I explore decoupling limits that lead to matrix theories on D-branes, focusing on their BPS nature and the emergence of non-Lorentzian target space geometries. In these limits, D-branes experience instantaneous gravitational forces, and when applied to curved geometries, it is shown that a single decoupling limit leads to the AdS/CFT correspondence. By applying two such limits, we generate new holographic examples, including those with non-Lorentzian bulk geometries. I also discuss the relationship between matrix theories and non-relativistic string theory, and their uplift to M-theory. Finally, we demonstrate that reversing these decoupling limits connects to the TTbar deformation in two dimensions. This provides a new perspective on the near-horizon brane geometry and leads to TTbar-like flow equations for the Dp-brane DBI action.

I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry. Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.