# On the Black Holes in Alternative Theories of Gravity: The Case of Non-linear Massive Gravity

## Abstract

It is already known that a positive Cosmological Constant \(\varLambda \) sets the scale \(r_0=\left( \frac{3}{2}r_s r_\varLambda ^2\right) ^{1/3}\), which depending on the mass of the source, can be of astrophysical order of magnitude. This scale was interpreted before as the maximum distance in order to get bound orbits. The same scale corresponds to the static observer position if we want to define the Black Hole temperature in an asymptotically de-Sitter space. \(r_0\) also appears inside the non-linear theory of massive gravity (dRGT) as the Vainshtein radius for the \(\varLambda _3\) version of the theory. I compare the role that this scale plays inside these different scenarios.

## Notes

### Acknowledgments

The author would like to thank Gia Dvali for a very useful discussion during the Karl Schwarzschild meeting 2013 organized in FIAS, Frankfurt/Germany. This work is supported by MEXT (The Ministry of Education, Culture, Sports, Science and Technology) in Japan and KEK Theory Center.

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