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We consider the question of whether solutions of Klein--Gordon equations on asymptotically Anti-de Sitter spacetimes can be uniquely continued from the conformal boundary. Positive answers were first given by the second author with G.…
Our main aim in this paper is to investigate the rigidity of complete noncompact gradient steady Ricci solitons with harmonic Weyl tensor. More precisely, we prove that an $n$-dimensional ($n\geq 5$) complete noncompact gradient steady…
The $1/c$-expansion of general relativity appropriately sourced by matter can be used to derive an action principle for Newtonian gravity. The gravitational part of this action is known as non-relativistic gravity (NRG). It is possible to…
In this thesis, we investigate the method of conformal renormalization applied to theories with degrees of freedom beyond the metric ones. Specifically, we examine this method in the presence of a scalar field. To do this, as part of a…
We study the gravitational action induced by coupling two-dimensional non-conformal, massive matter to gravity on a compact Riemann surface. We express this gravitational action in terms of finite and well-defined quantities for any value…
We construct and investigate non conformal anisotropic Bianchi type VII solutions in 5 dimensions. The solutions are asymptotically flat, but they contain a naked singularity at the origin. We also construct solutions of Einstein-Maxwell…
We present a concise description of the basic features of gravity-matter models based on the formalism of non-canonical spacetime volume-forms in its two versions: the method of non-Riemannian volume-forms (metric-independent covariant…
Using an approach similar to arXiv:2409.15460, we give a new proof of the nonlinear stability of de Sitter space as a solution to the Einstein vacuum equations with positive cosmological constant in $n+1$ dimensions, with $n\geq3$. Using…
We present an analysis of the perturbative realization of the $TTJJ$ correlator, with two stress energy tensors and two conserved currents, using free field theory realizations, integrating out conformal sectors in the quantum corrections.…
Non-trivial outer algebra automorphisms may be utilized in $\lambda$-deformations of (gauged) WZW models thus providing an efficient way to construct new integrable models. We provide two such integrable deformations of the exact coset CFT…
In this paper, we construct the first analytic examples of (3+1)-dimensional self-gravitating regular cosmic tube solutions which are superconducting, free of curvature singularities and with non-trivial topological charge in the…
The theory described by the sum of the Einstein-Hilbert action and the action of conformal scalar field possesses the duality symmetry which includes some special conformal transformation of the metric, and also inversion of scalar field…
We obtain an infinite number of exact static, Ricci-flat spherically symmetric vacuum solutions for a class of f(R) theories of gravity. We analytically derive two exact vacuum black-hole solutions for the same class of f(R) theories. The…
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are…
Starting from the space of Lorentzian metrics, we examine the full gravitational path integral in 3 and 4 space-time dimensions. Inspired by recent results obtained in a regularized, dynamically triangulated formulation of Lorentzian…
A new 8-dim conformal gauging solves the auxiliary field problem and eliminates unphysical size change from Weyl's electromagnetic theory. We derive the Maurer-Cartan structure equations and find the zero curvature solutions for the…
We study conformal gravity as an alternative theory of gravitation. For conformal gravity to be phenomenologically viable requires that the conformal symmetry is not manifest at the energy scales of the other known physical forces. Hence we…
When quantizing Conformal Dilaton Gravity there is a conformal anomaly which starts at two loop order. This anomaly stems from evanescent operators on the divergent parts of the effective action. The general form of the finite counterterm…
Classical linearized gravity admits a dual formulation in terms of a higher-rank tensor field. Proposing a prescription for the instanton sectors of linearized gravity and its dual, we show that they may be quantum inequivalent in even…
We study a non-relativistic realisation of two-dimensional de Sitter gravity both from its boundary and bulk description with the goal of learning about de Sitter space and paving the way for extending the holographic duality into a…