Abstract
A new family of (2+1)-dimensional black holes are investigated in the background of Born–Infeld type theories coupled to a Riemannian curved spacetime. We know that both the scale and dual invariances are violated for these nonlinear electromagnetic theories. In this set-up, first we consider a pure magnetic source in a model of exponential electrodynamics and find a magnetically charged (2+1)-dimensional black hole solution in terms of magnetic charge q and nonlinearity parameter beta . In the second case we consider a pure electric source of gravity in the framework of arcsin electrodynamics and derive the associated (2+1)-dimensional black hole solution in terms of electric charge Q and the parameter beta . The asymptotic behaviour of the solutions at infinity as well as at rrightarrow 0 in both the frameworks is discussed. The asymptotic expressions of curvature invariants in the case of exponential electrodynamics shows that there exists a finite value of curvature at the origin, while in arcsin electrodynamics, the corresponding asymptotic behaviour shows that there is a true curvature singularity at the centre of the charged object. Furthermore, thermodynamics of the resulting charged black holes within the context of both the models is studied. It is shown that the thermodynamic quantities corresponding to these objects satisfy the first law of black hole thermodynamics.
Highlights
Thermodynamics of magnetically charged black holesWe study thermodynamics of the black hole solutions described by Eq (2.16). For doing this we use an alternative method to determine the local Hawking temperature with the help of the Unruh effect in curved spacetime [55–57]
In the same way, (2 + 1)-dimensional black holes are studied in the presence of NED [34,35,36] where the power of Maxwell’s invariant is taken as an arbitrary real rational number k. (For more discussions related to (2 + 1)dimensional black holes and NED, the reader is referred to Refs. [37,38,39,40,41].) Recently, the new NED models such as arcsin electrodynamics and modified Born–Infeld electrodynamics have been used and static spherically symmetric electrically charged solutions are determined [42,43,44,45]
Black holes of Einstein’s theory and modified gravities have been studied within the context of these NED models
Summary
We study thermodynamics of the black hole solutions described by Eq (2.16). For doing this we use an alternative method to determine the local Hawking temperature with the help of the Unruh effect in curved spacetime [55–57]. Xa represents a Killing vector field that generates the outer horizon rh This expression of local Hawking temperature implies that at r → rh, TH (r ) is undefined and at r → ∞, it is zero. Since we are interested in electrically charged black hole solution, we should assume magnetic field B = 0 which makes Maxwell’s invariant equal to F = −(E(r ))2/2. From Eq (4.2) on using the (2 + 1)-dimensional line element (2.7), it is straightforward to obtain the value of electric field as. This non-Maxwellian behaviour of electric field and electric potential is due to the nonlinear electromagnetic nature of Lagrangian density (4.1) Using this Lagrangian density, the components of matter tensor (4.3) can be calculated as.
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