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Advisor(s)
Abstract(s)
It 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.
Description
Keywords
General relativity Infinite derivative gravity
Citation
Publisher
American Physical Society