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arXiv 1504.04009gr-qchep-th
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与非线性电动力学场耦合的伸缩子黑洞

Dilaton black holes coupled to nonlinear electrodynamic field

A. Sheykhi, S. Hajkhalili

摘要:

非线性电动力学理论近年来受到了广泛的关注。结果表明,Born-Infeld非线性电动力学并不是使带电点粒子的电场在原点保持有限的线性Maxwell场的唯一修正,其它类型的非线性拉格朗日量如指数和对数非线性电动力学也可以起到同样的作用。本文通过在作用量上加标量场,推广了指数型非线性电动力学的研究。通过适当地选择物质场与声子场的耦合,我们改变了作用量,得到了相应的场方程。然后,通过适当的处理,构造了一类新的耦合到指数非线性电动力学场的带电玻色子黑洞解,其中玻色子场具有两个Liouville型势.由于声子场的存在,这些解的渐近行为既不是平坦的,也不是(A)dS。在非线性参数$β^2$趋于无穷大的极限情况下,我们的解简化为黑洞上的爱因斯坦-麦克斯韦方程组。我们得到了这些解的质量、温度、熵和电势。我们还研究了电场的行为,以及这些黑洞的电势附近的起源。我们发现电场的原点有一个有限值\textit{near},这与Born-Infeld非线性电动力学的电场相同,但它可以根据模型参数的不同而精确地在$r=0$处发散.我们还研究了激子场对电场和电势行为的影响。最后,我们在黑洞视界上检验了黑洞热力学第一定律的有效性。

英文摘要:

The theory of nonlinear electrodynamics has got a lot of attentions in recent years. It was shown that Born-Infeld nonlinear electrodynamics is not the only modification of the linear Maxwell's field which keeps the electric field of a charged point particle finite at the origin, and other type of nonlinear Lagrangian such as exponential and logarithmic nonlinear electrodynamics can play the same role. In this paper, we generalize the study on the exponential nonlinear electrodynamics by adding a scalar dilaton field to the action. By suitably choosing the coupling of the matter field to the dilaton field, we vary the action and obtain the corresponding field equations. Then, by making a proper ansatz, we construct a new class of charged dilaton black hole solutions coupled to the exponential nonlinear electrodynamics field in the presence of two Liouville-type potentials for the dilaton field. Due to the presence of the dilaton field, the asymptotic behavior of these solutions are neither flat nor (A)dS. In the limiting case where the nonlinear parameter $β^2$ goes to infinity, our solution reduces to the Einstein-Maxwell dilaton black holes. We obtain the mass, temperature, entropy and electric potential of these solutions. We also study the behaviour of the electric field as well as the electric potential of these black holes near the origin. We find that the electric field has a finite value \textit{near} the origin, which is the same as the electric field of Born-Infeld nonlinear electrodynamics, but it can diverge exactly at $r=0$ depending on the model parameters. We also investigate the effects of the dilaton field on the behaviour of the electric field and electric potential. Finally, we check the validity of the first law of black hole thermodynamics on the black hole horizon.

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