Related papers: The negative energy N-body problem has finite diam…
We study Einstein gravity coupled to a massless scalar field in a static spherically symmetric space-time in four dimensions. Black hole solutions exist when the kinetic energy of the scalar field is negative, that is, for a phantom field.…
We present a geometric approach to the three-body problem in the non-relativistic context of the Barbour-Bertotti theories. The Riemannian metric characterizing the dynamics is analyzed in detail in terms of the relative separations.…
We pose several questions for the classical N-body problem inspired by connections between the virial equation and the Jacobi-Maupertuis formulationof mechanics. We answer some.
We characterize the null energy condition for an $(n+1)$-dimensional Lorentzian manifold in terms of convexity of the relative $(n-1)$-Renyi entropy along displacement interpolations on null hypersurfaces. More generally, we also consider…
The extensivity for the thermodynamics of general $D$-dimensional rotating black holes with or without a cosmological constant can be proved analytically, provided the effective number of microscopic degrees of freedom and the chemical…
The equilibrium properties of a Janus fluid made of two-face particles confined to a one-dimensional channel are revisited. The exact Gibbs free energy for a finite number of particles $N$ is exactly derived for both quenched and annealed…
Using sophisticated string theory calculations, Maldacena and Susskind have intriguingly shown that near-extremal black holes are characterized by a {\it finite} mass gap above the corresponding zero-temperature (extremal) black-hole…
We discuss consequences of an entropic view of gravity, which differs in details from the original proposals of Jacobson and Verlinde. We assume the entropy is localized in the degrees of freedom of the systems interacting gravitationally.…
Let $n\geq 3$ and let $\Omega \subset \mathbb{R}^n$ be a $\mathcal{C}^1$ bounded domain which is diffeomorphic to a ball. We investigate here the problem of finding critical points of the $n$-energy in the space $\mathcal{I}=\{v\in…
We investigate the shadow behaviors of the superentropic black holes in arbitrary dimensions. Using the Hamilton-Jacobi mechanism, we first obtain the associated null geodesic equations of motion. By help of a spheric stereographic…
We report the existence of horizonless compact object solutions supported by dust in the Minimal Exponential Measure (MEMe) model, a theory which modifies the couplings between gravity and matter without introducing dynamical degrees of…
We study the symmetry and uniqueness of maps which minimise the $np$-Dirichlet energy, under the constraint that their Jacobian is a given radially symmetric function $f$. We find a condition on $f$ which ensures that the minimisers are…
For Einstein's General Relativity (GR) or the alternatives suggested up to date the vacuum energy gravitates. We present a model where a new measure is introduced for integration of the total action in the D-dimensional space-time. This…
We show that there exist convex bodies of constant width in $\mathbb{E}^n$ with illumination number at least $(\cos(\pi/14)+o(1))^{-n}$, answering a question by G. Kalai. Furthermore, we prove the existence of finite sets of diameter $1$ in…
We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the motion of the rigid body is described by the…
In his fondamental "Essay on the 3-body problem", Lagrange, well before Jacobi's "reduction of the node", carries out the first complete reduction of symetries. Discovering the so-called homographic motions, he shows that they necessarily…
Let $M$ be an open (complete and non-compact) manifold with $\mathrm{Ric}\ge 0$ and escape rate not $1/2$. It is known that under these conditions, the fundamental group $\pi_1(M)$ has a finitely generated torsion-free nilpotent subgroup…
A quantum field theory has finite zero-point energy if the sum over all boson modes $b$ of the $n$th power of the boson mass $ m_b^n $ equals the sum over all fermion modes $f$ of the $n$th power of the fermion mass $ m_f^n $ for $n= 0$, 2,…
In this paper is proposed a geometric solution to the dark energy, assuming that the space can be divided into regions of size $\sim L_{p}$ and energy $\sim E_{p}$. Significantly this assumption generate a energy density similar to the…
A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary…