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Register a new userRotating metric in Non-Singular Infinite Derivative Theories of Gravity
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Added by
Gerhard Harmsen Mr.
Publication date
2017
fields
Physics
and research's language is
English
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In this paper we will provide a non-singular rotating space time metric for a ghost free infinite derivative theory of gravity. We will provide the predictions for the Lense-Thirring effect for a slowly rotating system, and how it is compared with that from general relativity.
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We present the most general quadratic curvature action with torsion including infinite covariant derivatives and study its implications around the Minkowski background via the Palatini approach. Provided the torsion is solely given by the background axial field, the metric and torsion are shown to decouple, and both of them can be made ghost and singularity free for a fermionic source.
In this paper we will construct a linearized metric solution for an electrically charged system in a {it ghost-free} infinite derivative theory of gravity which is valid in the entire region of spacetime. We will show that the gravitational potential for a point-charge with mass $m$ is non-singular, the Kretschmann scalar is finite, and the metric approaches conformal-flatness in the ultraviolet regime where the non-local gravitational interaction becomes important. We will show that the metric potentials are bounded below one as long as two conditions involving the mass and the electric charge are satisfied. Furthermore, we will argue that the cosmic censorship conjecture is not required in this case. Unlike in the case of Reissner-Nordstrom in general relativity, where $|Q|leq m/M_p$ has to be always satisfied, in {it ghost-free} infinite derivative gravity $|Q|>m/M_p$ is also allowed, such as for an electron.
The vacuum solution of Einsteins theory of general relativity provides a rotating metric with a ring singularity, which is covered by the inner and outer horizons, and an ergo region. In this paper, we will discuss how ghost-free, quadratic curvature, Infinite Derivative Gravity (IDG) may resolve the ring singularity. In IDG the non-locality of the gravitational interaction can smear out the delta-Dirac source distribution by making the metric potential finite everywhere including at $r=0$. We show that the same feature also holds for a rotating metric. We can resolve the ring singularity such that no horizons are formed in the linear regime by smearing out a delta-source distribution on a ring. We will also show that the Kerr-metric does not solve the full non-linear equations of motion of ghost-free quadratic curvature IDG.
In literature there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress-energy momentum tensor $T=T_{mu}^{mu}$. This type of modified gravity is called as $f(R,T)$ in which $R$ is Ricci scalar $R=R_{mu}^{mu}$. We extend manifestly this model to include the higher derivative term $Box R$. We derived equation of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter solution is unstable for a generic type of $f(R,Box R, T)$ model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.
We consider static and cylindrically symmetric interior string type solutions in the scalar-tensor representation of the hybrid metric-Palatini modified theory of gravity. As a first step in our study, we obtain the gravitational field equations and further simplify the analysis by imposing Lorentz invariance along the $t$ and $z$ axes, which reduces the number of unknown metric tensor components to a single function $W^2(r)$. In this case, the general solution of the field equations can be obtained, for an arbitrary form of the scalar field potential, in an exact closed parametric form, with the scalar field $phi$ taken as a parameter. We consider in detail several exact solutions of the field equations, corresponding to a null and constant potential, and to a power-law potential of the form $V(phi)=V_0phi ^{3/4}$, in which the behaviors of the scalar field, of the metric tensor components and of the string tension can be described in a simple mathematical form. We also investigate the string models with exponential and Higgs type scalar field potentials by using numerical methods. In this way we obtain a large class of novel stable string-like solutions in the context of hybrid metric-Palatini gravity, in which the basic parameters, such as the scalar field, metric tensor components, and string tension, depend essentially on the initial values of the scalar field, and of its derivative, on the $r=0$ circular axis.
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