Conformal Symmetries of the Strumia–Tetradis’ Metric

In a recent paper, a new conformally flat metric was introduced, describing an expanding scalar field in a spherically symmetric geometry. The spacetime can be interpreted as a Schwarzschild-like model with an apparent horizon surrounding the curvature singularity. For the above metric, we present t...

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Bibliographic Details
Published in:Physical sciences forum 2023-03, Vol.7 (1), p.46
Main Authors: Pantelis S. Apostolopoulos, Christos Tsipogiannis
Format: Article
Language:English
Subjects:
conformal vector fields
geometric symmetries
relativistic cosmology
scalar fields
Online Access:Get full text
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Summary:In a recent paper, a new conformally flat metric was introduced, describing an expanding scalar field in a spherically symmetric geometry. The spacetime can be interpreted as a Schwarzschild-like model with an apparent horizon surrounding the curvature singularity. For the above metric, we present the complete conformal Lie algebra consisting of a six-dimensional subalgebra of isometries (Killing Vector Fields or KVFs) and nine proper conformal vector fields (CVFs). An interesting aspect of our findings is that there exists a gradient (proper) conformal symmetry (i.e., its bivector Fab vanishes) which verifies the importance of gradient symmetries in constructing viable cosmological models. In addition, the 9-dimensional conformal algebra implies the existence of constants of motion along null geodesics that allow us to determine the complete solution of null geodesic equations.
ISSN:2673-9984
DOI:10.3390/ECU2023-14100