Abstract
We present an exact static, spherically symmetric black hole solution to the third-order Lovelock gravity with a string cloud background in seven dimensions for the special case when the second- and third-order Lovelock coefficients are related via $$\tilde{\alpha }^2_2=3\tilde{\alpha }_3\;(\equiv \alpha ^2)$$ . Further, we examine thermodynamic properties of this black hole to obtain exact expressions for mass, temperature, heat capacity and entropy, and also perform the thermodynamic stability analysis. We see that a string cloud background has a profound influence on the horizon structure, thermodynamic properties, and the stability of black holes. Interestingly the entropy of the black hole is unaffected due to the string cloud background. However, the critical solution for thermodynamic stability is affected by the string cloud background.
Highlights
Black holes by quantum results show that they radiate due to the Hawking effect [1]
One shows that black holes have the standard thermodynamic quantities, such as temperature, entropy, and heat capacity and so on, and they even possess abundant phase structures like the Hawking–Page phase transition [2] and similar critical phenomena to ordinary thermodynamic systems
We show that a string cloud background has a profound influence on horizon structures and the thermodynamic quantities, but entropy is not changed
Summary
Black holes by quantum results show that they radiate due to the Hawking effect [1]. In the absence of established theories of quantum gravity, black holes have become a major playground to divulge quantum gravity effects through their thermodynamics. Lovelock theory may play an important role in a string theory where the low energy effective field theory of gravity contains higher curvature terms In this sense Lovelock gravity [3] is a natural extension to Einstein gravity. Spherically symmetric black hole solutions in Lovelock gravity with general energymomentum tensors in any arbitrary dimension can be found in [14] and [15,16,17,18,19,20,21,22] and its thermodynamics in [23]. We begin with finding static, spherically symmetric black hole solutions for a string cloud background for a specific case, i.e., α 22 = 3α 3, and examine thermodynamic properties in third-order Lovelock gravity.
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