In this paper we study properties that the vacuum must possess in the minimal extension to the teleparallel equivalent of general relativity (TEGR) where the action is supplemented with a quadratic ...torsion term. No assumption is made about the weakness of the quadratic term although in the weak-field regime the validity of our previously derived perturbative solution is confirmed. Regarding the exact nature of the vacuum, it is found that if the center of symmetry is to be regular, the mathematical conditions on the tetrad at the isotropy point mimic those of general relativity. With respect to horizons it is found that, under very mild assumptions, a smooth horizon cannot exist unless the quadratic torsion coupling, \(\alpha\), vanishes, which is the TEGR limit (with the Schwarzschild tetrad as its solution). This analysis is then supplemented with computational work utilizing asymptotically Schwarzschild boundary data. It is verified that in no case studied does a smooth horizon form. For \(\alpha > 0\) naked singularities occur which break down the equations of motion before a horizon can form. For \(\alpha < 0\) there is a limited range of \(\alpha\) where a vacuum horizon might exist but, if present, the horizon is singular. Therefore physically acceptable black hole horizons are problematic in the studied theory at least within the realm of vacuum static spherical symmetry. These results also imply that static spherical matter distributions generally must have extra restrictions on their spatial extent and stress-energy bounds so as to render the vacuum solution invalid in the singular region and make the solutions finite.
Solutions for the static spherically symmetric extremally charged dust in the Majumdar-Papapetrou system have been found. For a certain amount of the allocated mass and (or) charge, the solutions ...have singularities of a type that could render them physically unacceptable, since the corresponding physically relevant quantities are singular as well. These solutions, with a number of zero-nodes in the metric tensor, are regularized through the δ-shell formalism, thus redefining the mass and (or) charge distributions. The bifurcating behaviour of regular solutions found before is no longer present in these singular solutions, but quantized-like behaviour in the total mass is observed. The spectrum of regularized solutions restores the equality of the Tolman-Whittaker and Arnowitt-Deser-Misner (ADM) mass, as well the equality of the net charge and ADM mass, which is the distinctive feature of Majumdar-Papapetrou systems.PACS No.:04.40.Nr
Swarms with canonical active Brownian motion Glück, Alexander; Hüffel, Helmuth; Ilijić, Saša
Physical review. E, Statistical, nonlinear, and soft matter physics
83, Številka:
5 Pt 1
Journal Article
Odprti dostop
We present a swarm model of Brownian particles with harmonic interactions, where the individuals undergo canonical active Brownian motion, i.e., each Brownian particle can convert internal energy to ...mechanical energy of motion. We assume the existence of a single global internal energy of the system. Numerical simulations show amorphous swarming behavior as well as static configurations. Analytic understanding of the system is provided by studying stability properties of equilibria.
Within the paradigm of non-perturbative Einstein gravity we study continuous manifolds which possess de Sitter interiors and Kerr exteriors. These manifolds could represent the spacetime of rotating ...gravastars or other similar black hole mimickers. The scheme presented here allows for a \(C^{n}\) transition from the exactly de Sitter interior to the exactly Kerr exterior, with \(n\) arbitrarily large. Generic properties that such models must possess are discussed, such as the changing of the topology of the ergosphere from \(S^{2}\) to \(S^{1}\times S^{1}\). It is shown how in the outer layers of the transition region (the "atmosphere" as it is often called in astrophysics) the dominant/weak and strong energy conditions can be respected. However, much like in the case of its static spherically symmetric gravastar counterpart, there must be some assumptions imposed in the atmosphere for the energy conditions to hold. These assumptions turn out to not be severe. The class of manifolds presented here are expected to possess all the salient features of the fully generic case. Strictly speaking, a number of the results are also applicable to the locally anti-de Sitter core scenario, although we focus on the case of a positive cosmological constant.
Istražujemo regularizaciju rješenja za statičku sferno simetričnu potpuno nabijenu prašinu u Majumdar-Papapetrouovom sistemu. Rješenja u njihovim koordinatama pokazuju singularnosti. Te su ...singularnosti takve naravi da su rješenja fizikalno neprihvatljiva jer su važne fizičke veličine (metričke invarijante) također singularne. Ta se rješenja mogu regularizirati jednostavnom promjenom definicije raspodjela naboja/energije. Našli smo spektar rješenja s nekoliko nul-čvorova u metričkom tenzoru, i pokazali da se može postići njihova regularizacija bilo s δ sferom, ili s debelom sfernom raspodjelom tvari. Nestaje grananje regularnih rješenja, ali se za ukupnu masu pridruženu rješenjima opaža ponašanje slično kvantizaciji.
