相关论文: Asymptotic Flatness, Taub-NUT, and Variational Pri…
We prove that a $4d$ theory of non-linear electrodynamics has equations of motion which are equivalent to those of the Maxwell theory in curved spacetime, but with the usual metric $g_{\mu \nu}$ replaced by a unit-determinant metric $h_{\mu…
A compact oriented 4-manifold is defined to be of ``superconformal simple type'' if certain polynomials in the basic classes (constructed using the Seiberg-Witten invariants) vanish identically. We show that all known 4-manifolds of…
A gauge invariant mathematical formalism based on deformation quantization is outlined to model an $\mathcal{N}=2$ supersymmetric system of a spin $1/2$ charged particle placed in a nocommutative plane under the influence of a vertical…
The calculation of conserved charges of black holes is a rich problem, for which many methods are known. Until recently, there was some controversy on the proper definition of conserved charges in asymptotically anti-de Sitter (AdS) spaces…
We define a noncommutative Lorentz symmetry for canonical noncommutative spaces. The noncommutative vector fields and the derivatives transform under a deformed Lorentz transformation. We show that the star product is invariant under…
Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev <S> which defines the GUT scale will be determined via dimensional transmutation at a scale M where the…
Shear-free or asymptotically shear-free null geodesic congruences possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant affects. It…
We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two key cases: cubic nonlinearities and higher-order power…
This article begins with a brief introduction to numerical relativity aimed at readers who have a background in applied mathematics but not necessarily in general relativity. I then introduce and summarise my work on the problem of treating…
We study the null asymptotic structure of Einstein-Maxwell theory in three-dimensional (3D) spacetimes. Although devoid of bulk gravitational degrees of freedom, the system admits a massless photon and can therefore accommodate…
In this paper we study the rotationally invariant harmonic cohomology of a 2-parameter family of Einstein metrics $g$ which admits a cohomogeneity one action of $SU (2) \times U (1) $ and has AdS asymptotics. Depending on the values of the…
We establish the full asymptotic stability of the sine-Gordon kink outside symmetry under small perturbations in weighted Sobolev norms. Our proof consists of a space-time resonances approach based on the distorted Fourier transform to…
We consider invariant transports of stationary random measures on $\mathbb{R}^d$ and establish natural mixing criteria that guarantee persistence of asymptotic variances. To check our mixing assumptions, which are based on two-point Palm…
We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent…
We present details of the harmonic space construction of a quaternionic extension of the four-dimensional Taub-NUT metric. As the main merit of the harmonic space approach, the metric is obtained in an explicit form following a generic set…
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In…
We analyze $SO(N)$ and $SU(N)$ gauge theories with scalars in adjoint and fundamental representations, coupled to renormalisable, classically scale invariant gravity. In the specific case of $SO(12),$ we show that the quantum field theory…
We analyze the class of four-dimensional N = 4 supergravities obtained by gauging the axionic shift and axionic rescaling symmetries. These theories are formulated with the machinery of embedding tensors and shown to be deducible from…
We apply the recent derivations of dual charges in asymptotically flat spacetimes to asymptotically locally AdS spacetimes. In contrast to the results in the flat case, in the AdS case with a Dirichlet boundary the dual charge contribution…
In this paper, we derive the consistent thermodynamics of the four-dimensional Lorentzian charged Reissner-Nordstr\"om-NUT (RN-NUT), Kerr-Newman-NUT (KN-NUT), and RN-NUT-AdS spacetimes in the framework of the ($\psi-\mathcal{N}$)-pair…