Black holes, fluids and gravity A tale of friends

The deep connection between black holes, fluids and gravity has been a recurring theme in modern theoretical physics and is mathematically established through long-wavelength effective theories. In this thesis, we exploit and generalise the current understanding of this long-lasting friendship.
In the first part of the thesis, we exploit the blackfold formalism, an effective theory which studies long-wavelength deformations of (black) branes, to expand the phase space of solutions of higher-dimensional black holes. In this case we consider both higher-dimensional Einstein gravity with a cosmological constant, (higher-form) gauge field and dilaton; as well as string theory/supergravity with AdS$_{l}\times S^{m}$ backgrounds, with $(l,m)=\{(4,7),\ (5,5),\ (7,4)\}$, in the presence of $F_l$ fluxes.
In the second part of the thesis, we focus on the formulation of relativistic fluids with null flow and the existence of a consistent neutral fluid theory at zero temperature. Here, null hydrodynamics can be derived from first principles using symmetry as a guiding principle, and it also emerges from a null limit of relativistic hydrodynamics in which the temperature is sent to zero while the timelike fluid velocity is boosted to the speed of light. Interestingly, null fluids are linearly causal and stable in any hydrodynamic frame.
In the final part of the thesis, we formulate null fluid/gravity correspondence and null blackfold approach. Here we consider long-wavelength perturbations of (AdS-)pp-waves (or specific Kaigorodov metrics) parametrised by an amplitude and direction. In the context of holography, the map identifies these parameters with the null momentum density and null flow of the dual null fluid. Finally, a subset of these solutions can be obtained by taking the null limit of hydrodynamically perturbed (AdS) black branes.