Zipoy-Voorhees Gravitational Object as a Source of High-Energy Relativistic Particles

The Zipoy-Voorhees solution is known as the γ-metric and/or q-metric being static and axisymmetric vacuum solution of Einstein field equations which becomes strong curvature naked singularity. The metric is characterized by two parameters, namely, the mass M and the dimensionless deformation parameter γ. It is shown that the velocity of test particle orbiting around the central γ-object can reach the speed of light, consequently, the total energy of the particle will be very high for a specific value the deformation parameter of the spacetime. It is also shown that causality problem arises in the interior region of the physical singularity for the specific value of the deformation parameter when test particles can move with superluminal velocity being greater than the speed of light that might be an additional tool for explaining the existence of tachyons for γ>1/2 which are invisible for an observer.

Can Naked Singularities Exist Without Violating The Laws of Black Hole Thermodynamics?

According to the cosmic censorship conjecture, it is impossible for nature to have a physical singularity without a horizon because if it were to arise in any formalism, for instance as an extremal black hole (Kerr or Reissner-Nordstrom) then the surface gravity κ = 0, which is a strict violation of the third law of black hole thermodynamics. In this paper we explore whether a true singularity can exist without defying this law.

Could the black hole singularity be a field singularity?

In the wake of interest to find black hole solutions with scalar hair, we investigate the effects of disformal transformations on static spherically symmetric spacetimes with a nontrivial scalar field. In particular, we study solutions that have a singularity in a given frame, while the action is regular. We ask if there exists a different choice of field variables such that the geometry and the fields are regular. We find that in some cases disformal transformations can remove a singularity from the geometry or introduce a new horizon. This is possible since the Weyl tensor is not invariant under a general disformal transformation. There exists a class of metrics which can be brought to Minkowksi geometry by a disformal transformation, which may be called disformally flat metrics. We investigate three concrete examples from massless scalar fields to Horndeski theory for which the singularity can be removed from the geometry. This might indicate that no physical singularity is present. We also propose a disformal invariant tensor.

Black holes

Black holes are introduced as solutions of Einsteins equations contain-ing a physical singularity covered by an event horizon. The properties of Schwarzschild and of Kerr black holes are examined. It is demonstrated that the event horizon of a black hole can only increase within classical physics. However, the event horizon is an infinite redshift surface and emits in the semi-classical picture thermal radiation. This Hawking radiation leads in turn to the information paradox.

Maximal acceleration and radiative processes

We derive the radiation characteristics of an accelerated, charged particle in a model due to Caianiello in which the proper acceleration of a particle of mass [Formula: see text] has the upper limit [Formula: see text]. We find two power laws, one applicable to lower accelerations, the other more suitable for accelerations closer to [Formula: see text] and to the related physical singularity in the Ricci scalar. Geometrical constraints and power spectra are also discussed. By comparing the power laws due to the maximal acceleration (MA) with that for particles in gravitational fields, we find that the model of Caianiello allows, in principle, the use of charged particles as tools to distinguish inertial from gravitational fields locally.

Spherically symmetric vacuum solutions arising from trace dynamics modifications to gravitation

We derive the equations governing static, spherically symmetric vacuum solutions to the Einstein equations, as modified by the frame-dependent effective action (derived from trace dynamics) that gives an alternative explanation of the origin of "dark energy". We give analytic and numerical results for the solutions of these equations, first in polar coordinates, and then in isotropic coordinates. General features of the static case are that: (i) there is no horizon, since g00 is nonvanishing for finite values of the polar radius, and only vanishes (in isotropic coordinates) at the internal singularity, (ii) the Ricci scalar R vanishes identically, and (iii) there is a physical singularity at cosmological distances. The large distance singularity may be an artifact of the static restriction, since we find that the behavior at large distances is altered in a time-dependent solution using the McVittie Ansatz.

SINGULARITY STRUCTURE OF ${\mathcal N} = 2$ SUPERSYMMETRIC YANG–MILLS THEORIES

In this paper, we consider the case where electrons, magnetic monopoles and dyons become massless. Here, we consider the [Formula: see text] supersymmetric Yang–Mills (SYM) theories with classical gauge groups with a rank r, SU(r+1), SO(2r), Sp(2r) and SO(2r+1) which are studied by Riemann surfaces called Seiberg–Witten curves. We discuss physical singularity associated with massless particles, which can be studied by geometric singularity of vanishing 1-cycles in Riemann surfaces in hyperelliptic form. We pay particular attention to the cases where mutually nonlocal states become massless (Argyres–Douglas theories), which corresponds to Riemann surfaces degenerating into cusps. We discuss nontrivial topology on the moduli space of the theory, which is reflected as monodromy associated to vanishing 1-cycles. We observe how dyon charges get changed as we move around and through singularity in moduli space.

EXTENDED CRITICAL SITUATIONS: THE PHYSICAL SINGULARITY OF LIFE PHENOMENA

In this paper, we propose to consider living systems as "coherent critical structures," though extended in space and time, their unity being ensured through global causal relations between levels of organization (integration/regulation). This may be seen as a further contribution to the large amount of work already done on the theme of self-organized criticality. More precisely, our main physical paradigm is provided by the analysis of "phase transitions," as this peculiar form of critical state presents interesting aspect of emergence: the formation of extended correlation lengths and coherence structures, the divergence of some observables with respect to the control parameter(s), etc…. However, the "coherent critical structures" which are the main focus of our work cannot be reduced to existing physical approaches, since phase transitions, in physics, are treated as "singular events," corresponding to a specific well-defined value of the control parameter. Whereas our claim is that in the case of living systems, these coherent critical structures are "extended" and organized in such a way that they persist in space and time. The relation of this concept to the theory of autopoiesis, as well as to various forms of teleonomy, often present in biological analyses, will be also discussed.