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We obtain new exact solutions for the gravitational field equations in the context of $f(R,T)$ gravity, thereby obtaining different classes of black holes surrounded by fluids, taking into account some specific values of the parameter of the equations of state, $w$. In order to obtain these solutions in the context of $f(R,T)$ gravity, we consider viable particular choices of the $f(R,T)$. Considering an anisotropic energy-momentum tensor, we write the field equations with the required symmetries for this type of solution. Then, we analyze the conditions of energy in a general way and also for particular values of the parameter $w$ of the equation of state. In addition, thermodynamic quantities, such as Hawking temperature and mass associated to the horizons of solutions, are taken into account in our analysis.

We investigate non-inertial effects induced by a rotating frame on a non-relativistic quantum harmonic oscillator as well as of the topology associated to a screw dislocation, which corresponds to a distortion of a vertical line into a vertical spiral. To do this, we obtain the analytical solutions of the time-independent Schr\"odinger equation for this harmonic oscillator potential in this background. The expressions for the energy spectrum are obtained and the solutions for four quantum states, namely $n=0,1,2$ and $3$, are analysed. Our results show that the presence of the topological defect (screw dislocation) as well the fact that we are analysing the system from the point of view of a rotating frame, changes the solutions of Schr\"odinger equation and the corresponding spectrum. Now these quantities depend on the angular velocity of the rotating frame, $\Omega$, and also on the parameter $\beta$, which codifies the presence of the screw dislocation. Particularly, with respect to the energy spectrum of the system the changing is such that when $\Omega$ increases, the energy can increase or decrease depending on the values we assign to the eigenvalues of the angular and linear momenta. Additionally, we observe that the values of the parameter $\beta$ that characterizes the screw dislocation causes a shift in the energy spectrum.

In this work, we study the influence of $f(R,T)$ gravity on rapidly rotating neutron stars. First we discuss the main aspects of this modified theory of gravity where the gravitational Lagrangian is an arbitrary function of the Ricci scalar $R$ and of the trace of the energy-momentum tensor $T$. Then we present the basic equations for neutron stars including the equations of state used in the present work to describe the hadronic matter. Some physical quantities of interest are calculated such as mass-radius relations, moments of inertia, angular momentum, and compactness. By considering four different rotation regimes, we obtain results that indicate substantial modifications in the physical properties of neutron stars in $f(R,T)$ gravity when compared to those in the context of general relativity. In particular, the mass-radius relation for sequences of stars indicates that $f(R,T)$ gravity increases the mass and the equatorial radius of the neutron stars for stars rotating with an angular velocity smaller than Kepler limit.

We analyze the dynamics of scalar particles in gravity's rainbow considering the space-time of a cosmic string in this modified gravity. Thus, we solve the Klein-Gordon equation for two types of potential in which two possible rainbow functions are selected. In all cases studied we obtain exact solutions for the wave equation, derive the energy spectrum, analyze it in detail and discuss the dependence of the results with the choice of the rainbow functions.

In this study, we analyze solutions of the wave equation for scalar particles in a space-time with nontrivial topology. Solutions for the Klein--Gordon oscillator are found considering two configurations of this space-time. In the first one, it is assumed the $S^{1}\times R^{3}$ space where the metric is written in the usual inertial frame of reference. In the second case, we consider a rotating reference frame adapted to the circle S1. We obtained compact expressions for the energy spectrum and for the particles wave functions in both configurations. Additionally, we show that the energy spectrum of the solution associated to the rotating system has an additional term that breaks the symmetry around $E = 0$.