NUT Charge Research Articles

Circular motion and particle collisions in ergoregion of rotating and twisting charged black holes

The presence of clouds of strings, quintessential fields, and NUT charges has significant consequences for spacetime geometry, and their study is much more important from an observational and theoretical perspective. Hence, in this article, we aim to explore the rotating and twisting charged black holes with the cloud of strings and quintessential field through horizons, ergoregions, photon regions, circular motion, and energy efficiency. First, we derive the equation of motion and the expressions for studying the photon region. To investigate circular motion, we derive the mathematical expressions of energy and angular momentum. The cloud of stings reduces the stability of angular momentum and energy in prograde particle motions and shifts their minima from the black hole’s center to the right. Static black holes with clouds of strings have the greatest angular momentum in prograde orbital motion, while rotating ones without clouds of strings have the least. Furthermore, we examine the efficiency of energy extraction through the Penrose process. The known energy extraction efficiency of the Penrose process for an extreme Kerr black hole is about 21%, but in the presence of clouds of strings, it exceeds 100%.

Sgr A* Shadow Study with KTN Space Time and Investigation of NUT Charge Existence

In this paper, I investigate the existence of the NUT charge through the KTN spacetime using shadow observations of Sgr A*. I report that the range of my constraint for the NUT charge is between −0.5 and 0.5 for Schwarzschild-like and very slowly rotating KTN black holes. This range extends to 1.5 for spins up to −2 and −1.5 for spins up to 2 based on Keck observations for both 40° and 10° viewing angles. For VLTI observations, Schwarzschild-like and very slowly rotating KTN black holes are excluded for a 40° viewing angle, and the NUT charge is constrained to a very narrow range for a 10° viewing angle. I report that the possibility of having KTN naked singularities in Sgr A* is small, considering the uncertainties in the shadow size.

Thermodynamics of Taub-NUT-AdS spacetimes

We apply the generalised Komar method proposed in [arXiv:2208.05494] to Taub-NUT-AdS spacetime in the theory of Einstein gravity plus a cosmological constant. Based on a generalised closed 2-form, we derive the total mass and NUT charge of the Taub-NUT-AdS spacetime. Together with other thermodynamic quantities calculated through standard method, we conform the first law and Smarr relation. Then, we consider charged AdS NUT spacetimes in Einstein–Maxwell theory with a cosmological constant, and show that the generalised Komar method works, too. We obtain all the thermodynamic quantities, and the first law and Smarr relation are checked to be satisfied automatically.

No U(1) ‘electric-magnetic’ duality in Einstein gravity

We revisit the question of whether classical general relativity obeys, beyond the linearised order, an analogue of the global U(1) electric-magnetic duality of Maxwell theory, with the Riemann tensor playing the role analogous to the field strength. Following contradictory claims in the literature, we present a simple gauge-invariant argument that the duality does not hold. The duality condition is the conservation of the helicity charge. Scattering amplitudes of gravitons in general relativity, and of gluons in Yang-Mills theory, violate this selection rule already at tree level. Indeed, the maximally-helicity-violating (MHV) amplitudes are famous for their simplicity. The duality in the linearised theories is, therefore, broken by the interactions. In contrast, the tree-level scattering amplitudes in duality-invariant theories of non-linear electromagnetism are known to obey helicity conservation. While the duality is not a symmetry of the full theory of general relativity, it does hold within a sector of the solution space, including vacuum type D solutions, where the duality is known to rotate between mass and NUT charge.

Revisiting mass formulas of the four-dimensional Reissner-Nordström-NUT-AdS solutions in a different metric form

Recently, the so-called “consistent thermodynamics” of the Lorentzian Reissner-Nordström (RN)-NUT-AdS4 spacetimes has been pursued by a lot of efforts via different means. Among these attempts, we had proposed a novel idea that “The NUT charge is a thermodynamical multihair” to successfully tackle with the subject. In this paper, we will adopt this strategy to reconsider the mass formulas of the RN-NUT-AdS4 solutions but written in an alternative form, which had not been studied before in any existing literature and might be a most appropriate ansatz for the higher dimensional multiply NUTty-charged AdS spacetimes without any constraint condition. Here, we shall discuss the Christodoulou-Ruffini-like squared mass formula and the first law as well as the Bekenstein-Smarr mass formula by introducing the secondary hair Jn=Mn. For the sake of generality, we have introduced a dimensionless constant w into the constant factor Ξ in the solution expression so that when w=1, all obtained results can reproduce those delivered in our previous work.

