The partial entanglement entropy (PEE) $s_{\mathcal{A}}(\mathcal{A}_i)$ characterizes how much the subset $\mathcal{A}_i$ of $\mathcal{A}$ contribute to the entanglement entropy $S_{\mathcal{A}}$. We find one additional physical requirement for $s_{\mathcal{A}}(\mathcal{A}_i)$, which is the invariance under a permutation. The partial entanglement entropy proposal satisfies all the physical requirements. We show that for Poincar\'e invariant theories the physical requirements are enough to uniquely determine the PEE (or the entanglement contour) to satisfy a general formula. This is the first time we find the PEE can be uniquely determined. Since the solution of the requirements is unique and the \textit{PEE proposal} is a solution, the \textit{PEE proposal} is justified for Poincar\'e invariant theories.

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By studying the infra-red fixed point of an N = (0, 2) Landau-Ginzburg model, we find an example of modular invariant partition function beyond the ADE classification. This stems from the fact that a part of the left-moving sector is a new conformal field theory which is a variant of the parafermion model.

In this summary article, we review and discuss the non-existence of stationary black hole solutions for the Einstein-Dirac-Maxwell equations.

Gravitational waves are predicted by the general theory of relativity. In [6] D. Christodoulou showed that gravitational waves have a nonlinear memory. We proved in [3] that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves. In the present paper, we study this electromagnetic Christodoulou memory effect and compute it for binary neutron star mergers. These are typical sources of gravitational radiation. During these processes, not only mass and momenta are radiated away in form of gravitational waves, but also very strong magnetic fields are produced and radiated away. Thus the observed effect on test masses of a laser interferometer gravitational wave detector will be enlarged by the contribution of the electromagnetic field. Therefore, the present results are important for the planned experiments. Looking at the null asymptotics of spacetimes, which are solutions of the Einstein-Maxwell (EM) equations, we derived in [3] the electromagnetic Christodoulou memory effect. Moreover, our results allow to answer astro-physical questions, as the knowledge about the amount of energy radiated away in a neutron star binary merger enables us to gain information about the source of the gravitational waves.