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Smoothness of Null Infinity in General Relativity

Project: 
It is a unique property of the general theory of relativity that energy is a non-local quantity: It does not make sense to describe how much energy is contained within a given volume. This is because the background geometry is coupled to the fields propagating in the space-time, unlike Newtonian physics where they are not coupled, and there is no way to separate them in general. However if one goes to the "infinity" of a space-time, in particular null infinity the end point of all nullrays, it can be shown that the fields decouple from the background there. Thus null infinity is important for several physical reasons. An important task then is to investigate its properties. One particular question is when is null infinity, which is a 3-dimensional surface, smooth? A conjecture exists by Friedrich which specifies what type of initial data sets give rise to a smooth null infinity, however this is just a conjecture and has not been proven. The conformal field equations are a regular extension of the Einstein equations from general relativity to null infinity. In recent years a wellposed initial boundary value problem formulation has been created for their numerical evolution. The aim of this project is to investigate this conjecture numerically using the conformal field equation framework mentioned above. This will be used to numerically evolve initial data sets that do and do not satisfy the conjecture and to see whether the resulting null infinity is in fact regular.
Node This Project Is Offered On: 
(UCT)(UKZN)(NWU)

Supervisor

Chris
Stevens

Co-Supervisor

Requirements for students to address: 
Basis knowledge of general relativity would be an advantage.
Research Area: 
General Astrophysical Sciences


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