Discretely self-similar solutions govern critical gravitational collapse and have been known only numerically since Choptuik's pioneering work. We construct, in closed analytic form, an infinite family of such solutions of the Einstein-massless-Klein-Gordon system using the large-D expansion. We characterize their structure and compare them with numerical critical solutions at finite D, identifying both universal features and distinctly large-D behavior.

We numerically construct a one-parameter family of critical spacetimes in arbitrary continuous dimensions D>3. This generalizes Choptuik's D=4 solution to spherically symmetric massless scalar-field collapse at the threshold of D-dimensional Schwarzschild-Tangherlini black hole formation. We refer to these solutions, which share the discrete self-similarity of their four-dimensional counterpart, as critical spacetime crystals. Our main results are the echoing period and Choptuik exponent of the crystals as continuous functions of D, with detailed data for the interval 3.05<D<5.5. Notably, the echoing period has a maximum near D=3.76. As a by-product, we recover the echoing periods and Choptuik exponents in D=4 (5): Delta=3.445453 (3.22176) and gamma=0.373961 (0.41322). We support these numerical results with analytical expansions in 1/D and D-3. They suggest that both the echoing period and Choptuik exponent vanish as D approaches 3 from above. This paves the way for a small-(D-3) expansion, paralleling the large-D expansion of general relativity. We also extend our results to two-dimensional dilaton gravity.

Discretely self-similar solutions govern critical collapse and have been known only numerically since Choptuik's pioneering work. Using the large-D expansion, where D is the spacetime dimension, we construct an infinite family of analytic solutions of the Einstein-massless-Klein-Gordon equations. In this limit, the field equations simplify drastically, and the solutions are encoded in a single function of time. We characterize their structure and compare them with numerical critical solutions at finite D, identifying both universal features and effects specific to large D.

This thesis explores several facets of Carroll symmetries through their applications to field theories and gravity. The geometric description of curved Carroll manifolds is developed from a Cartan-geometric viewpoint, reviewed at the outset. On these backgrounds, we study various field theories, including scalar and vector Carroll swiftons. Imposing causality and locality, we derive a universal sector of the commutators between Carroll stress-energy tensor components valid for any Carroll quantum field theory. In two dimensions, we confirm the connection to holography by showing that a Carroll boost anomaly gives rise to additional Schwinger-like terms in these brackets, sourcing the familiar central extensions of the asymptotic symmetries of three-dimensional asymptotically flat Einstein gravity. Afterwards, we come to theories of Carroll gravity which, as we argue, provide a valuable playground for understanding quantum gravity in a specific scaling limit which we refer to as the tantum gravity limit. At first, we review Carroll gravity in general dimensions and subsequently restrict to two spacetime dimensions where we introduce Carroll dilaton gravity. We define Carroll black holes as massive vacuum solutions to these theories that admit well-defined thermodynamic properties but have a Carroll extremal surface instead of an event horizon. After investigating several models and their solutions we finally add quantum matter to these backgrounds and study how the thermodynamic properties of a Carroll black hole reflect in its vacuum states. For the Carroll-Schwarzschild black hole we find a non-vanishing asymptotic energy density. We refer to this phenomenon as the Carroll-Hawking effect.

We construct rotating black holes in Carroll gravity using two distinct approaches. In one of them, we exploit the freedom in the Carroll compatible connection to encode rotation. In particular, we construct rotating solutions in magnetic Carroll gravity by dressing the Carroll-Schwarzschild black hole with a rotational charge. This solution is intrinsically Carrollian and has no Lorentzian analog. In the other approach, we construct an extension of magnetic Carroll gravity from general relativity in an odd-power expansion in the speed of light. This theory contains magnetic Carroll gravity as a subsector but has in general more physical degrees of freedom. We show that this theory admits a Carroll analog of the Kerr black hole as a solution, which we refer to as the "Kerroll black hole". Its rotation appears as an intrinsically odd-power effect in the Carroll data. We compute the corresponding conserved charges for both theories.

We identify a new critical parameter in Choptuik's gravitational collapse: the angle at which null energy condition (NEC) saturation lines intersect at the center of the critical spacetime. These NEC lines coincide with regions of vanishing curvature, dividing spacetime into stripes of positive and negative curvature. By numerically solving Choptuik's original system, we find the NEC angle to be alpha approximate to 0.64 (approximate to 37 degrees) and analytically derive alpha = 2arccot(D-1) for any spacetime dimension D > 3.

We construct postcarrollian gravity models in two, three, and four spacetime dimensions by applying algebraic expansion methods. As a byproduct, we present the most general postcarrollian 2d dilaton gravity model, construct its solutions and discuss some boundary aspects, including Schwarzian-type boundary actions. In 3d, we propose Brown-Henneaux-like boundary conditions, generalizing a corresponding Carrollian analysis, and derive the postcarrollian asymptotic symmetry algebra with its central extensions.

We argue there is an interesting triple-scaling limit of quantum gravity, namely when Planck’s constant scales to infinity while Newton’s constant and the speed of light tend to zero, keeping fixed the gravitational coupling GNc−4 and the combination ℏc. We refer to this limiting theory as “tantum gravity” and describe in this Letter some of its main properties and prospects for physics. Most notably, the laws of black hole thermodynamics survive this limit, which means that puzzles related to black holes and their evaporation could be addressed more easily in tantum gravity than in fully fledged quantum gravity. Published by the American Physical Society 2025

We construct Carroll-invariant theories with fields propagating outside the Carroll lightcone, i.e., at a speed strictly greater than zero (`Carroll swiftons'). We first consider models in flat Carroll spacetime in general dimensions, where we present scalar and vector Carroll swifton field theories. We then turn to the coupling to gravity and achieve in particular in two dimensions a Carroll invariant scalar swifton by coupling it suitably to Carroll dilaton gravity. Its backreaction on the geometry generates dynamical torsion.

We construct Carroll-invariant theories with fields propagating outside the Carroll light cone, i.e., at a speed strictly greater than zero (“Carroll swiftons”). We first consider models in flat Carroll spacetime in general dimensions, where we present scalar and vector Carroll swifton field theories. We then turn to the coupling to gravity and achieve in particular in two dimensions a Carroll-invariant scalar swifton by coupling it suitably to Carroll dilaton gravity. Its backreaction on the geometry generates dynamical torsion. Published by the American Physical Society 2024

Carroll black holes with an associated Carroll temperature were introduced recently. So far, it is unclear if they exhibit a Hawking-like effect. To solve this, we study scalar fields on Carroll black hole backgrounds. Inspired by anomaly methods, we derive a Hawking-like energy-momentum tensor compatible with the Carroll temperature and the Stefan-Boltzmann law. Key steps in our derivation are the finiteness of energy at the Carroll extremal surface and compatibility with the Carroll Ward identities, thereby eliminating, respectively, the Carroll-analogs of the Boulware and Unruh vacua.

Dilaton gravities in two dimensions can be formulated as particular Poisson sigma models. Target space diffeomorphisms map different models to each other and establish a one-to-one correspondence between their classical solutions. We obtain a general form of such diffeomorphisms in Lorentzian and Euclidean signatures and use them to extend known holographic results, including the Schwarzian action on the asymptotic boundary, from JT to a large class of dilaton gravity models.

Despite the absence of a lightcone structure, some solutions of Carroll gravity show black hole-like behaviour. We define Carroll black holes as solutions of Carroll gravity that exhibit Carroll thermal properties and have a Carroll extremal surface, notions introduced in our work. The latter is a Carroll analogue of a Lorentzian extremal surface. As examples, we discuss the Carroll versions of Schwarzschild, Reissner-Nordström, and BTZ black holes and black hole solutions of generic 1+1 dimensional Carroll dilaton gravity, including Carroll JT and Carroll Witten black holes.

We introduce a family of 2D dilaton gravity models with state-dependent constant curva-ture so that dS2 emerges as an excitation of AdS2. Curiously, the strong coupling region corresponds to the asymptotic region geometrically. Apart from these key differences, many features resemble the Almheiri-Polchinski model. We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shock -waves, and semiclassical backreaction effects. In some of these models, we find that low temperatures are dominated by AdS2 but high temperatures are dominated by dS2, concurrent with a recent proposal by Susskind.

We introduce a family of 2D dilaton gravity models with state-dependent constant curvature so that dS 2 emerges as an excitation of AdS 2 .Curiously, the strong coupling region corresponds to the asymptotic region geometrically.Apart from these key differences, many features resemble the Almheiri-Polchinski model.We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shockwaves, and semiclassical backreaction effects.In some of these models, we find that low temperatures are dominated by AdS 2 but high temperatures are dominated by dS 2 , concurrent with a recent proposal by Susskind.

We introduce a family of 2D dilaton gravity models with state-dependent constant curvature so that dS_22 emerges as an excitation of AdS_22. Curiously, the strong coupling region corresponds to the asymptotic region geometrically. Apart from these key differences, many features resemble the Almheiri–Polchinski model. We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shockwaves, and semiclassical backreaction effects. In some of these models, we find that low temperatures are dominated by AdS_22 but high temperatures are dominated by dS_22, concurrent with a recent proposal by Susskind.

We introduce a family of 2D dilaton gravity models with state-dependent constant curvature so that dS_2 emerges as an excitation of AdS_2. Curiously, the strong coupling region corresponds to the asymptotic region geometrically. Apart from these key differences, many features resemble the Almheiri–Polchinski model. We discuss perturbative and non-perturbative thermodynamical stability, bubble nucleation through matter shockwaves, and semiclassical backreaction effects. In some of these models, we find that low temperatures are dominated by AdS_2 but high temperatures are dominated by dS_2, concurrent with a recent proposal by Susskind.

Having in mind extensions of 2D holography beyond the Jackiw-Teitelboim model we propose holographic counterterms and asymptotic conditions for a family of asymptotically AdS$_2$ dilaton gravity models leading to a consistent variational problem and a finite on-shell action. We show the presence of asymptotic Virasoro symmetries in all these models. The Schwarzian action generates (a part) of the equations of motion governing the asymptotic degrees of freedom. We also analyse the applicability of various entropy formulae. By a dilaton-dependent conformal transformation our results are extended to an even larger class of models having exotic asymptotic behavior. We also analyse asymptotic symmetries for some other classes of dilaton gravities without, however, constructing holographic counterterms.