Area product and mass formula for Kerr–Newman–Taub–NUT spacetime
Area product and mass formula for Kerr–Newman–Taub–NUT spacetime
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DOI：
10.1142/s0217732315501709
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发表时间：
2013-10
影响因子：
1.4
通讯作者：
P. Pradhan
中科院分区：
文献类型：
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作者：
P. Pradhan
导出了四维洛伦兹几何中Kerr-Newman-Taub-NUT （newman - untii - tamburino）黑洞的视界和柯西视界的面积积、熵积、面积和熵和。我们观察到这些热力学产物对于这个黑洞（BH）来说不是普遍的（与质量无关的），而对于克尔-纽曼黑洞（KN）来说，这些产物是普遍的（与质量无关的）。我们还研究了熵和和面积和。结果表明，它们都与背景时空的质量、电荷和NUT参数有关。因此，我们可以得出结论，Kerr-Newman-Taub-NUT （KNTN）黑洞的面积积与熵积、面积和与熵和的普遍（质量无关）行为失效，并且与KN黑洞也有很大的不同。我们进一步证明了KNTN黑洞不具备黑洞热力学第一定律和Smarr-Gibbs-Duhem关系，并且这种关系在KN的情况下不太可能存在。上述这些特征的失效是由于非平凡的NUT电荷的存在，使得时空渐近非平坦，与KN BH相反。失败的另一个原因是洛伦兹KNTN几何包含狄拉克-米斯纳型奇点，这是流形的非平凡拓扑扭曲的表现。导出了KNTN黑洞的质量公式和Christodoulou-Ruffini质量公式。最后，我们计算了视界的面积界，即视界的彭罗斯不等式。从面积界推导出熵界。这些多视界上的热力学产物对于理解黑洞熵的微观性质在黑洞热力学中起着至关重要的作用。
We derive area product, entropy product, area sum and entropy sum of the event horizon and Cauchy horizons for Kerr–Newman–Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. We observe that these thermodynamic products are not universal (mass-independence) for this black hole (BH), whereas for Kerr–Newman (KN) BH such products are universal (mass-independence). We also examine the entropy sum and area sum. It is shown that they all depend on mass, charge and NUT parameter of the background spacetime. Thus, we can conclude that the universal (mass-independence) behavior of area product and entropy product, area sum and entropy sum for Kerr–Newman–Taub–NUT (KNTN) BH fails and which is also quite different from KN BH. We further show that the KNTN BH do not possess first law of BH thermodynamics and Smarr–Gibbs–Duhem relations, and that such relations are unlikely in the KN case. The failure of these aforementioned features are due to presence of the nontrivial NUT charge which makes the spacetime to be asymptotically non-flat, in contrast with KN BH. The other reason of the failure is that Lorentzian KNTN geometry contains Dirac–Misner type singularity, which is a manifestation of a nontrivial topological twist of the manifold. The BH mass formula and Christodoulou–Ruffini mass formula for KNTN BHs are also derived. Finally, we compute the area bound which is just Penrose like inequality for event horizon. From area bound we derive entropy bound. These thermodynamic products on the multi-horizon play a crucial role in BH thermodynamics to understand the microscopic nature of BH entropy.