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arXiv 2202.09251gr-qchep-th
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四维双子NUT荷电时空的一致质量公式

Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes

Di Wu, Shuang-Qing Wu

摘要:

在我们以前的工作中,提出了一种新颖的观点,即NUT荷可以被看作是一个几何多毛,以完美地描述一般四维Taub-NUT时空的几何特征。在这个方案中,Komar质量M、重磁荷和/或对偶(磁)质量N,以及一个新的二次毛J_N=MN,即类Kerr守恒角动量,都进入第一定律和Bekenstein-Smarr质量公式的标准形式。区别于其他最近的尝试,我们一致的热力学微分和积分质量公式都可以从一个有意义的克里斯托杜卢-鲁菲尼型平方质量公式几乎所有的四维NUT荷电时空。作为一个极好的结果,著名的贝肯斯坦-霍金四分之一面积熵关系不仅可以在洛伦兹扇区中自然恢复,而且可以在一般的陶布-NUT型时空的欧几里得对应物中自然恢复,而不需要施加任何约束条件。然而,只有纯带电的情况下,在四维爱因斯坦-麦克斯韦引力理论与NUT收费已被解决。在本文中,我们将遵循这篇文章中提出的简单、系统的方法,进一步研究双子NUT荷电的情况。结果表明,在不增加新的二次电荷的条件下,标准热力学关系仍然成立,但由此得到的静电势和静磁势与标准方法计算的结果不一致。为了纠正这种不一致,我们提出了一个简单的策略,即进一步引入两个额外的次级毛:Q_N=QN和P_N=PN,以及它们的共轭势,使第一定律和Bekenstein-Smarr质量公式仍然满足。

英文摘要:

In our previous work, a novel idea that the NUT charge can be thought of as a thermodynamical multi-hair has been advocated to describe perfectly the thermodynamical character of the generic four-dimensional Taub-NUT spacetimes. According to this scheme, the Komar mass M, the gravito-magnetic charge and/or the dual (magnetic) mass N, together with a new secondary hair J_N=MN, namely, a Kerr-like conserved angular momentum, enter into the standard forms of the first law and Bekenstein-Smarr mass formula. Distinguished from other recent attempts, our consistent thermodynamic differential and integral mass formulae are both obtainable from a meaningful Christodoulou-Ruffini-type squared mass formula of almost all of the four-dimensional NUT-charged spacetimes. As an excellent consequence, the famous Bekenstein-Hawking one-quarter area-entropy relation can be naturally restored not only in the Lorentzian sector and but also in the Euclidian counterpart of the generic Taub-NUT-type spacetimes without imposing any constraint condition. However, only purely electric-charged cases in the four-dimensional Einstein-Maxwell gravity theory with a NUT charge have been addressed there. In this paper, we shall follow the simple, systematic way proposed in that article to further investigate the dyonic NUT-charged case. It is shown that the standard thermodynamic relations continue to hold true provided that no new secondary charge is added, however, the so-obtained electrostatic and magneto-static potentials are not coincident with those computed via the standard method. To rectify this inconsistence, a simple strategy is provided by further introducing two additional secondary hairs: Q_N=QN and P_N=PN, together with their thermodynamical conjugate potentials, so that the first law and Bekenstein-Smarr mass formula are still satisfied.

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