Raspetljavanje složenih spektara je obećavajuća metoda za proučavanje dvojnih zvjezdanih sustava. Ta metoda primjenjuje rutinu za razdvajanje kojom se izlučuje spektre zvijezda komponenata modela iz ...vremenskog niza opaženih složenih spektara. Usredotočujući se na razlike u pristupu pri izvedbi rutine za rastavljanje, uspoređujemo ograničenja koja iz njih proizlaze. Proveli smo ispitivanje s umjetnim podacima i zaključili da je rastavljanje u području valnih duljina svestranije u više pogleda, dok rastavljanje primjenom Fourierovog transformata dozvoljava rad s većim skupovima podataka, što je povoljno u potpunom procesu raspetljavanja složenih spektara.
In this paper we study the so called "warp drive" spacetimes within the \(U_{4}\) Riemann-Cartan manifolds of Einstein-Cartan theory. Specifically, the role that spin may play with respect to energy ...condition violation is considered. It turns out that with the addition of spin, the torsion terms in Einstein-Cartan gravity do allow for energy condition respecting warp drives. Limits are derived which minimize the amount of spin required in order to have a weak/null-energy condition respecting system. This is done both for the traditional Alcubierre warp drive as well as for the modified warp drive of Van Den Broeck which minimizes the amount of matter required for the drive. The ship itself is in a region of effectively vacuum and hence the torsion, which in Einstein-Cartan theory is localized in matter, does not affect the geodesic nature of the ship's trajectory. We also comment on the amount of spin and matter required in order for these conditions to hold.
Phys. Rev. D 98, 064047 (2018) We consider static spherically symmetric self-gravitating configurations of
the perfect fluid within the framework of the torsion-based extended theory of
gravity. In ...particular, we use the covariant formulation of $f(T)$ gravity with
$f(T) = T + \frac{\alpha}{2} T^2$, and for the fluid we assume the polytropic
equation of state with the adiabatic exponent $\Gamma = 2$. The constructed
solutions have a sharply defined radius as in General Relativity (GR) and can
be considered as models of nonrotating compact stars. The particle
number--to--stellar radius curves reveal that with positive (negative) values
of $\alpha$ smaller (greater) number of particles can be supported against
gravity then in GR. For the interpretation of the energy density and the
pressure within the star we adopt the GR picture where the effects due to
nonlinearity of $f(T)$ are seen as a $f(T)$ fluid, which together with the
polytropic fluid contributes to the effective energy momentum. We find that
sufficiently large positive $\alpha$ gives rise to an abrupt sign change (phase
transition) in the energy density and in the principal pressures of the $f(T)$
fluid, taking place within the interior of the star. The corresponding radial
profile of the effective energy density is approximately constant over the
central region of the star, mimicking an incompressible core. This interesting
phenomenon is not found in configurations with negative $\alpha$.
Phys. Rev. D 98, 064056 (2018) We consider extended covariant teleparallel $(f(T))$ gravity whose action is
analytic in the torsion scalar and which is sourced by an $su(2)$ valued
Yang-Mills field. ...Specifically, we search for regular solutions to the coupled
$f(T)$ Yang-Mills system. For $f(T)=T$ we, not surprisingly, recover the
Bartnik-McKinnon solitons of Einstein Yang-Mills theory. However, interesting
effects are discovered with the addition of terms in the action which are
nonlinear in the torsion scalar, which we specifically study up to cubic order.
With the addition of the nonlinear terms the number of regular solutions
becomes finite. As well, beyond critical values of the coupling constants we
find that there exist \emph{no} regular solutions. These behaviors are
asymmetric with respect to the sign of the nonlinear coupling constants and the
elimination of regular solutions turns out to be extremely sensitive to the
presence of the cubic coupling. It may be possible, therefore, that with
sufficiently high powers of torsion in the action, there may be no regular
Yang-Mills static solutions.
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