arXiv subjects
Publications and source records attributed to C. J. Ramírez-Valdez.
We study the connected sum of Hopf links in $S^3$. Particularly, we compute the entanglement entropy (EE) as a function of the number of link components. We find evidence of lower and upper bounds for the entanglement entropy. We show that the $SU(2)$ theory exhibits sensitivity to the parity of links. We also find evidence suggesting the existence of a well-defined limit of the large number of link components.
In the present paper we argue that the dyonic black hole spacetimes must be studied within the theory of two electromagnetic potentials, and we use the dyonic Reissner-Nordström solution to demonstrate that the field of the monopole magnetic charge is correctly described by the $t$-component of the dual electromagnetic potential. As a result, the Dirac string associated with the $φ$-component of the usual electromagnetic 4-potential becomes just a mathematical object, without any physical content, that arises in some calculations when one employs unsymmetrical representations of the electromagnetic field. We use three different, though equivalent, forms of the electromagnetic energy-momentum tensor to calculate the Komar mass of the Reissner-Nordström black hole, and in one case the Dirac string is linked to the magnetic charge, in another to the electric charge, while the third, symmetrical case, is string-free.
The results obtained in our previous paper are now extended to the case of stationary axially symmetric dyonic black boles within the theory of two electromagnetic potentials. We slightly enlarge the classical Ernst formalism by introducing, with the aid of the $t$- and $φ$-components of the dual potential $B_μ$, the magnetic potential $Φ_m$ which, similar to the known electric potential $Φ_e$, also takes constant value on the black hole horizon. We analyze in detail the case of the dyonic Kerr-Newman black hole and show how the Komar mass must be evaluated correctly in this stationary dyonic model. In particular, we rigorously prove the validity of the standard Tomimatsu mass formula and point out that attempts to "improve" it made in recent years are explained by misunderstanding of the auxiliary role that singular potentials play in the description of magnetic charges. Our approach is symmetrical with respect to electric and magnetic charges and, like in the static case considered earlier, Dirac strings of all kind are excluded from the physical picture of the stationary black hole dyonic spacetimes.
In the present paper, we compute the Euclidean action of a generic system consisting of $N$ arbitrary Kerr-Newman black holes located on the symmetry axis and separated from each other by massless struts. This allows us to introduce the {\it Hawking average temperature} (HAT) $\hat T$ of the multi-black hole system via the condition of vanishing the entire set of terms involving the singular horizons due to periodic time, and the resulting formula for this temperature contains solely the surface gravities $κ_i$ and horizon areas $A^H_i$ of the black hole constituents. We also show that the corresponding expression for the {\it free energy} of the system defined by $\hat T$ is consistent with the first law of thermodynamics and Smarr mass relations.
Using the notion of thermodynamic length, the first law of thermodynamics is consistently derived for two binary configurations of equal Kerr-Newman black holes separated by a massless strut. Like in the electrostatic systems of two Reissner-Nordström black holes and stationary vacuum systems of two Kerr black holes considered earlier, the thermodynamic length $\ell$ turns out to be defined by the same simple formula $\ell=L\exp(γ_0)$, $L$ being the coordinate length of the strut and $γ_0$ the value of the metric function $γ$ on the strut, which permits the elaboration of $\ell$ in a concise analytic form. The expression of the free energy in the case of two generic Kerr-Newman black holes is also proposed.
We investigate the first law of thermodynamics in the stationary axisymmetric configurations composed of two Kerr black holes separated by a massless strut. Our analysis employs the recent results obtained for the extended double-Kerr solution and for thermodynamics of the static single and binary black holes. We show that, similar to the electrostatic case, in the stationary binary systems the thermodynamic length $\ell$ is defined by the formula $\ell=L\exp(γ_0)$, where $L$ is the coordinate length of the strut, and $γ_0$ is the value of the metric function $γ$ on the strut.