Conformal Fourth-Rank Gravity
| dc.creator | Tapia, Victor | |
| dc.creator | Marrakchi, A. L. | |
| dc.creator | Cataldo, M. | |
| dc.date | 1993-03-03 | |
| dc.date.accessioned | 2026-07-07T03:30:01Z | |
| dc.date.available | 2026-07-07T03:30:01Z | |
| dc.description | We consider the consequences of describing the metric properties of space- time through a quartic line element $ds^4=G_{μνλρ}dx^μdx^νdx^λdx^ρ$. The associated "metric" is a fourth-rank tensor $G_{μνλρ}$. We construct a theory for the gravitational field based on the fourth-rank metric $G_{μνλρ}$ which is conformally invariant in four dimensions. In the absence of matter the fourth-rank metric becomes of the form $G_{μνλρ}=g_{(μν}g_{λρ)}$ therefore we recover a Riemannian behaviour of the geometry; furthermore, the theory coincides with General Relativity. In the presence of matter we can keep Riemannianicity, but now gravitation couples in a different way to matter as compared to General Relativity. We develop a simple cosmological model based on a FRW metric with matter described by a perfect fluid. Our field equations predict that the entropy is an increasing function of time. For $k_{obs}=0$ the field equations predict $Ω\approx 4y$, where $y={p\overρ}$; for $Ω_{small}=0.01$ we obtain $y_{pred}=2.5\times 10^{-3}$. $y$ can be estimated from the mean random velocity of typical galaxies to be $y_{random}=1\times10^{-5}$. For the early universe there is no violation of causality for $t>t_{class}\approx10^{19}t_{Planck}\approx 10^{-24}s$. | |
| dc.description | 39 pages, plain TEX | |
| dc.identifier | https://arxiv.org/abs/gr-qc/9303009 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/9303009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/35408 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Conformal Fourth-Rank Gravity | |
| dc.type | text |