Universal black holes (Q2188573)

The (\(n+2\))-dimensional Schwarzschild spacetime has the Lorentzian metric \( g= - f(t) dt^2 + \frac{1}{f(t)} dr^2 + r^2 h \), where \(h\) is the metric of the \(n\)-dimensional sphere. In the paper under review, the authors consider a family of Schwarzschild-like metrics, by multiplying the previous metric on the (\(t,r\))-plane with a (positive) conformal factor function \(e^{a(r)}\), and by relaxing the hypothesis on \(h\), which is a Riemannian metric on an \(n\)-dimensional ``universal'' space. The main purpose of the paper is to obtain sufficient conditions on the metric \(h\) and on the functions \(f\) and \(a\), which enable the new Lorentzian metric to be consistently employed in theories of gravity modelling a static vacuum black hole. Examples are constructed in concrete contexts as solutions in particular theories, such as Gauss-Bonnet, quadratic, F(R) and F(Lovelock) gravity, and certain conformal gravities.