On the internal state of the Schwarzschild black hole

Abstract

If the classical gravitational Lagrangian contains higher-derivative terms [Formula: see text], where [Formula: see text], then vacuum solutions of the Einstein–Hilbert theory [Formula: see text] are subject to modification at sufficiently large spacetime curvatures. Previously, we have calculated the effective energy–momentum tensor [Formula: see text] due to the quartic gravitational terms [Formula: see text] of the heterotic superstring theory in the four-dimensional background spacetime of the Schwarzschild black hole, obtaining an expression which satisfies the strong energy condition, and thereby suggests that the [Formula: see text] might not remove the central singularity. This conjecture was put forward from a different viewpoint by Horowitz and Myers, who argued that a non-singular black-hole interior resulting from the [Formula: see text] would be unstable, necessitating reappraisal of the notion of a singular interior spacetime. Here, we show that the chief features of the solution can be simulated by a Bardeen-type ansatz, assuming the spherically symmetric line element [Formula: see text], where [Formula: see text], which, when [Formula: see text], can explain heuristically why [Formula: see text] in the shell region [Formula: see text] of a macroscopic black hole for which [Formula: see text], while [Formula: see text] remains finite at [Formula: see text].