Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theories

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Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global stability of paradigmatic f(R) models. In addition, we revise some attempts to extend the Cardy-Verlinde formula, including modified gravity, where a relation between entropy bounds is obtained. Moreover, a deep study on cosmological singularities, which appear as a real possibility for some kind of modified gravity theories, is performed, and the validity of the entropy bounds is studied.
© 2012 by the authors; licensee MDPI, Basel, Switzerland. AdlCD acknowledges financial support from URC and NRF (South Africa), MICINN (Spain) project numbers FIS2011-23000, FPA2011-27853-C02-01 and Consolider-Ingenio MULTIDARK CSD2009-00064.DSG acknowledges support from a postdoctoral contract from the University of the Basque Country (UPV/EHU). DSG is also supported by the research project FIS2010-15492, and also by the Basque Government through the special research action KATEA and UPV/EHU under program UFI 11/55.
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