Investigation of weak null singularities inside spherically symmetric black holes in the presence of matter fields

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The proposed PhD project for Raya Valentinova Mancheva is on the investigation of the behaviour of matter fields near spherically symmetric weak null singularities inside black holes and their back-reaction on the gravitational field. In a first step the spherically symmetric Euler equations and elasticity will be considered on a fixed background and the temporal behaviour of the state variables determined. In a more challenging second step, the coupling to the spherically symmetric Einstein-Maxwell-scalar field system is taken into account to determine the fate of the weak null singularity under the presence of those matter fields.