## Universal black holes.(English)Zbl 1460.83046

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.

### MSC:

 83C57 Black holes 83C15 Exact solutions to problems in general relativity and gravitational theory 83E15 Kaluza-Klein and other higher-dimensional theories 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 53Z05 Applications of differential geometry to physics
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