Shadow of rotating and twisting charged black holes with cloud of strings and quintessence

Testing gravity theories is an important and interesting issue in relativistic astrophysics using astrophysical observations. In recent years, Event horizon telescope collaboration provided valuable data from shadow of supermassive black holes located at the center of the galaxies Milky Way and Meissner 87, which may help to get information about the spacetime around the black holes. In this work, first, we consider rotating black hole solution for charged black hole with the NUT charge in the presence of clouds of strings, and study the event horizon properties of spacetime around rotating twisting and charged black holes in the cloud of strings and quintessential fields. The null geodesics of the spacetime is derived and the shadow case, radius of the shadow of the black and its distortion, due to the effects of the black hole spin, also analyzed. It is obtained that gravitational effects of black hole charge and quintessential field compensate each other and the rotating black hole’s shadow can be circular. We obtain constraints on charge and spin parameters of supermassive black holes Sgr hbox {A}^* and hbox {M87}^* using observational data from their shadow (size and observational angle) for various values of the NUT charge, cloud of strings and quintessential field parameters. Moreover, we also investigate gravitational capture cross-section for electromagnetic waves and emission rate of the black hole radiation energy through Hawking evaporation.

Plebanski-Demianski goes NUTs (to remove the Misner string)

We present a general procedure, based on the Ehlers transformation of the Ernst equations, to add the gravitomagnetic mass to the whole Plebanski-Demianski family of solutions. We can efficiently generate a large class of accelerating black holes, such as Reissner-Nordstrom or Kerr-Newman, endowed with the NUT parameter. The full rotating version carries a couple of independent NUT charges, one associated to the black hole and the other to the accelerating Rindler background.The two NUT parameters can be coupled to remove the axial irregularity which causes the Misner string, still remaining with a Lorentzian spacetime, without the need to impose periodic time.All the metrics we build are not of D-type according to the Petrov classification, but type-I, so they belong to a more general category with respect to C-metrics and the Plebanski-Demianski seed.A convenient form of the most general type D black hole solution in general relativity, coupled with Maxwell electromagnetism, is obtained when switching off one of the two NUT parameters.

Consistent thermodynamics and topological classes for the four-dimensional Lorentzian charged Taub-NUT spacetimes

In this paper, we derive the consistent thermodynamics of the four-dimensional Lorentzian Reissner-Nordström-NUT (RN-NUT), Kerr–Newman-NUT (KN-NUT), and RN-NUT-AdS spacetimes in the framework of the (psi -mathscr {N})-pair formalism, and then investigate their topological numbers by using the uniformly modified form of the generalized off-shell Helmholtz free energy. We find that these solutions can be included into one of three categories of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the perspective of the topological thermodynamic defects. In addition, we demonstrate that although the existence of the NUT charge parameter seems to have no impact on the topological number of the charged asymptotically locally flat spacetimes, it has a remarkable effect on the topological number of the charged asymptotically locally AdS spacetime.

Entropy product function and central charges in NUT geometry

We define an entropy product function (EPF) for Taub–Newman–Unti–Tamburino (TNUT) black hole (BH) following the prescription suggested by Wu et al. [Phys. Rev. D 100, 101501(R) (2019)]. The prescription argues that a generic four-dimensional TNUT space–time might be expressed in terms of three or four different types of thermodynamic hairs. They can be defined as the Komar mass ([Formula: see text]), the angular momentum ([Formula: see text]), the gravitomagnetic charge ([Formula: see text]), the dual (magnetic) mass [Formula: see text]. Taking this prescription and using the EPF, we derive the central charges of dual conformal field theory (CFT) via Cardy’s formula. Remarkably, we find that for TNUT BH there exists a relation between the central charges and EPF as [Formula: see text], where [Formula: see text] is EPF and [Formula: see text] is one of the integer-valued charges i.e. the NUT charges ([Formula: see text]) or any new conserved charges ([Formula: see text]). We reverify these results by calculating the exact values of different thermodynamic parameters. We define the EPF [Formula: see text] from the first law of thermodynamics of both horizons. Moreover, we write the first laws of both the horizons for left-moving and right-moving sectors. Introducing the Bézout’s identity, we show that for TNUT BH one can generate more holographic descriptions described by a pair of integers [Formula: see text]. More holographic pictures have a great significance towards understanding the holographic nature of quantum gravity. Furthermore, using the EPF we derive the central charges for Reissner–Nordström–NUT (RNNUT) BH, Kerr–Taub–NUT (KNUT) BH and Kerr–Newman–NUT (KNNUT) BH. Finally we prove that they are equal in both sectors provided that the EPF is mass-independent (or universal).

Aligned fields double copy to Kerr-NUT-(A)dS

We find Abelian gauge fields that double copy to a large class of black hole spacetimes with spherical horizon topology known as the Kerr-NUT-(A)dS family. Using a multi-Kerr-Schild prescription, we extend the previously-known double copy structure for arbitrarily rotating general dimension black holes, to include NUT charges and an arbitrary cosmological constant. In all cases, these single copy gauge fields are ‘aligned fields’, because their nonzero components align with the principal tensor which generates the Killing structure of the spacetime. In five dimensions, we additionally derive the same single-copy field strengths via the Weyl double copy procedure.

