Related papers: Lower bound on the compactness of isotropic ultra-…
In a spherically symmetric and static spacetime of a compact object, such as that of a Schwarzschild black hole, the light-ring is a 2-sphere where photons experience the only possible circular orbits. As a "Gedankenexperiment", we imagine…
We establish a structure theorem for minimizing sequences for the isoperimetric problem on noncompact $\mathsf{RCD}(K,N)$ spaces $(X,\mathsf{d},\mathcal{H}^N)$. Under the sole (necessary) assumption that the measure of unit balls is…
We establish sharp universal upper bounds on the length of the shortest closed geodesic on a punctured sphere with three or four ends endowed with a complete Riemannian metric of finite area. These sharp curvature-free upper bounds are…
We study field theories in the limit that a compactified dimension becomes lightlike. In almost all cases the amplitudes at each order of perturbation theory diverge in the limit, due to strong interactions among the longitudinal zero…
We prove compactness of the embeddings in Sobolev spaces for fractional super and sub harmonic functions with radial symmetry. The main tool is a pointwise decay for radially symmetric functions belonging to a function space defined by…
We construct an exact relativistic cosmology in which an inhomogeneous but isotropic local region has fractal number counts and matches to a homogeneous background at a scale of the order of $10^2$ Mpc. We show that Einstein's equations and…
We give an effective upper bound, for certain arithmetic hyperbolic 3-manifold groups obtained from a quadratic form construction, on the minimal index of a subgroup that embeds in a fixed 6-dimensional right-angled reflection group,…
If a significant fraction of dark matter is in the form of compact objects, they will cause microlensing effects in the gravitational wave (GW) signals observable by LIGO and Virgo. From the non-observation of microlensing signatures in the…
We show that the upper bounds for the $L^2$-norms of $L^1$-normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize compact manifolds of constant sectional curvature using the…
In a very interesting paper, Andr\'easson has recently proved that the gravitational mass of a spherically symmetric compact object of radius $R$ and electric charge $Q$ is bounded from above by the relation…
Beyond black holes and neutron stars, new hypothetical compact objects have been proposed as potential astrophysical entities. In general, their properties have not yet been fully explored or understood, nor has it been proven whether or…
In this paper we study the minimal and maximal $L^{2}$-cohomology of oriented, possibly not complete, Riemannian manifolds. Our focus will be on both the reduced and the unreduced $L^{2}$-cohomology groups. In particular we will prove that…
We derive upper and lower bounds on the mass-radius ratio of stable compact objects in extended gravity theories, in which modifications of the gravitational dynamics via-{\' a}-vis standard general relativity are described by an effective…
In this paper, we shall give a lower diameter bound for compact domain manifolds of shrinking Ricci-harmonic solitons. Our result may be regarded as a generalization to Ricci-harmonic geometry of the recent works by Fern\'andez-L\'opez and…
We argue that if, in order to reverse an object's dynamics, we need to be able to keep track of it with enough precision, then there is an upper bound on the size of the object whose dynamics we can reverse - even using all the available…
This paper aims to study the $(m,\rho)$-quasi Einstein manifold. This article shows that a complete and connected Riemannian manifold under certain conditions becomes compact. Also, we have determined an upper bound of the diameter for such…
In this paper, we discuss general relativistic, self-gravitating and uniformly rotating perfect fluid bodies with a toroidal topology (without central object). For the equations of state describing the fluid matter we consider polytropic as…
Black holes are thought to describe the geometry of massive, dark compact objects in the universe. To further support and quantify this long-held belief requires knowledge of possible, if exotic alternatives. Here, we wish to understand how…
We consider on-center and off-center observers in an inhomogeneous, spherically symmetric, isocurvature (flat) concentration of dark energy with typical size of a few Gpc. Such a concentration could be produced e.g. by a recently formed…
We present a deep H-band image of the region in the vicinity of the cluster Abell 1942 containing the puzzling dark matter concentration detected in an optical weak lensing study by Erben et al. (2000). We demonstrate that our limiting…