Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity

TL;DR

This paper demonstrates that in ghost-free quadratic curvature infinite derivative gravity, Schwarzschild-like singular solutions are not allowed within the non-locality scale, contrasting with standard quadratic curvature gravity.

Contribution

It shows that non-locality in ghost-free quadratic curvature gravity prevents Schwarzschild singular solutions, unlike local quadratic curvature gravity.

Findings

Schwarzschild solutions are forbidden within the non-locality scale in ghost-free infinite derivative gravity.

Local quadratic curvature gravity admits Schwarzschild-type singular solutions.

Non-locality modifies the solution space, excluding classical singularities.

Abstract

In 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 {\it permissible}. Therefore, Schwarzschild-type vacuum solution which is a prediction in Einstein-Hilbert gravity may {\it 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.