It is well-known that $f(R)$ theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the $f(R)$ extension of the Einstein-Hilbert action of general relativity, $f(T)$ theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than $f(R)$ theories. It is interesting to investigate whether $f(T)$ theories have the similar conformal features possessed in $f(R)$ theories. It is shown, however, that $f(T)$ theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation.

We investigate whether the new horizon first law proposed recently still work in f( R) theory. We identify the entropy and the energy of black hole as quantities proportional to the corresponding...

Quantum gravity corrections to accretion onto a Schwarzschild black hole are considered in the context of the asymptotically safe scenario. The possible positions of the critical points are discussed and the general conditions for critical points are obtained. The explicit expressions for the matter density compression and the temperature profile, both below the critical radius and at the event horizon, are derived. For polytropic matter, we determine the corrected temperature and the integrated flux resulting from quantum gravity effects at the event horizon, which might be considered as a test of the asymptotically safe scenario.