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Register a new userThermodynamic stability of black holes surrounded by quintessence
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We study the thermodynamic stabilities of uncharged and charged black holes surrounded by quintessence (BHQ) by means of effective thermodynamic quantities. When the state parameter of quintessence $omega_q$ is appropriately chosen, the structures of BHQ are something like that of black holes in de Sitter space. Constructing the effective first law of thermodynamics in two different ways, we can derive the effective thermodynamic quantities of BHQ. Especially, these effective thermodynamic quantities also satisfy Smarr-like formulae. It is found that the uncharged BHQ is always thermodynamically unstable due to negative heat capacity, while for the charged BHQ there are phase transitions of the second order. We also show that there is a great deal of difference on the thermodynamic properties and critical behaviors of BHQ between the two ways we employed.
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Basing on the ideas used by Kiselev, we study the Hayward black hole surrounded by quintessence. By setting for the quintessence state parameter at the special case of $omega=-frac{2}{3}$, using the metric of the black hole surrounded by quintessence and the definition of the effective potential, we analyzed in detail the null geodesics for different energies. We also analyzed the horizons of the Hayward black hole surrounded by quintessence as well as the shadow of the black hole.
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