308 |
7 Gravitational Waves and the Binary Pulsars |
Fig. 7.17 The Parkes radio-telescope located in Australia and used for the discovery of the double pulsar system PSR J0737-3039A/B
Table 7.2 Data of the binary pulsar system PSR J0737-3039A/B
Constellation |
Canis Major |
Right ascension |
07 h 37 m 51.247 s |
Declination |
−30◦39 40.74 |
Distance |
2,000 light years |
Mass of pulsar A |
1.337 × MSun |
Mass of pulsar B |
1.250 × MSun |
Rotational period of pulsar A |
23 ms |
Rotational period of pulsar B |
2.8 s |
Diameter of each neutron star |
20 km |
Orbital period |
2.4 h |
Eccentricity |
0.088 |
Semilatus rectum |
0.86 × 106 km |
obtain an estimate of the life-time of this system of approximately 80 millions of years, which is considerably shorter than the life-time of PSR1913+16.
tf = |
3T08/3 |
80 × 106 years |
(7.4.51) |
8α |
Last, but not least, the system PSR J0737-3039A/B is much closer to Earth than PSR1913+16. It is only 2000 light years away from us. All these properties make it an extraordinary laboratory of General Relativity which, so far, has confirmed all of its predictions.
7.5 Conclusive Remarks on Gravitational Waves
Although very difficult to be directly detected, Gravitational Waves are a must for General Relativity that, at almost one hundred years from its birth is more solid than
ever, having passed all possible experimental tests. Moreover General Relativity is the conceptual framework in which modern Cosmology has been understood and it is entangled in an essential way with all proposed schemes for the unification of all fundamental interactions. The quantum particle responsible for the gravitational interaction is the spin s = 2 graviton and General Relativity appears to be its only possible low energy effective description. Just as in quantum electrodynamics the spin s = 1 photon is the quantum of the electromagnetic waves, in the same way the graviton makes sense only as the quantum of the gravitational waves which should also exist and propagate classically. The absence of these classical waves would be a deadly blow not only for General Relativity but for the entire structure of our present understanding of the fundamental physical laws. In that case the whole fabric of Physics should be reconsidered.
It is however very much rewarding that indirect evidence of gravitational wave emission from binary systems is constantly piled up in simple and absolute agreement with the 1918 Einstein perturbative formula. In this respect the recent discovery of the double pulsar system is exceptionally relevant. This means a further confirmation of our standard approach to the interpretation of classical and quantum field theories and implies that the final detection of the elusive gravitational waves, although difficult should come true in a reasonably near future.
References
1.Einstein, A.: Über Gravitationswellen. In: Sitzungsberichte der Königlich Preussischen Akademie der Wissenshaften, pp. 154–167. Königlich Preussischen Akademie der Wissenshaften, Berlin (1918)
2.Einstein, A.: Näherungsweise Integration der Feldgleichungen der Gravitation. In: Sitzungsberichte der Königlich Preussischen Akademie der Wissenshaften, pp. 688–696. Königlich Preussischen Akademie der Wissenshaften, Berlin (1916)
3.Einstein, A., Rosen, N.: On gravitational waves. J. Franklin Inst. 223, 43–54 (1937)
4.Hu, N.: Radiation damping in the gravitational field. Proc. R. Ir. Acad. A 51, 87–111 (1957)
5.Hulse, R.A., Taylor, J.H.: A high sensitivity pulsar survey. Astrophys. J. Lett. 191, L59–L61 (1974)
6.Hulse, R.A., Taylor, J.H.: Discovery of a pulsar in a binary system. Astrophys. J. 195, L51–L53 (1975)
7.Hulse, R.A.: The discovery of the binary pulsar. In: Les Prix Nobel, 1993, pp. 58–79. The Nobel Foundation (1994)
8.Straumann, N.: General Relativity and Relativistic Astrophysics. Springer, Berlin (1981)
Chapter 8
Conclusion of Volume 1
In the first volume we have presented the theory of General Relativity comparing it at all times with the other Gauge Theories that describe non-gravitational interactions. We have also followed the complicated historical development of the ideas and of the concepts underlying both of them. In particular we have traced back the origin of our present understanding of all fundamental interactions as mediated by connections on principal fibre-bundles and emphasized the special status of Gravity within this general scheme. While recalling the historical development we have provided a, hopefully rigorous, exposition of all the mathematical foundations of gravity and gauge theories in a contemporary geometrical approach.
In the last two chapters of Volume 1 we have considered relevant astrophysical applications of General Relativity that also provide some of the most accurate tests of its predictions. In Chap. 6 we considered stellar equilibrium and the mass-limits which combine General Relativity and Quantum Mechanics. In Chap. 7 we considered the emission of gravitational waves and the stringent tests of Einstein’s theory that come from the binary pulsar systems.
The further historical and conceptual development of the theory is addressed in Volume 2 which covers the following topics:
1.Extended Space-Times, Causal Structure and Penrose Diagrams.
2.Rotating Black-Holes and Thermodynamics.
3.Cosmology and General Relativity: From Hubble to WMAP.
4.The theory of the inflationary universe.
5.The birth of String Theory and Supersymmetry.
6.The conceptual and algebraic foundations of Supergravity.
7.An introduction to the Bulk-Brane dualism with a glance at brane solutions.
8.An introduction to the Supergravity Bestiary.
9.A bird-eye review of various type of solutions of higher dimensional supergravities.
P.G. Frè, Gravity, a Geometrical Course, DOI 10.1007/978-94-007-5361-7_8, |
311 |
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