Related papers: Upper bounds on the compactness at the innermost l…
The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most…
We discuss photon number bounds for a system of non-relativistic particles coupled to the quantized electromagnetic field (non-relativistic QED), below the ionization threshold. Such a bound was assumed in the proof of asymptotic…
It is often stated in the physics literature that maximally-spinning Kerr black-hole spacetimes are characterized by near-horizon co-rotating circular geodesics of radius $r_{\text{circular}}$ with the property $r_{\text{circular}}\to…
Although the black holes are an integral part of the standard model of astrophysics and cosmology, their existence poses some serious fundamental problems. In recent years, several horizonless compact object models were proposed to address…
An infinite class of exact static anisotropic spheres is developed. All members of the class satisfy (i) regularity (meaning no singularities), and in particular at the origin, (ii) positive but monotone decreasing energy density…
Black holes are the most compact objects in the Universe. According to general relativity, black holes have a horizon that hides a singularity where Einstein's theory breaks down. Recently, gravitational waves opened the possibility to…
A connection between regular black holes and horizonless ultracompact objects was proposed in~\cite{Carballo-Rubio:2022nuj}. In this paper, we construct a model of a horizonless compact object, specifically an anisotropic gravastar with…
Large-scale cosmic microwave background anisotropies in homogeneous, globally anisotropic cosmologies are investigated. We perform a statistical analysis in which the four-year data from the Cosmic Background Explorer satellite is searched…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
In contrast to five-dimensional Schwarzschild-Tangherlini and Myers-Perry backgrounds, we show that there are stable bound orbits of massive/massless particles in five-dimensional black lens backgrounds, in particular, the supersymmetric…
Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…
Two different versions of an optical theorem for a scattering body embedded inside a lossy background medium are derived in this paper. The corresponding fundamental upper bounds on absorption are then obtained in closed form by elementary…
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 Part I we gave a polynomial growth lower-bound for the number of nodal domains of a Hecke-Maass cuspform in a compact part of the modular surface, assuming a Lindel\"of hypothesis. That was a consequence of a topological argument and…
Scattering theory for p-forms on manifolds with cylindrical ends has a direct interpretation in terms of cohomology. Using the Hodge isomorphism,the scattering matrix at low energy may be regarded as operator on the cohomology of the…
The photon sphere, a hypersurface of null circular geodesics, plays a fundamental role in characterizing black hole spacetimes, influencing phenomena such as black hole shadows, gravitational lensing, and quasinormal modes. In this work, we…
We provide an explicit lower bound for the sytole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.
We prove an intrinsic analogue of Hawking's rigidity theorem for extremal horizons in arbitrary dimensions: any compact cross-section of a rotating extremal horizon in a spacetime satisfying the null energy condition must admit a Killing…
In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of…
Motivated by recent results reporting the instability of horizonless objects with stable light rings, we revisit the linearized stability of such structures. In particular, we consider an exterior Kerr spacetime truncated at a surface where…