger gravity

  • to maintain constant light speed, the lower frequency must be compensated by a longer wavelength, called redshift

  • because it is gravity and not motion that produces the longer wavelengths, this effect is called a gravitational redshift

black hole

• on object from which light cannot escape

  • the escape velocities of black holes exceed the speed of light

  • the concentration o matter has curved spacetime, in which light cannot move in perpendicular straight lines from the object, thus travel along curved paths which lead back into the object

• the star’s geometry cuts of communication with the universe when the escape velocity becomes equal to the speed of light

  • event horizon

  • events inside can never again affect events outside it

  • radius: Schwarzschild radius

  • boundary of the black hole

  • radius is 3 times the size of the solar masses that collapsed into a black hole

  • all matter falling into a black hole will also appear to an outside observer to stop at the event horizon

singularity

• the collapsing star-core that made the black hole is predicted to continue to collapse under its own weight, forming an infinitely squozen point (a place of zero volume and infinite density)

• spacetime ceases to exist

• laws of physics break down

gravitational wave

• disturbance in spacetime

• relativity predicts that it should spread outward at the speed of light