Related papers: About the Cauchy problem in Stelle's quadratic gra…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
There are a number of reasons to entertain the possibility that locality is violated on microscopic scales, for example through the presence of an infinite series of higher derivatives in the fundamental equations of motion. This type of…
In this paper we consider the Cauchy problem for $2m$-order stochastic partial differential equations of parabolic type in a class of stochastic Hoelder spaces. The Hoelder estimates of solutions and their spatial derivatives up to order…
We use perturbations in order to study the stability of the Cauchy Horizon in a Reissner-Nordstr\"om space-time. The perturbations are either scalar or gravitational, and indicate some strong instabilities.
Proposing new solution problems of the hierarchy and smallness of the cosmological constant using the Tev scale of the Standard Model in new framework of the higher-order gravity.
We consider full perturbations to a covariantly defined Schwarzschild spacetime. By constructing complex quantities, we derive two decoupled, covariant and gauge-invariant, wave-like equations for spin-weighted scalars. These arise…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
The preceding talks given at this conference have dealt mainly with general ideas for, main problems of and techniques for the task of quantizing gravity canonically. Since one of the major motivations to arrange for this meeting was that…
We explore how the initial value problem may be formulated for globally hyperbolic, Hadamard, solutions of the semiclassical Einstein-Klein-Gordon equations. Given a set of data on an initial 3-surface, consisting of the values on the…
Theories of modified gravity, in both the linear and fully non-linear regime, are often studied under the assumption that the evolution of the new (often scalar) degree of freedom present in the theory is quasi-static. This approximation…
We consider the Cauchy problem and the source problem for normally hyperbolic operators on the Minkowski spacetime, and study the determination of solutions from their integrals along null geodesics. For the Cauchy problem, we give a new…
Finding effective theories of modified gravity that can resolve cosmological singularities and avoid other physical pathologies such as ghost and gradient instabilities has turned out to be a rather difficult task. The concept of limiting…
The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein's general relativity could alleviate the different problems associated with it that result…
Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in…
We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = \Delta u+ f(u,|x|), \end{equation*} where $x \in \mathbb{R}^n$, $n >2$, and $f=f(u,|x|)$ is either critical or supercritical with…
A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the…
The 2023 second edition of a 2006 encyclopedia article on mathematical aspects of quantum field theory in curved spacetimes (QFTCST). Section-titles (with new sections indicated with stars) are: Introduction and preliminaries, Construction…
This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk…
"Brane Induced Gravity" is regarded as a promising framework for addressing the cosmological constant problem, but it also suffers from a ghost instability for parameter values that make it phenomenologically viable. We carry out a detailed…
This paper presents a new higher derivative gravity which in spontaneous breaking electroweak symmetry state does not have ghost in gravity sector. We show that Newton constant of the gravity and dark energy density they depend on the…