Quadratic gravity and the black-hole singularity

Details Quadratic gravity and the black-hole singularity Quadratic gravity and the black-hole singularity

Jun 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991phrvd..43.3923p&link_type=abstract

Physical Review D (Particles and Fields), Volume 43, Issue 12, 15 June 1991, pp.3923-3928

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2

Black Holes

Scientific paper

It is rather natural in the context of semiclassical, or first-order quantum, corrections to general relativity to consider an effective theory in which the Lagrangian consists of the Hilbert-Einstein term, linear in curvature, and correction terms quadratic in curvature, with coefficients typically of the order of the Planck length squared. Given such a candidate for a semiclassical theory, it is interesting to ask whether the simulated quantum effects can help reduce the strength of curvature near classical singularities, in particular, those found in the interior of black holes. In this article, I shall examine the effects on the Schwarzschild singularity of a particular semiclassical model based on the Gauss-Bonnet quadratic combination, in a spacetime possessing more than four dimensions. In this model, the field equations are nontrivial and consist of a system of second-order differential equations for the metric tensor (any other combination would yield fourth-order equations). The results depend strongly on the overall sign of the quadratic term: for positive coupling, as dictated by string theory, the singularity occurs sooner than in the classical description; for negative coupling, the model breaks down because the radius of the compactified space is forced to collapse to zero for some nonvanishing value of the radial coordinate.

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