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Stability and gravitational collapse in extended theories of gravity: from singularities to bouncing scenarios
Einstein theory of General Relativity was well adapted and accepted until limitations in the form of an unexplained form of energy, referred today as Dark Energy, were observed. For this reason, modifications to the standard Theory of General Relativity were proposed: the so-called f(R) theories. In...
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| Format: | Thesis |
| Language: | English |
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Department of Maths and Applied Maths
2020
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| Summary: | Einstein theory of General Relativity was well adapted and accepted until limitations in the form of an unexplained form of energy, referred today as Dark Energy, were observed. For this reason, modifications to the standard Theory of General Relativity were proposed: the so-called f(R) theories. In this dissertation, after a passage on the generalities of cosmology, we use the metric formalism technique to derive the field equations for the general f(R) function. Thereafter we analyse and check the solutions proposed in [85] for the quadratic model in f(R) gravity, for spherically symmetric and static neutron stars, using two different viable equations of state. We also check the accuracy of our code through a forward-backward integration technique, to show that in both directions, we obtain the same results. We then perform a thorough analysis in the case of f(R) = R1+ models. Results will show that for a negative value, we have non-Schwarzschild, but asymptotically flat solutions, for which we can use the backward integration technique to retrieve the solutions from the forward integration. However, for the case of positive values, we will show the existence of horizons, which deny us the possibility of using the backward integration technique. One of the aims of this thesis is to check, through the backward integration technique that we developed, whether the exact exterior solutions proposed in [86], are indeed realistic solutions for neutron stars. We will see that for some cases, we do have realistic profiles, while for some others, although solutions exist, they are rejected due to their disagreement with the equation of state used therein. |
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