In this paper, we will obtain the solution corresponding to a static spherically symmetric black hole with a cloud of strings in a special class of higher curvature gravity, namely, pure Lovelock gravity. Some aspects of the thermodynamics of this black hole will be investigated, with special emphasis on the behavior of the entropy, Hawking temperature and heat capacity. The difference between these quantities and the ones corresponding the Einstein gravity is pointed out.

We obtain the solution corresponding to a static charged black hole (Reissner–Nordström black hole) surrounded by quintessence and a cloud of strings, study its thermodynamics and calculate the quasinormal frequencies for a scalar field in this background spacetime. The mass, Hawking temperature and heat capacity are analyzed and the roles played by the sources corresponding to the quintessence and the cloud of strings are showed up. In what concerns the quasinormal modes, we fixed the value of the quintessence parameter [Formula: see text], taking [Formula: see text], calculate the quasinormal frequencies and emphasize the effects due to the cloud of strings.

In this paper we investigate the combined effects of the cloud of strings and quintessence which surround a Reissner-Nordstrom AdS black hole on its thermodynamics. We treat the cosmological constant as a thermodynamic pressure whose conjugate variable is the volume. It is shown how the cloud of strings affect the thermodynamic variables, as for example, temperature, entropy, internal energy and heat capacity. The critical expressions for temperature, pressure and specific volume are obtained and the critical exponents calculated. Concerning the heat engine, we calculate its efficiency and show how this quantity is influenced by the presence of the cloud of strings and quintessence.

The Lovelock gravity is a natural extension of the Theory of General Relativity (TGR) to higher dimensions, which presents the criteria of general covariance and whose field equations are of second order. Its action contains higher order curvature terms and is reduced to the Einstein-Hilbert action when we consider a four dimensional spacetime. In this work, we obtain solutions corresponding to static spherically symmetric black holes with a cloud of strings and surrounded by quintessence. The study of the thermodynamical properties of these black holes is performed, with special emphasis on the mass, entropy, Hawking temperature and heat capacity. The graphs corresponding to the mass and the Hawking temperature are shown for different dimensions of spacetime, namely, D = 4, 5, 6 and 7. Concerning Hawking radiation, it is shown that the radiation spectrum is related to the change of entropy which codifies the presence of the cloud of strings as well as of the quintessence.

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