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1. This, the Riemann curvature tensor, quantifies space-time curvature.

2. These lines therefore form boundaries to the space-time in these regions.

3. The gravitational forces are the manifestation of space-time curvature due to the presence of matter.

4. The method for recasting all space-time derivatives so that they are all tensors under general coordinate transformations is described in Chapter 6.

5. Why space-time should be four-dimensional is a question that is normally considered to be outside the realm of physics.

6. Space-time is therefore an extremely stiff medium, and by the same token small-amplitude waves carry large energies.

7. The b -boundary is the projection into a space-time of a natural boundary attached to a higher-dimensional Riemannian manifold.

8. First, there is space-time, playing a primary role as the arena for all the varied activity of physics.

9. It laid the foundations of topology, the differential geometry of manifolds and the theory of space-time and gravitation.

10. Let us try to understand the basics of special relativity in terms of the magnificent space-time of Minkowski.

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11. Equations between tensors have the property that they remain valid under the general transformations between Gaussian coordinate systems in curved space-time.

12. The different components refer to the different curvatures in different directions in the space-time.

13. Perhaps the damage here was only minor, a last tremor before the fabric of space-time mended again.

14. The three space directions and imaginary time would form a space-time that was closed in on itself, without boundaries or edges.

15. An alternative cosmology is the Hartle / Hawking model, which does not assume a background space-time in which the universe arises.

16. In the real time direction, this inevitably leads to singularities, places where space-time comes to an end.

17. We also have to take into account the passage of light rays through the highly curved space-time near the expanding object.

18. This last result can be expressed in a more compact form using the subscript comma notation for space-time derivatives:.

19. He had the revolutionary idea that gravity was not just a force that operated in a fixed background of space-time.

20. At this point the strong equivalence principle supplies a key ingredient to understanding curved space-time.

21. As the first results came in, so too did the first signs of a strange disruption in the space-time continuum.

22. The first component of tE is the journey time in flat space-time; hence the excess time taken is.

23. There is therefore a fundamental link between the curvature of space-time and the existence of classical tidal forces.

24. The family of light cones at all the points may be regarded as part of the Minkowskian geometry of space-time.

25. This provides an analytic extension beyond the Cauchy horizon which is another part of Kerr space-time.

26. Whatever may happen to different orders of reality, this space-time and its laws will cease to exist.

27. The analysis of Mercury's motion commences with the statement that Mercury follows a geodesic in the Schwarzschild space-time around the Sun.

28. Using subscript comma and subscript semicolon notation a standard space-time derivative is written whilst a covariant derivative is written.

29. The Cambridge professor's brain dances around such sub-atomic particles as leptons and anti-quarks and the possibility of infinitely curved space-time.

30. During the passage of gravitational waves it is the structure of space-time itself which oscillates.