On the Black Holes in alternative theories of gravity: The case of non-linear massive gravity

Abstract

I derive general conditions in order to explain the origin of the Vainshtein radius inside dRGT. The set of equations, which I have called "Vainshtein" conditions are extremal conditions of the dynamical metric ($g_{\mu \nu }$) containing all the degrees of freedom of the theory. The Vainshtein conditions are able to explain the coincidence between the Vainshtein radius in dRGT and the scale $r_0={\left(\frac{3}{2}{r}_s{r}_{\Lambda }^2\right)}^{1/3}$, obtained naturally from the Schwarzschild de-Sitter (S-dS) space inside General Relativity (GR). In GR, this scale was interpreted 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. In dRGT, the scale marks a limit after which the extra degrees of freedom of the theory become relevant.

Final version to appear at Int.J.Mod.Phys. D. arXiv admin note: substantial text overlap with arXiv:1305.0475

References in corpus (6)

• Extended Theories of Gravity
• Extra force in $f(R)$ modified theories of gravity
• Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
• Equatorial circular orbits in the Kerr-de Sitter spacetimes
• Stability of the Schwarzschild-de Sitter black hole in the dRGT massive gravity theory
• Velocity and velocity bounds in static spherically symmetric metrics

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