Phys. Rev. D 94, 124025 (2016) Recently, a fully covariant version of the theory of $F(T)$ torsion gravity
has been introduced (arXiv:1510.08432v2 gr-qc). In covariant $F(T)$ gravity
the ...Schwarzschild solution is not a vacuum solution for $F(T)\neq T$ and
therefore determining the spherically symmetric vacuum is an important open
problem. Within the covariant framework we perturbatively solve the spherically
symmetric vacuum gravitational equations around the Schwarzschild solution for
the scenario with $F(T)=T + (\alpha/2)\, T^{2}$, representing the dominant
terms in theories governed by Lagrangians analytic in the torsion scalar. From
this we compute the perihelion shift correction to solar system planetary
orbits as well as perturbative gravitational effects near neutron stars. This
allows us to set an upper bound on the magnitude of the coupling constant,
$\alpha$, which governs deviations from General Relativity. We find the bound
on this nonlinear torsion coupling constant by specifically considering the
uncertainty in the perihelion shift of Mercury. We also analyze a bound from a
similar comparison with the periastron orbit of the binary pulsar PSR
J0045-7319 as an independent check for consistency. Setting bounds on the
dominant nonlinear coupling is important in determining if other effects in the
solar system or greater universe could be attributable to nonlinear torsion.
We propose a novel type of ergostats and thermostats for molecular dynamics simulations. A general class of active particle swarm models is considered, where any specific total energy (alternatively ...any specific temperature) can be provided at a fixed point of the evolution of the swarm. We identify the extended system feedback force of the Nosé - Hoover thermostat with the "internal energy" variable of active Brownian motion.
Recently, a fully covariant version of the theory of \(F(T)\) torsion gravity has been introduced (arXiv:1510.08432v2 gr-qc). In covariant \(F(T)\) gravity the Schwarzschild solution is not a vacuum ...solution for \(F(T)\neq T\) and therefore determining the spherically symmetric vacuum is an important open problem. Within the covariant framework we perturbatively solve the spherically symmetric vacuum gravitational equations around the Schwarzschild solution for the scenario with \(F(T)=T + (\alpha/2)\, T^{2}\), representing the dominant terms in theories governed by Lagrangians analytic in the torsion scalar. From this we compute the perihelion shift correction to solar system planetary orbits as well as perturbative gravitational effects near neutron stars. This allows us to set an upper bound on the magnitude of the coupling constant, \(\alpha\), which governs deviations from General Relativity. We find the bound on this nonlinear torsion coupling constant by specifically considering the uncertainty in the perihelion shift of Mercury. We also analyze a bound from a similar comparison with the periastron orbit of the binary pulsar PSR J0045-7319 as an independent check for consistency. Setting bounds on the dominant nonlinear coupling is important in determining if other effects in the solar system or greater universe could be attributable to nonlinear torsion.
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 \(\alpha\).
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.
Within the framework of the extended teleparallel gravity, a new class of boson stars has recently been constructed by introducing the nonminimal coupling of the scalar field to the torsion scalar. ...An interesting feature of these static, spherical, self-gravitating configurations of the massive complex scalar field is their central region with outwardly increasing energy density, surrounded by a thick shell within which the joining with the usual asymptotically Schwarzschild tail takes place. In this work we extend the original model with the \(U(1)\) gauge field and we find that the combined effect of the charge and coupling of the field to torsion leads to a significant increase of the maximal mass and the particle number that can be supported against gravity. We also show that some charged configurations preserve the property of having the outwardly increasing energy density over the central region, regardless of the fact that charging the configurations affects the anisotropy of the pressures in the opposite way relative to that of the field-to-torsion coupling terms.
We study the nonminimally coupled complex scalar field within the framework of teleparallel gravity. Coupling of the field nonminimally to the torsion scalar destroys the Lorentz invariance of the ...theory in the sense that the resulting equations of motion depend on the choice of a tetrad. For the assumed static spherically symmetric spacetime, we find a tetrad which leads to a self-consistent set of equations, and we construct the self-gravitating configurations of the scalar field---boson stars. The resulting configurations develop anisotropic principal pressures and satisfy the dominant energy condition. An interesting property of the configurations obtained with sufficiently large field-to-torsion coupling constant is the outwardly increasing energy density, followed by an abrupt drop towards the usual asymptotic tail. This feature is not present in the boson stars with the field minimally or nonminimally coupled to the curvature scalar, and therefore appears to be a torsion--only effect.
Radial stability of the continuous pressure gravastar is studied using the conventional Chandrasekhar method. The equation of state for the static gravastar solutions is derived and Einstein ...equations for small perturbations around the equilibrium are solved as an eigenvalue problem for radial pulsations. Within the model there exist a set of parameters leading to a stable fundamental mode, thus proving radial stability of the continuous pressure gravastar. It is also shown that the central energy density possesses an extremum in rho_c(R) curve which represents a splitting point between stable and unstable gravastar configurations. As such the rho_c(R) curve for the gravastar mimics the famous M(R) curve for a polytrope. Together with the former axial stability calculations this work completes the stability problem of the continuous pressure gravastar.
We consider the gravastar model where the vacuum phase transition between the de Sitter interior and the Schwarzschild or Schwarzschild-de Sitter exterior geometries takes place at a single spherical ...delta-shell. We derive sharp analytic bounds on the surface compactness (2m/r) that follow from the requirement that the dominant energy condition (DEC) holds at the shell. In the case of Schwarzschild exterior, the highest surface compactness is achieved with the stiff shell in the limit of vanishing (dark) energy density in the interior. In the case of Schwarzschild-de Sitter exterior, in addition to the gravastar configurations with the shell under surface pressure, gravastar configurations with vanishing shell pressure (dust shells), as well as configurations with the shell under surface tension, are allowed by the DEC. Respective bounds on the surface compactness are derived for all cases. We also consider the speed of sound on the shell as derived from the requirement that the shell is stable against the radial perturbations. The causality requirement (sound speed not exceeding that of light) further restricts the space of allowed gravastar configurations.
A static, spherically symmetric, asymptotically flat spacetime may allow for circular, closed null-geodesics which are said to belong to a photon sphere. In the context of gravitational lensing in ...the strong deflection regime, the presence of a photon sphere leads to an unbounded angle of deflection of light (multiple turns) and formation of relativistic images. In this paper, we show that photon spheres may form in some configurations of boson stars constructed with a free massive complex scalar field nonminimally coupled to gravity. Assuming that the boson star is transparent to light, photon spheres would give raise not only to phenomena in the realm of strong gravitational lensing, but also to considerably increased photon flux in the central region of the star, relative to the flux in its surroundings.
