On the Thermodynamical Black Hole Stability in the Space-Time of a Global Monopole in f(R)-Gravity

In this work, we re-assess a class of black hole solutions in a global monopole spacetime in the framework of an f(R)-gravity model. Our main line of investigation consists in considering a region close enough to the black hole, but such that the weak field approximation is still valid. The stability of the black hole is studied in terms of its thermodynamical properties, with the radial coordinate written as a power-law function with the status of the main factor underneath the stability of the model. We obtain the explicit expressions for the thermodynamical quantities of the black hole as functions of the event horizon, by considering both the Hawking and the local temperatures. The phase transitions that may occur in this system, including the Hawking-Page phase transition, are inspected with particular attention. We work out and contemplate a solution of special interest in which one of the parameters is related to the cosmological constant. Our main result sets out to establish a comparison between both the Hawking and the local formalisms for the black hole in the framework of the f(R)-gravity in the particular space-time adopted here.

Instability of a black hole with f(R) global monopole under extended uncertainty principle

We consider the evolution of a black hole involving an f(R)global monopole based on the Extended Uncertainty Principle(EUP).The black hole evolutions refer to the instability due to the Parikh-Kraus-Wilczeck tunneling radiation or fragmentation.It is found that the EUP corrections make the entropy difference larger to encourage the black hole to radiate more significantly.We also show that the appearance of the EUP effects results in the black hole’s division.The influence from the global monopole and the revision of general relativity can also adjust the black hole evolution simultaneously but cannot change the final result that the black hole will not be stable because of the EUP’s effects.

Effects of a global monopole on the thermodynamic phase transition of a charged AdS black hole

We study the dynamical properties of the thermodynamic phase transition(PT)of a charged AdS black hole(BH)with a global monopole via the Gibbs free energy landscape and reveal the effects of the global monopole on the kinetics of thermodynamic PTs.First,we briefly review the thermodynamics of a charged AdS BH with a global monopole.Then,we introduce the Gibbs free energy landscape to investigate the thermodynamic stability of the BH states.Because of thermal fluctuations,the small black hole(SBH)state can transit to a large black hole(LBH)state,and vice versa.Further,we use the Fokker-Planck equation with the reflecting boundary condition to study the probability evolution of the BH state with and without a global monopole separately.It is found that for both the SBH and LBH states,the global monopole could slow down the evolution of the BH state.In addition,we obtain the relationship between the first passage time and the monopole parameterη.The result shows that as the monopole parameterηincreases,the mean first passage time becomes longer for both the SBH and LBH states.