LIMITS OF SPACETIMES AND THEIR CURV ATURES IN GENERAL RELATIVITY
Ahmed Tawfeek Ali Abdel-Wahhab;
Abstract
This thesis is concerned with limiting processes of spacetimes and its associated geometry in general relativity. This field is con sidered an important branch in mathematics, astrophysics and cos mology.
In the first few years of research in general relativity, only rather a small number of exact solutions were derived. These mostly arose from highly idealized physical problems, and had very high sym metry. As examples, one may mention the spherically symmet ric solutions of Schwarzschild (1916), Reissner (1916), Nordstrom (1918), Tolman (1939), and Friedmann (1922), (1924), the axisym metric static electromagnetic and vacuum solutions ofWeyl (1917), and the cylindrically symmetric solutions of Levi-Civita (1919a, b), and Lewis (1932). After some years, with growing interest in G.R., many scientists worked on Einstein's field equations, and an enor mous number of exact solutions were derived. Important solutions include those of Kerr (1963), Newman et al (1965), Tomimatsu and Sato (1972), (1973) and one well-known solution of the Papa petrou class is the NUT-solution [Papapetrou (1953)]. Some solu tions have played a very important role in the discussion of phys ical problems. Obvious examples are the Schwarzschild and Kerr solutions for black holes, the Friedmann solutions for cosmology, and the plane wave solutions (they were discovered by Brinkmann (1932) and subsequently rediscovered by several authors [Jordan et al (1960), Takeno (1961), Ehlers and Kundt (1962), Zakharov (1972) and Schimming (1974)]) which resolved some of the contro versies about the existence of gravitational radiation [Kramer et a! (1980)].
In the first few years of research in general relativity, only rather a small number of exact solutions were derived. These mostly arose from highly idealized physical problems, and had very high sym metry. As examples, one may mention the spherically symmet ric solutions of Schwarzschild (1916), Reissner (1916), Nordstrom (1918), Tolman (1939), and Friedmann (1922), (1924), the axisym metric static electromagnetic and vacuum solutions ofWeyl (1917), and the cylindrically symmetric solutions of Levi-Civita (1919a, b), and Lewis (1932). After some years, with growing interest in G.R., many scientists worked on Einstein's field equations, and an enor mous number of exact solutions were derived. Important solutions include those of Kerr (1963), Newman et al (1965), Tomimatsu and Sato (1972), (1973) and one well-known solution of the Papa petrou class is the NUT-solution [Papapetrou (1953)]. Some solu tions have played a very important role in the discussion of phys ical problems. Obvious examples are the Schwarzschild and Kerr solutions for black holes, the Friedmann solutions for cosmology, and the plane wave solutions (they were discovered by Brinkmann (1932) and subsequently rediscovered by several authors [Jordan et al (1960), Takeno (1961), Ehlers and Kundt (1962), Zakharov (1972) and Schimming (1974)]) which resolved some of the contro versies about the existence of gravitational radiation [Kramer et a! (1980)].
Other data
| Title | LIMITS OF SPACETIMES AND THEIR CURV ATURES IN GENERAL RELATIVITY | Other Titles | نهايات الزمكانيات وانحناءاتها فى النسبية العامة | Authors | Ahmed Tawfeek Ali Abdel-Wahhab | Issue Date | 2001 |
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