Abstract
In the present work a generalization of the BTZ black hole is studied, for the case of scale dependent couplings. One starts by using the effective action for scale dependence couplings to get a generalization of the Einstein field equations. Self consistent solutions for lapse function, cosmological coupling and Newtons coupling are found. The effect of scale dependent couplings with respect to the classical solution is shown. Moreover, asymptotic behavior as well as thermodynamic properties were investigated. Finally, an alternative way to get the scale dependent Newton coupling, from the so-called “Null Energy Condition” is presented.
Highlights
Great effort has been made to try to unify general relativity with quantum mechanics
For example it is known that this theory has a close connection with Chern-Simons theory [11, 12]. Another interesting feature of this theory is that there are non-trivial black hole solutions with a negative cosmological constant, found by Banados, Teitelboim and Zanelli (BTZ) [13, 14]. We investigate this black hole in light of the possibility of scale dependent couplings, such as they arise in the asymptotic safety approach
To summarize, in this article the BTZ black hole is investigated in the light of scale dependence
Summary
Great effort has been made to try to unify general relativity with quantum mechanics. Two well known candidates for this unification are String theory [1,2] and Loop quantum gravity [3] Another promising framework for quantum gravity arises from the so called Asymptotic safety scenario [4,5,6,7,8,9], in which the couplings do not need to be small or tend to zero in the high energy limit. Another interesting feature of this theory is that there are non-trivial black hole solutions with a negative cosmological constant, found by Banados, Teitelboim and Zanelli (BTZ) [13, 14] We investigate this black hole in light of the possibility of scale dependent couplings, such as they arise in the asymptotic safety approach. One only needs to solve the E.O.M. for the radial coordinate r [17,18,19], if one chooses to eliminate one of those functions by a suitable ansatz or a physically motivated condition
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