- Weyl curvature hypothesis
The Weyl curvature hypothesis, which arises in the application of
Albert Einstein 'sgeneral theory of relativity tophysical cosmology , was introduced by the British mathematician and theoretical physicistSir Roger Penrose in an article in 1979 [cite conference | author = R. Penrose | title = Singularities and Time-Asymmetry | booktitle = General Relativity: An Einstein Centenary Survey | editor = S. W. Hawking and W. Israel | publisher = Cambridge University Press | year = 1979 | pages = 581–638] in an attempt to provide explanations for two of the most fundamental issues in physics. On the one hand one would like to account for aUniverse which on its largest observational scales appears remarkably spatially homogeneous and isotropic in its physical properties (and so can be described by a simple Friedmann-Lemaître model), on the other hand there is the deep question on the origin of thesecond law of thermodynamics .Penrose suggests that the resolution of both of these problems is rooted in a concept of the
entropy content ofgravitational field s. Near the initial cosmological singularity (theBig Bang ), he proposes, the entropy content of the cosmological gravitational field was extremely low (compared to what it theoretically could have been), and started rising monotonically thereafter. This process manifested itself e.g. in the formation of structure through the clumping of matter to formgalaxies andclusters of galaxies . Penrose associates the initial low entropy content of the Universe with the effective vanishing of theWeyl curvature tensor of the cosmological gravitational field near the Big Bang. From then on, he proposes, its dynamical influence gradually increased, thus being responsible for an overall increase in the amount of entropy in the Universe, and so inducing a cosmologicalarrow of time .The Weyl curvature represents such gravitational effects as tidal fields and
gravitational radiation . Mathematical treatments of Penrose's ideas on the Weyl curvature hypothesis have been given in the context of isotropic initial cosmological singularities e.g. in the articles. [cite journal | author=S. W. Goode and J. Wainwright | title=Isotropic Singularities in Cosmological Models | journal=Class. Quantum Grav. | volume=2 | year=1985 | pages=99-115 | doi=10.1088/0264-9381/2/1/010] [cite journal | author=R. P. A. C. Newman | title=On the Structure of Conformal Singularities in Classical General Relativity | journal=Proc. R. Soc. Lond. A | volume=443 | year=1993 | pages=473-492 | doi=10.1098/rspa.1993.0158] [cite journal | author=K. Anguige and K. P. Tod | title=Isotropic Cosmological Singularities I. Polytropic Perfect Fluid Spacetimes | journal=Ann. Phys. N.Y. | volume=276 | year=1999 | pages=257-293 | doi=10.1006/aphy.1999.5946 | id=arxiv|archive=gr-qc|id=9903008] [cite journal | author=W. C. Lim, H. van Elst, C. Uggla and J. Wainwright| title=Asymptotic Isotropization in Inhomogeneous Cosmology | journal=Phys. Rev. D | volume=69 | year=2004 | pages=103507 (1-22) | doi=10.1103/PhysRevD.69.103507 | id=arxiv|archive=gr-qc|id=0306118] . Penrose views the Weyl curvature hypothesis as a physically more credible alternative tocosmic inflation (a hypothetical phase of accelerated expansion in the early life of the Universe) in order to account for the presently observed almost spatial homogeneity and isotropy of our Universe. [cite conference | author = R. Penrose | title = Difficulties with Inflationary Cosmology | booktitle = Proc. 14th Texas Symp. on Relativistic Astrophysics | editor = E. J. Fergus | publisher = New York Academy of Sciences | year = 1989 | pages = 249-264 | doi = 10.1111/j.1749-6632.1989.tb50513.x]ee also
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Gravitational entropy
*Gravitational singularity
*Unsolved problems in physics
*White hole References
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