We consider metric fðRÞ theories of gravity without mapping them to their scalar-tensor counterpart, but using the Ricci scalar itself as an ''extra'' degree of freedom. This approach avoids then the introduction of a scalar-field potential that might be ill defined (not single valued). In order to explicitly show the usefulness of this method, we focus on static and spherically symmetric spacetimes and deal with the recent controversy about the existence of extended relativistic objects in certain class of fðRÞ models.

We use holographic techniques to study photon production in a class of finite temperature, strongly coupled, large-N c SU (N c ) quark-gluon plasmas with N f ≪ N c quark flavours. Our results are valid to leading order in the electromagnetic coupling constant but non-perturbatively in the SU (N c ) interactions. The spectral function of electromagnetic currents and other related observables exhibit an interesting structure as a function of the photon frequency and the quark mass. We discuss possible implications for heavy ion collision experiments.

We calculate the DC conductivity tensor of strongly coupled N = 4 super-Yang-Mills (SYM) plasma in a presence of a strong external magnetic field B T 2 by using its gravity dual and employing both the RG flow approach and membrane paradigm which give the same results. We find that, since the magnetic field B induces anisotropy in the plasma, different components of the DC conductivity tensor have different magnitudes depending on whether its components are in the direction of the magnetic field B. In particular, we find that a component of the DC conductivity tensor in the direction of the magnetic field B increases linearly with B while the other components (which are not in the direction of the magnetic field B) are independent of it. These results are consistent with the lattice computations of the DC conductivity tensor of the QCD plasma in an external magnetic field B. Using the DC conductivity tensor, we calculate the soft or low-frequency thermal photon and dilepton production rates of the strongly coupled N = 4 SYM plasma in the presence of the strong external magnetic field B T 2. We find that the strong magnetic field B enhances both the thermal photon and dilepton production rates of the strongly coupled N = 4 SYM plasma in a qualitative agreement with the experimentally observed enhancements at the heavy-ion collision experiments.

We consider a class of metric f (R) modified gravity theories, analyze them in the context of a Friedmann-Robertson-Walker cosmology and confront the results with some of the known constraints imposed by observations. In particular, we focus in correctly reproducing the matter and effective cosmological constant eras, the age of the Universe, and supernovae data. Our analysis differs in many respects from previous studies. First, we avoid any transformation to a scalar-tensor theory in order to be exempted of any potential pathologies (e.g. multivalued scalar potentials) and also to evade any unnecessary discussion regarding frames (i.e. Einstein .vs. Jordan). Second, based on a robust approach, we recast the cosmology equations as an initial value problem subject to a modified Hamiltonian constraint. Third, we solve the equations numerically where the Ricci scalar itself is one of the variables, and use the constraint equation to monitor the accuracy of the solutions. We compute the "equation of state" (EOS) associated with the modifications of gravity using several inequivalent definitions that have been proposed in the past and analyze it in detail. We argue that one of these definitions has the best features. In particular, we present the EOS around the so called "phantom divide" boundary and compare it with previous findings.

We use the gauge/gravity correspondence to calculate the rate of photon production in a strongly coupled N = 4 plasma in the presence of an intense magnetic field. We start by constructing a family of back reacted geometries that include the black D3-brane solution, as a smooth limiting case for B = 0, and extends to backgrounds with an arbitrarily large constant magnetic field. This family provides the gravitational dual of a field theory in the presence of a very strong magnetic field which intensity can be fixed as desired and allows us to study its effect on the photon production of a quark-gluon plasma. The inclusion of perturbations in the electromagnetic field on these backgrounds is consistent only if the metric is perturbed as well, so we use methods developed to treat operator mixing to manage these general perturbations. Our results show a clear enhancement of photon production with a significant anisotropy, which, in qualitative agreement with the experiments of heavy ion collisions, is particularly noticeable for low P.