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Register a new userEffective delta sources and regularity in higher-derivative and ghost-free gravity
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It is shown that polynomial gravity theories with more than four derivatives in each scalar and tensor sectors have a regular weak-field limit, without curvature singularities. This is achieved by proving that in these models the effect of the higher derivatives can be regarded as a complete regularization of the delta-source. We also show how this result implies that a wide class of non-local ghost-free gravities have a regular Newtonian limit too, and discuss the applicability of this approach to the case of weakly non-local models.
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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.
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 manuscript we will present the theoretical framework of the recently proposed infinite derivative theory of gravity with a non-symmetric connection. We will explicitly derive the field equations at the linear level and obtain new solutions with a non-trivial form of the torsion tensor in the presence of a fermionic source, and show that these solutions are both ghost and singularity-free.
In the present work we investigate the Newtonian limit of higher-derivative gravity theories with more than four derivatives in the action, including the non-analytic logarithmic terms resulting from one-loop quantum corrections. The first part of the paper deals with the occurrence of curvature singularities of the metric in the classical models. It is shown that in the case of local theories, even though the curvature scalars of the metric are regular, invariants involving derivatives of curvatures can still diverge. Indeed, we prove that if the action contains $2n+6$ derivatives of the metric in both the scalar and the spin-2 sectors, then all the curvature-derivative invariants with at most $2n$ covariant derivatives of the curvatures are regular, while there exist scalars with $2n+2$ derivatives that are singular. The regularity of all these invariants can be achieved in some classes of nonlocal gravity theories. In the second part of the paper, we show that the leading logarithmic quantum corrections do not change the regularity of the Newtonian limit. Finally, we also consider the infrared limit of these solutions and verify the universality of the leading quantum correction to the potential in all the theories investigated in the paper.
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.
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