Astronomy 162:
Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30 |

General Relativity

- General Relativity:
- Modern Theory of Gravitation
- Matter tells spacetime how to curve.
- Curved spacetime tells matter how to move.
- Tests of General Relativity:
- Perihelion Precession of Mercury
- Bending of Starlight near the Sun

- Matter tells gravitation how to exert a
**Force**. - A Force tells matter how to
**accelerate**.

A mass m is accelerated by another mass M:

- The force law (line 1) implies
**instantaneous**knowledge of the distance, R, but information is only transmitted at the**speed of light**. - The same mass, m, appears in both the force and acceleration
laws (lines 1 & 2), but
**disappears**from the final acceleration (line 3). This seems to be coincidental.

- The laws of physics are the same for all
**uniformly moving**observers.

In 1907, Einstein generalized this statement:

- The laws of physics are the same for any
**freely falling**observer.

There is no distinction between gravitational and inertial accelerations.

For example, a person sealed in a closed box (no windows) drops an apple and watches it fall down with an acceleration of 1-g. There are no experiments that can be performed inside the boxes that will distinguish between two possibilities:

- They and the box are at rest on the surface of the Earth, and the
apple is accelerated downward by the Earth's gravity at 1-g.
- They and the box are in free space accelerating upwards at 1-g by constantly burning rocket engines, and the apple appears to accelerate downwards because the floor of the box rises up to meet it.

But how does matter "know" that the other matter is "out there"?

The Goal: Generalize Relativity

- Special Relativity uses light to unify space & time into
**spacetime**, but leaves matter separate. - Need to unite matter & gravity through the agency of spacetime.

Least Action Principle:

- An object moves between two points along the path that takes
the
**least**amount of time.

Use **geometry** to describe the paths of objects moving through
space.

**But,**

Einstein showed:

- Space & Time are
**relative**, not absolute. - Only spacetime is observer-independent.

Modified the Least Action Principle:

- An object moves along the
**shortest path**between two points in**spacetime**.

Need to describe the geometry of **spacetime**.

- The shortest path between two points is a
**straight line**. - Parallel lines stay parallel always.

On a curved surface:

- The shortest path is a
**curved line**. - Lines that start parallel can converge or diverge at some distance away.

- The least paths are
**straight lines**.

Moving objects follow straight lines.

Newton would have said:

- "It moves in a straight line because it feels no external force to change its motion."

- The least paths are
**curved**lines. - More mass = Greater spacetime curvature.
- Closer = Greater spacetime curvature.

A freely falling object follows a **curved** path.

Newton would have said:

- "It feels a force deflecting it from a straight line path."

*Matter tells spacetime how to curve.*

Curved spacetime tells matter how to move.

This replaces the Newtonian idea of a "force" with the curvature of spacetime as the agent of Gravity.

GR has so far withstood all experimental tests.

[Note: The summary statement above is due to physicist John Archibald Wheeler, who also coined the term "black hole" in the 1960s].

Einstein 1, Newton 0

Newtonian gravity:

- Predicts ~531 arcseconds/century.
- ~43 arcsec/century
**smaller**than observed.

General Relativity:

- Spacetime curvature changes as Mercury gets closer to the sun on its orbit.
- Gives the orbit a little twist.
- This adds an extra 43 arcsec/century!!

Prediction:

- Gravity bends light passing a massive object.

Another manifestation of gravitational bending of light by
massive objects is the phenomenon of "strong gravitational lensing".
This is seen in some massive clusters of galaxies (and a few individual
galaxies) with bright objects (galaxies or quasars) directly behind them.
The *Hubble Space Telescope* has made some spectacular images
of such gravitational lenses:

- Massive galaxy cluster Abell 2218 lensing background galaxies.
- Cross-shaped Gravitational Lens made by a foreground galaxy between us and a distant quasar.
- Primeval Galaxy lensed by the Cluster Cl0024+1654
- Most Distant galaxy (yet) uncovered with the help of gravitational lensing by the Galaxy Cluster Cl1358+62

Conditions:

- weak gravitational fields
- speeds much slower than the speed of light.

Newton's Laws:

- Work accurately in the "everyday" world.
- Are mathematically much simpler.

However, Relativity (both Special and General) do have real-world applications. For example, The GPS Navigation System.

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Updated: 2006 February 18

Copyright © Richard W. Pogge, All Rights Reserved.