Black holes in higher dimensional gravity theory with corrections quadratic in curvature
Abstract
Static spherically symmetric black holes are discussed in the framework of higher dimensional gravity with quadratic in curvature terms. Such terms naturally arise as a result of quantum corrections induced by quantum fields propagating in the gravitational background. We focus our attention on the correction of the form C^{2}=C_{αβγδ}C^{αβγδ}. The GaussBonnet equation in fourdimensional spacetime enables one to reduce this term in the action to the terms quadratic in the Ricci tensor and scalar curvature. As a result the Schwarzschild solution which is Ricci flat will be also a solution of the theory with the Weyl scalar C^{2} correction. An important new feature of the spaces with dimension D>4 is that in the presence of the Weyl curvaturesquared term a necessary solution differs from the corresponding “classical” vacuum Tangherlini metric. This difference is related to the presence of secondary or induced hair. We explore how the Tangherlini solution is modified by “quantum corrections,” assuming that the gravitational radius r_{0} is much larger than the scale of the quantum corrections. We also demonstrated that finding a general solution beyond the perturbation method can be reduced to solving a single third order ordinary differential equation (master equation).
 Publication:

Physical Review D
 Pub Date:
 August 2009
 DOI:
 10.1103/PhysRevD.80.044034
 arXiv:
 arXiv:0907.1411
 Bibcode:
 2009PhRvD..80d4034F
 Keywords:

 04.50.h;
 04.60.Bc;
 04.70.s;
 97.60.Lf;
 Higherdimensional gravity and other theories of gravity;
 Phenomenology of quantum gravity;
 Physics of black holes;
 Black holes;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 12 pages, 4 figures. A few references added, some details added to better illustrate the result. Version accepted in Physical Review D