Conformally-flat, non-singular static metric in infinite derivative gravity

Abstract

In 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 infinite 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 effective scale of non-locality. arXiv:1804.08195v2 [gr-qc]

Testing the nature of dark compact objects: a status report

“…[278][279][280][281][282]. Recently, a quantum mechanical framework to describe astrophysical, horizonless objects devoid of curvature singularities was put forward in the context of nonlocal gravity (arising from infinite derivative gravity) [246,283,284]. The corresponding stars can be ultracompact, although never reaching the ClePhO category.…”

Finite entanglement entropy of black holes

“…Notice, that the content of this section is general and independent on the particular solution as long as it shows an event horizon. Therefore, we can for example apply our analysis to any black hole solution, singular [44] or singularity-free [33][34][35][36][37][38][39][40][41][42][43]. Moreover, as we remarked in the introduction, our results can be easily exported to local higher derivative theories [60,75], where in the conditions stipulated above, we are sure that the Schwarzschild metric is an exact black hole solution.…”

“…In section II we briefly introduce a class of weakly non-local theories of gravity, which are unitary (ghost-free) and perturbatively super-renormalizable or finite in the quantum field theory framework [9][10][11][12][13][14][15][16][17][18][19][20][21][22]. At classical level evidences endorse that we are dealing with "singularity-free gravitational " the-ories [33][34][35][36][37][38][39][40][41] (see also the recent papers [42,43]). However, the Einstein spaces seem still to be exact solutions of the nonlocal theory [44,45], although it is still a debated open problem what kind of energy tensor could source such spacetimes in a non-local theory [46].…”

Generalized ghost-free propagators in nonlocal field theories

“…[20] for a more general treatment including some non-maximally symmetric spacetime. It was also noticed that the presence of nonlocality can regularize infinities and many efforts have been made towards the resolution of black hole [17,18,[21][22][23][24][25][26][27][28][29][30][31][32][33] and cosmological [16,[34][35][36][37] singularities. At the quantum level, the high energy behavior of loop integrals has been investigated in [38][39][40][41] and properties of causality and unitarity in [42,43] and [44][45][46][47], respectively.…”