Related papers: Failure of a Stability Conjecture in General Relat…
The paper is devoted to the study of Gromov-Hausdorff convergence and stability of irreversible metric-measure spaces, both in the compact and noncompact cases. While the compact setting is mostly similar to the reversible case developed by…
In recent years, the AdS instability conjecture, put forward by Dafermos-Holzegel in 2006, has attracted a substantial amount of numerical and heuristic studies. Following the pioneering work of Bizon-Rostworowski, research efforts have…
We revisit the phenomenon of instability of solitons in the two dimensional generalization of the Korteweg-de Vries equation, the generalized Zakharov-Kuznetsov (ZK) equation, $u_t + \partial_{x_1} (\Delta u + u^p) = 0, (x_1,x_2) \in…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them is reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the Eotvos experiment, tests of special…
We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably…
A quantitative test for the validity of the semi-classical approximation in gravity is given. The criterion proposed is that solutions to the semi-classical Einstein equations should be stable to linearized perturbations, in the sense that…
In this paper, we have studied non stationary dust spherically symmetric spacetime, in general covariant theory ($U(1)$ extension) of the Ho\v{r}ava-Lifshitz gravity with the minimally coupling and non-minimum coupling with matter, in the…
Although quantitative stability for critical points of the Sobolev and fractional Sobolev inequalities has been extensively studied, the corresponding stability theory for critical points of the Hardy--Littlewood--Sobolev (HLS) inequality…
We consider a spherical gravitational collapse of inhomogeneous dust (and null dust) in Einstein gravity with the Gauss-Bonnet (GB) combination of quadratic curvature terms. It turns out that the presence of the coupling constant of the GB…
We study the degrees of freedom in New General Relativity -- flat and metric compatible family of theories -- around the Minkowski background in a gauge invariant manner. First, we confirm the decoupling case, in which the theory reduces to…
A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and…
We find analytical vacuum stability or bounded below conditions for general scalar potentials of a few fields. After a brief review of copositivity we go beyond it. We discuss the vacuum stability conditions of the general potential of two…
We consider the gravitational collapse of a spherically symmetric ball of dust in the general relativistic weak gravity regime. The velocity of the matter as viewed by external observers is compared to the velocity gauged by local…
In this work we contrast the behaviour of two spherically symmetric matter models in a class of spherically symmetric spacetimes which feature a weak null singularity. This class in particular contains spherically symmetric perturbations of…
The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After…
We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans-Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a…
In this comment we show that the experimental results for a universally valid uncertainty relation in ref.[J. Erhart et al. Nat. Phys.(2012)10.1038/nphys2194]cannot be justified. The experiments cannot be recognized to establish a violation…
The universe today, with structure such as stars, galaxies and black holes, seems to have evolved from a very homogeneous initial state. From this it appears as if the entropy of the universe is decreasing, in violation of the second law of…
We show that starting with a cosmological constant in a curved space-time, the Einstein-Hilbert term of general relativity is generated through a ghost condensation. We fix Weyl symmetry, or equivalently local scale symmetry by a gauge…
The assumptions of the Hawking-Penrose singularity theorem are not covariant under field redefinitions. Thus we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with any other…