The study of conformal geometry and its exact solution of the geodesic deviation equation

B. T. T. Wong

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arXiv · 2204.02188

The study of conformal geometry and its exact solution of the geodesic deviation equation

B. T. T. Wong

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Abstract

In this paper, the geometric properties of the conformal metric are studied and its exact solution of the geodesic deviation equation is presented. We also find out the stress-energy tensor of this geometry and compare it with the usual prefect-fluid case, obtaining an equation of state as $P = -\frac{1}{3}\rho$ in 4D space-time dimension. Finally, the low-energy regime of the metric is studied, in which we obtain the stress-energy tensor proportional to the projection tensor.

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B. T. T. Wong. 2022-03-31. The study of conformal geometry and its exact solution of the geodesic deviation equation. https://arxiv.org/abs/2204.02188

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