Focusing versus defocusing properties of truly naked black holes

We study the properties of the congruence of null geodesics propagating near the so-called truly naked horizons (TNH) - objects having finite Kretschmann scalar but with diverging tidal acceleration for freely falling observers. The expansion of outgoing rays near the future horizon always tends to vanish for the non-extremal case but may be non-zero for the distorted (ultra)extremal one. It tends to diverge for the ingoing ones if the the null energy condition (NEC) is satisfied in the vicinity of the horizon outside. However, it also tends to zero for NEC violating cases except the remote horizons. We also discuss the validity of test particle approximation for TNHs and find the sufficient condition for backreaction remaining small.Comment: 16 pages. To appear in IJMP

Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we prove that the only types of the stationary planar solutions in the model are either of translational or axial symmetry of the flow. Within the proposed model we differentiate between finite and infinite flocking behavior by the finiteness of the kinetic energy functional.Comment: 12 pages, 1 figur

Spacetime thermodynamics without hidden degrees of freedom

A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.Comment: 12 pages, 1 figur

Stability properties and topology at infinity of f-minimal hypersurfaces

We study stability properties of $f$-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li-Tam theory, we investigate the topology at infinity of $f$-minimal hypersurfaces. On the way, we prove a new comparison result in weighted geometry and we provide a general weighted $L^1$-Sobolev inequality for hypersurfaces in Cartan-Hadamard weighted manifolds, satisfying suitable restrictions on the weight function.Comment: 30 pages. Final version: to appear on Geom. Dedicat

Confronting Finite Unified Theories with Low-Energy Phenomenology

Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite. The requirement of all-loop finiteness leads to a severe reduction of the free parameters of the theory and, in turn, to a large number of predictions. FUTs are investigated in the context of low-energy phenomenology observables. We present a detailed scanning of the all-loop finite SU(5) FUTs, where we include the theoretical uncertainties at the unification scale and we apply several phenomenological constraints. Taking into account the restrictions from the top and bottom quark masses, we can discriminate between different models. Including further low-energy constraints such as B physics observables, the bound on the lightest Higgs boson mass and the cold dark matter density, we determine the predictions of the allowed parameter space for the Higgs boson sector and the supersymmetric particle spectrum of the selected model.Comment: 25 pages, 8 figures. Discussion on models and on cold dark matter constraint extended, references added. Version to appear in JHE