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Geometric optimization problems are at the core of many applications in geometry processing. The choice of a representation fitting an optimization problem can considerably simplify solving the problem. We consider the Nonlinear…
The aim of this paper is to present a general way to calculate quasi-normal modes (QNM) of the Teukolsky equation for higher dimensional (d > 4) Kerr spacetime with compactified extra dimensions. In order to do so, we develop a formalism…
The numerical integration of particle trajectories in curved spacetimes is fundamental for obtaining realistic models of the particle dynamics around massive compact objects such as black holes and neutron stars. Generalized algorithms…
We study the orbital structure and precession dynamics of neutral test particles in the magnetized Kerr black hole (MKBH) spacetime-an exact electrovacuum solution of the Einstein-Maxwell equations that self-consistently incorporates the…
We study the degrees of freedom of the metric in a general class of higher derivative gravity models, which are interesting in the context of quantum gravity as they are (super)renormalizable. First, we linearize the theory for a flat…
We derive an effective Hamiltonian for a quantum system constrained to a submanifold (the constraint manifold) of configuration space (the ambient space) by an infinite restoring force. We pay special attention to how this Hamiltonian…
Curvature expansion for the heat kernel trace and the one-loop effective action is built for the wave operator of the theory in the quasi-thermal setup of a nonvacuum quantum state. This setup implies a non-static and non-stationary…
In the context of the absolute parallelism formulation of General Relativity, and because of the fact that the scalar curvature can be written in purely torsional terms, it was known for a long time that a surface term based solely on the…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
We investigate whether quasinormal modes (QNMs) can be used in the search for signatures of extra dimensions. To address a gap in the Beyond the Standard Model (BSM) literature, we focus here on higher dimensions characterised by negative…
Position based dynamics is a powerful technique for simulating a variety of materials. Its primary strength is its robustness when run with limited computational budget. We develop a novel approach to address problems with PBD for…
Gravitational waves from the explosive merger of distant black holes are encoded with details regarding the complex extreme-gravity spacetime present at their source. Famously described by the Kerr spacetime metric for rotating black holes…
High-capacity associative memories based on Kernel Logistic Regression (KLR) exhibit strong storage capabilities, but the dynamical and geometric mechanisms underlying their stability remain poorly understood. This paper investigates the…
We study a class of limits of the higher-dimensional Kerr-NUT-(A)dS spacetimes where particular roots of metric functions degenerate. Namely, we obtain the Taub-NUT-(A)dS and the extreme near-horizon geometries as two examples of our…
The ''ringdown'' stage of gravitational-wave signals from binary black hole mergers, mainly consisting of a superposition of quasinormal modes emitted by the merger remnant, is a key tool to test fundamental physics and to probe black hole…
The efficient simulation of complex quantum systems remains a central challenge due to the exponential growth of Hilbert space with system size. Tensor network methods have long been established as powerful approximation schemes, and their…
We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated…
In this article I present a simple Newtonian heuristic for deriving a weak-field approximation for the spacetime geometry of a point particle. The heuristic is based on Newtonian gravity, the notion of local inertial frames [the Einstein…
We describe the Kerr black hole in the ingoing and outgoing Kerr-Schild horizon penetrating coordinates. Starting from the null vector naturally defined in these coordinates, we construct the null tetrad for each case, as well as the…
The accurate computation of quasinormal modes from rotating black holes beyond general relativity is crucial for testing fundamental physics with gravitational waves. In this study, we assess the accuracy of the eikonal and post-Kerr…