Related papers: A Compact theorem on the compactness of ultra-comp…
Horizonless spacetimes describing spatially regular ultra-compact objects which, like black-hole spacetimes, possess closed null circular geodesics (light rings) have recently attracted much attention from physicists and mathematicians. In…
Ultra-compact objects describe horizonless solutions of the Einstein field equations which, like black-hole spacetimes, possess null circular geodesics (closed light rings). We study {\it analytically} the physical properties of spherically…
It is well known that a spherically symmetric compact star whose energy density decreases monotonically possesses an upper bound on its mass-to-radius ratio, $2M/R\leq 8/9$. However, field configurations typically will not be compact. Here…
In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least {\it two} (and,…
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…
It is proved, using the curved line element of a spherically symmetric charged object in general relativity and the Schwinger discharge mechanism of quantum field theory, that the orbital periods $T_{\infty}$ of test particles around…
We study the properties of ultra-compact spherically symmetric dark matter sector star objects, being the solution of Einstein equations with two $U(1)$-gauge fields. One of them is the ordinary Maxwell field, while the auxiliary gauge…
In the framework of a collisionless dark matter fluid which is non-minimally coupled to gravity, we investigate the existence and properties of static, spherically symmetric solutions of the general relativistic field equations. We show…
Static spherically-symmetric matter distributions whose energy-momentum tensor is characterized by a non-negative trace are studied analytically within the framework of general relativity. We prove that such field configurations are…
We prove the existence of a $C^{1,1}$ conformally compact Einstein metric on the ball that has asymptotic sectional curvature decay to $-1$ plus terms of order $e^{-2r}$ where $r$ is the distance from any fixed compact set. This metric has…
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…
Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this…
We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e.,…
We obtain bounds for the minimum and maximum mass/radius ratio of a stable, charged, spherically symmetric compact object in a $D$-dimensional space-time in the framework of general relativity, and in the presence of dark energy. The total…
Astrophysical compact objects are studied in the context of quadratic non-metricity gravity. The solutions to the gravitational field equations, which include fluid components, are analyzed to investigate the density and pressure properties…
The generic properties of compact objects made of two different fluids of dark matter are studied in a scale invariant approach. We investigate compact objects with a core-shell structure, where the two fluids are separated, and with mixed…
We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness…
Self-consistent solutions in Lorentz-violating gravity theories require the simultaneous satisfaction of: (i) the corresponding Einstein field equations, (ii) the matter field equations, and (iii) the Lorentz-violating field equations. In…
We consider a constrained minimal energy problem with an external field over noncompact classes of infinite dimensional vector measures on a locally compact space. The components are positive measures (charges) that are constrained from…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically…