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Black holes in six-dimensional conformal gravity

H. Lü1, Yi Pang2, and C. N. Pope2,3

  • 1Department of Physics, Beijing Normal University, Beijing 100875, China
  • 2George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, Texas 77843, USA
  • 3Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge University, Wilberforce Road, Cambridge CB3 OWA, United Kingdom

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Phys. Rev. D 87, 104013 – Published 10 May, 2013

DOI: https://doi.org/10.1103/PhysRevD.87.104013

Abstract

We study conformally invariant theories of gravity in six dimensions. In four dimensions, there is a unique such theory that is polynomial in the curvature and its derivatives, namely, Weyl-squared, and furthermore all solutions of Einstein gravity are also solutions of the conformal theory. By contrast, in six dimensions there are three independent conformally invariant polynomial terms one could consider. There is a unique linear combination (up to overall scale) for which Einstein metrics are also solutions, and this specific theory forms the focus of our attention in this paper. We reduce the equations of motion for the most general spherically symmetric black hole to a single fifth-order differential equation. We obtain the general solution in the form of an infinite series, characterized by five independent parameters, and we show how a finite three-parameter truncation reduces to the already known Schwarzschild-AdS metric and its conformal scaling. We derive general results for the thermodynamics and the first law for the full five-parameter solutions. We also investigate solutions in extended theories coupled to conformally invariant matter, and in addition we derive some general results for conserved charges in cubic-curvature theories in arbitrary dimensions.

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Phys. Rev. D 87, 104013– Published 10 May, 2013
  • Received 28 February 2013
Article part of CHORUS

© 2013 American Physical Society

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