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Register a new userSelf-Gravitating Spherically Symmetric Solutions in Scalar-Torsion Theories
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We studied spherically symmetric solutions in scalar-torsion gravity theories in which a scalar field is coupled to torsion with a derivative coupling. We obtained the general field equations from which we extracted a decoupled master equation, the solution of which leads to the specification of all other unknown functions. We first obtained an exact solution which represents a new wormhole-like solution dressed with a regular scalar field. Then, we found large distance linearized spherically symmetric solutions in which the space asymptotically is AdS.
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We search for self tuning solutions to the Einstein-scalar field equations for the simplest class of `Fab-Four models with constant potentials. We first review the conditions under which self tuning occurs in a cosmological spacetime, and by introducing a small modification to the original theory - introducing the second and third Galileon terms - show how one can obtain de Sitter states where the expansion rate is independent of the vacuum energy. We then consider whether the same self tuning mechanism can persist in a spherically symmetric inhomogeneous spacetime. We show that there are no asymptotically flat solutions to the field equations in which the vacuum energy is screened, other than the trivial one (Minkowski space). We then consider the possibility of constructing Schwarzschild de Sitter spacetimes for the modified Fab Four plus Galileon theory. We argue that the only model that can successfully screen the vacuum energy in both an FLRW and Schwarzschild de Sitter spacetime is one containing `John $sim G^{mu}{}_{ u} partial_{mu}phipartial^{ u}phi$ and a canonical kinetic term $sim partial_{alpha}phi partial^{alpha}phi$. This behaviour was first observed in (Babichev&Charmousis,2013). The screening mechanism, which requires redundancy of the scalar field equation in the `vacuum, fails for the `Paul term in an inhomogeneous spacetime.
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.
We study standard Einstein-Maxwell theory minimally coupled to a complex valued and self-interacting scalar field. We demonstrate that new, previously unnoticed spherically symmetric, charged black hole solutions with scalar hair exist in this model for sufficiently large gravitational coupling and sufficiently small electromagnetic coupling. The novel scalar hair has the form of a spatially oscillating wave packet and back-reacts on the space-time such that both the Ricci and the Kretschmann scalar, respectively, possess qualitatively similar oscillations.
We consider the Einstein-Dirac field equations describing a self-gravitating massive neutrino, looking for axially-symmetric exact solutions; in the search of general solutions, we find some that are specific and which have critical features, such as the fact that the space-time curvature turns out to be flat and the spinor field gives rise to a vanishing bi-linear scalar $overline{psi}psi=0$ with non-vanishing bi-linear pseudo-scalar $ioverline{psi}gamma^5psi ot=0$: because in quantum field theory general computational methods are built on plane-wave solutions, for which bi-linear pseudo-scalar vanishes while the bi-linear scalar does not vanish, then the solutions we found cannot be treated with the usual machinery of quantum field theory. This means that for the Einstein-Dirac system there exist admissible solutions which nevertheless cannot be quantized with the common prescriptions; we regard this situation as yet another issue of tension between Einstein gravity and quantum principles. Possible ways to quench this tension can be seen either in enlarging the validity of quantum field theory or by restricting the space of the solutions of the Einstein-Dirac system of field equations.
We present a detailed study of the spherically symmetric solutions in Lorentz breaking massive gravity. There is an undetermined function $mathcal{F}(X, w_1, w_2, w_3)$ in the action of St{u}ckelberg fields $S_{phi}=Lambda^4int{d^4xsqrt{-g}mathcal{F}}$, which should be resolved through physical means. In the general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also play a crucial role in Lorentz breaking massive gravity. $mathcal{F}$ will satisfy the constraint equation $T_0^1=0$ from the spherically symmetric Einstein tensor $G_0^1=0$, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The St{u}ckelberg field $phi^i$ is taken as a hedgehog configuration $phi^i=phi(r)x^i/r$, whose stability is guaranteed by the topological one. Under this ans{a}tz, $T_0^1=0$ is reduced to $dmathcal{F}=0$. The functions $mathcal{F}$ for $dmathcal{F}=0$ form a commutative ring $R^{mathcal{F}}$. We obtain a general expression of solution to the functional differential equation with spherically symmetry if $mathcal{F}in R^{mathcal{F}}$. If $mathcal{F}in R^{mathcal{F}}$ and $partialmathcal{F}/partial X=0$, the functions $mathcal{F}$ form a subring $S^{mathcal{F}}subset R^{mathcal{F}}$. We show that the metric is Schwarzschild, AdS or dS if $mathcal{F}in S^{mathcal{F}}$. When $mathcal{F}in R^{mathcal{F}}$ but $mathcal{F} otin S^{mathcal{F}}$, we will obtain some new metric solutions. Using the general formula and the basic property of function ring $R^{mathcal{F}}$, we give some analytical examples and their phenomenological applications. Furthermore, we also discuss the stability of gravitational field by the analysis of Komar integral and the results of QNMs.
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