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- Conformally-flat, non-singular static metric in infinite derivative gravityPublication . Buoninfante, Luca; Koshelev, Alexey; Lambiase, Gaetano; Marto, João; Mazumdar, AnupamIn Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within in nite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the e efective scale of non-locality.
- Non-singular rotating metric in ghost-free infinite derivative gravityPublication . Buoninfante, Luca; Cornell, Alan; Harmsen, Gerhard; Koshelev, Alexey; Lambiase, Gaetano; Marto, João; Mazumdar, AnupamIt is well-known that the vacuum solution of Einstein's 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-type singularity in nature. It is well-known that a class of IDG actions admit linearized metric solutions which can avoid point-like singularity by a smearing process of the Delta-source distribution induced by non-locality, which makes the metric potential finite everywhere including at $r=0$, and even at the non-linear level may resolve the Schwarzschild singularity. The same action can also resolve the ring singularity in such a way that no horizons are formed in the linear regime, where in this case non-locality plays a crucial role in smearing out a delta-source distribution on a ring. We will also study the full non-linear regime. First, we will argue that the presence of non-local gravitational interaction will not allow the Kerr metric as an exact solution, as there are infinite order derivatives acting on the theta-Heaviside and the delta-Dirac distributions on a ring. Second, we will explicitly show that the Kerr-metric is not a pure vacuum solution when the Weyl squared term, with a non-constant form-factor, is taken into account in the action.
- Schwarzschild 1/r-singularity is not permissible in ghost free quadratic curvature infinite derivative gravityPublication . Koshelev, Alexey; Marto, João; Mazumdar, AnupamIn this paper we will study the complete equations of motion for a ghost free quadratic curvature infinite derivative gravity. We will argue that within the scale of non-locality, Schwarzschild-type singular metric solution is not permissible. Therefore, Schwarzschild-type vacuum solution which is a prediction in Einstein-Hilbert gravity may not persist within the region of non-locality. We will also show that just quadratic curvature gravity, without infinite derivatives, always allows Schwarzschild-type singular metric solution.