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Register a new userOn the Hoop conjecture in Einstein gravity coupled to nonlinear electrodynamics
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The famous hoop conjecture by Thorne has been claimed to be violated in curved spacetimes coupled to linear electrodynamics. Hod cite{Hod:2018} has recently refuted this claim by clarifying the status and validity of the conjecture appropriately interpreting the gravitational mass parameter $M$. However, it turns out that partial violations of the conjecture might seemingly occur also in the well known regular curved spacetimes of gravity coupled to textit{nonlinear electrodynamic}s. Using the interpretation of $M$ in a generic form accommodating nonlinear electrodynamic coupling, we illustrate a novel extension that the hoop conjecture is textit{not} violated even in such curved spacetimes. We introduce a Hod function summarizing the hoop conjecture and find that it surprisingly encapsulates the transition regimes between horizon and no horizon across the critical values determined essentially by the concerned curved geometries.
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We consider a closed region $R$ of 3d quantum space modeled by $SU(2)$ spin-networks. Using the concentration of measure phenomenon we prove that, whenever the ratio between the boundary $partial R$ and the bulk edges of the graph overcomes a finite threshold, the state of the boundary is always thermal, with an entropy proportional to its area. The emergence of a thermal state of the boundary can be traced back to a large amount of entanglement between boundary and bulk degrees of freedom. Using the dual geometric interpretation provided by loop quantum gravity, we interprete such phenomenon as a pre-geometric analogue of Thornes Hoop conjecture, at the core of the formation of a horizon in General Relativity.
We obtain a class of regular black hole solutions in four-dimensional $f(R)$ gravity, $R$ being the curvature scalar, coupled to a nonlinear electromagnetic source. The metric formalism is used and static spherically symmetric spacetimes are assumed. The resulting $f(R)$ and nonlinear electrodynamics functions are characterized by a one-parameter family of solutions which are generalizations of known regular black holes in general relativity coupled to nonlinear electrodynamics. The related regular black holes of general relativity are recovered when the free parameter vanishes, in which case one has $f(R)propto R$. We analyze the regularity of the solutions and also show that there are particular solutions that violate only the strong energy condition
In this work we explore the possible existence of static, spherically symmetric and stationary, axisymmetric traversable wormholes coupled to nonlinear electrodynamics. Considering static and spherically symmetric (2+1) and (3+1)-dimensional wormhole spacetimes, we verify the presence of an event horizon and the non-violation of the null energy condition at the throat. For the former spacetime, the principle of finiteness is imposed, in order to obtain regular physical fields at the throat. Next, we analyze the (2+1)-dimensional stationary and axisymmetric wormhole, and also verify the presence of an event horizon, rendering the geometry non-traversable. Relatively to the (3+1)-dimensional stationary and axisymmetric wormhole geometry, we find that the field equations impose specific conditions that are incompatible with the properties of wormholes. Thus, we prove the non-existence of the general class of traversable wormhole solutions, outlined above, within the context of nonlinear electrodynamics.
We explore the possibility of dynamic wormhole geometries, within the context of nonlinear electrodynamics. The Einstein field equation imposes a contracting wormhole solution and the obedience of the weak energy condition. Furthermore, in the presence of an electric field, the latter presents a singularity at the throat, however, for a pure magnetic field the solution is regular. Thus, taking into account the principle of finiteness, that a satisfactory theory should avoid physical quantities becoming infinite, one may rule out evolving wormhole solutions, in the presence of an electric field, coupled to nonlinear electrodynamics.
A dynamically transversely trapping surface (DTTS) is a new concept of an extension of a photon sphere that appropriately represents a strong gravity region and has close analogy with a trapped surface. We study formation of a marginally DTTS in time-symmetric, conformally flat initial data with two black holes, with a spindle-shaped source, and with a ring-shaped source, and clarify that $mathcal{C}lesssim 6pi GM$ describes the condition for the DTTS formation well, where $mathcal{C}$ is the circumference and $M$ is the mass of the system. This indicates that an understanding analogous to the hoop conjecture for the horizon formation is possible. Exploring the ring system further, we find configurations where a marginally DTTS with the torus topology forms inside a marginally DTTS with the spherical topology, without being hidden by an apparent horizon. There also exist configurations where a marginally trapped surface with the torus topology forms inside a marginally trapped surface with the spherical topology, showing a further similarity between DTTSs and trapped surfaces.
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