On the internal state of the Schwarzschild black hole

If the classical gravitational Lagrangian contains higher-derivative terms R-m, where m >= 2, then vacuum solutions of the Einstein-Hilbert theory L-0 = -R/2 kappa(2) are subject to modification at sufficiently large spacetime curvatures. Previously, we have calculated the effective energy-momentum tensor S-ij due to the quartic gravitational terms alpha R-'3(4) 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 Rm 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 R-m 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 ds(2) = e(lambda(r)) dt(2) - e(-lambda(r)) dr(2) - r(2)(d theta(2) + sin(2) theta d phi(2)), where e(lambda(r)) = 1 - 2Mr(n(r)) / (r(2) + r(0)(2))([ n(r)+1]/2) , which, when S-i(j) similar to r(-12), can explain heuristically why S-0(0), S-1(1) < 0 in the shell region kappa M-4/3(1/3) << r << kappa M-2/4 pi of a macroscopic black hole for which kappa M >> 1, while root-gS(i)(j) remains finite at r = 0.