Motion of charged particles in a NUTty Einstein–Maxwell spacetime and causality violation

Abstract

We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner-Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion. *

General Smarr relation and first law of a NUT dyonic black hole

“…As shown by some recent studies [9][10][11], Taub-NUT solution in Lorentzian setup does not lead to serious problems as imagined previously, and when establishing the Smarr relation and first law of thermodynamics, the core ingredient is to introduce a pair of novel conjugate thermodynamic quantities, namely the Misner potential and charge ψ-N [12,16] to ensure that the NUT parameter n varies independently. The thermodynamics of the uncharged Lorentzian Taub-NUT-AdS maintaining the Misner strings present has been formulated, and from the Komar integral notions, it turns out that ψ is actually the surface gravity of the Misner strings and N is interpreted as the integration over it [16].…”

“…Utilizing the language of differential forms, we give the universal Smarr relation (35) directly. As a result of distinctive property of the electric and magnetic charges illustrated in (11), the gauge freedom of the electric and magnetic potentials is non-trivial, which demonstrates that there is bound to exist a myriad of Smarr relations and meanwhile, we give the necessary conditions to satisfy the first laws consistently. Based on this philosophy, we argue that the two types of thermodynamics discussed in [20] are just the special cases of Eq.…”

Misner gravitational charges and variable string strengths

“…However, it has been recently understood that the Taub-NUT spacetime with Misner strings present is less pathological than previously thought, and their complete removal may be unnecessary [7][8][9]. The Misner strings are transparent for geodesics, rendering the spacetime geodesically complete, and despite the occurrence of CTC regions, the spacetime is (at least for sufficiently small string strengths) free of causal pathologies for geodesic * aballonbordo@perimeterinstitute.ca † fgray@perimeterinstitute.ca ‡ rhennigar@mun.ca § dkubiznak@perimeterinstitute.ca observers [7][8][9][10]. In this paper we thus consider the whole spacetime with Misner strings present as 'physically relevant' and study its thermodynamic properties.…”

Thermodynamics of rotating NUTty dyons

“…For simplicity, we concentrate on the electric case and, similar to [23], work in an ensemble where we fix the Misner potential ψ (and thence the NUT parameter n) instead of the Misner charge N (which is quite algebraically complicated). Thus, starting from G given by ( 19) upon using (4.4)-(4.9). This is displayed as a function of temperature (4.7) in figure 1 for a purely rotating NUT with Q e = 0 and in figure 2 for Q e = 1 and various angular momenta.…”

“…These issues are non-existent if we periodically identify the time coordinate [5], and for many years the study of Taub-NUTs and their thermodynamics was restricted to the Euclidean solutions, see for example [6][7][8][9][10][11][12][13][14][15][16]. Nevertheless, in the light of some recent arguments that show that the Lorentzian solutions (without imposing the time periodiciy condition) are actually well-behaved for geodesic curves [17][18][19] (see also [20] for the Kruskal extension over the black hole horizon) the interest in the Lorentzian thermodynamics has currently gained momentum [21][22][23][24][25][26][27][28].…”