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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.

10. Sentencedict.com try its best to gather and create good sentences.

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[sentencedict.com], 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.