Wormholes, killing horizons and naked singularities: light surfaces in axially symmetric spacetimes

We study several classes of exterior and interior axially symmetric spacetimes, such as wormholes, accelerating black holes, and binary black hole systems, from the point of view of light surfaces related to the generators of Killing horizons. We show that light surfaces constitute a useful framework for the study of the more diverse axially symmetric geometries. In particular, we point out the existence of common properties of the light surfaces in different spacetimes. We introduce a deformation of the Kerr–Newman metric and apply the light surfaces framework to analyze several generalizations in a compact form. As particular examples, we analyze static and spinning wormhole solutions, black holes immersed in external (perfect fluid) dark matter, spacetimes with (Taub) NUT charge, acceleration, magnetic charge, and cosmological constant, binary Reissner–Nordström black holes, a solution of a (low-energy effective) heterotic string theory, and the (1+2) dimensional BTZ geometry.

Chaos bound in Kerr-Newman-Taub-NUT black holes via circular motions* *Supported in part by the NSFC (12105031), Tianfu talent plan and FXHU

In this study, we investigate the influence of the angular momentum of a charged particle around Kerr-Newman-Taub-NUT black holes on the Lyapunov exponent and find spatial regions where the chaos bound is violated. The exponent is obtained by solving the determination of the eigenvalues of a Jacobian matrix in the phase space. Equilibrium positions are obtained by fixing the charge-to-mass ratio of the particle and changing its angular momentum. For certain values of the black holes' electric charge, the NUT charge and rotational parameter, a small angular momentum of the particle, even with zero angular momentum, causes violation of the bound. This violation disappears at a certain distance from the event horizon of the non-extremal Kerr-Newman-Taub-NUT black hole when the angular momentum increases to a certain value. When the black hole is extremal, the violation always exists no matter how the angular momentum changes. The ranges of the angular momentum and spatial regions for the violation are found. The black holes and particle rotating in the same and opposite directions are discussed.

Thermodynamics of Taub-NUT and Plebanski solutions

We observe the parallel between the null Killing vector on the horizon and degenerate Killing vectors at both north and south poles in Kerr-Taub-NUT and general Plebanski solutions. This suggests a correspondence between the pairs of the angular momentum/velocity and the NUT charge/potential. We treat the time as a real line such that the Misner strings are physical. We find that the NUT charge spreads along the Misner strings, analogous to that the mass in the Schwarzschild black hole sits at its spacetime singularity. We develop procedures to calculate all the thermodynamic quantities and we find that the results are consistent with the first law (Wald formalism), the Euclidean action and the Smarr relation. We also apply the Wald formalism, the Euclidean action approach, and the (generalized) Komar integration to the electric and magnetic black holes in a class of EMD theories, and also to boosted black strings and Kaluza-Klein monopoles in five dimensions, to gain better understandings of how to deal with the subtleties associated with Dirac and Misner strings.

Black holes in Klein space

The analytic continuation of the general signature (1, 3) Lorentzian Kerr-Taub-NUT black holes to signature (2, 2) Kleinian black holes is studied. Their global structure is characterized by a toric Penrose diagram resembling their Lorentzian counterparts. Kleinian black holes are found to be self-dual when their mass and NUT charge are equal for any value of the Kerr rotation parameter a. Remarkably, it is shown that the rotation a can be eliminated by a large diffeomorphism; this result also holds in Euclidean signature. The continuation from Lorentzian to Kleinian signature is naturally induced by the analytic continuation of the S-matrix. Indeed, we show that the geometry of linearized black holes, including Kerr-Taub-NUT, is captured by (2, 2) three-point scattering amplitudes of a graviton and a massive spinning particle. This stands in sharp contrast to their Lorentzian counterparts for which the latter vanishes kinematically and enables a direct link to the S-matrix.

First law for Kerr Taub-NUT AdS black holes

The first law of black hole mechanics, which relates the change of energy to the change of entropy and other conserved charges, has been the main motivation for probing the thermodynamic properties of black holes. In this work, we investigate the thermodynamics of Kerr Taub-NUT AdS black holes. We present geometric Komar definitions for the black hole charges, that by construction satisfy the Smarr formula. Further, by a scaling argument based on Euler’s theorem, we establish the first law for the Kerr Taub-NUT AdS black holes. The corresponding first law includes variations in the cosmological constant, NUT charges and angular momenta. The key new ingredient in the construction are the independent variations of both angular momenta, the black hole and Misner string angular momenta. Employing the Brown-York quasi-local charge definitions we show that our expression for the mass and spin coincide with our generalized Komar expressions. We indicate the relevance of these results to the thermodynamics of rotating AdS black holes, including the proper choice of time-like Killing vector to produce the correct thermodynamic mass.

Collisional Penrose process in Kerr–Taub–NUT spacetime

Maximum efficiency of collisional Penrose process with spinning and non-spinning particles in Kerr–Taub–NUT spacetime has been studied. We consider three cases in detail: two massive particles collide near the horizon, one of the resulting massive particles escapes to infinity, and the other massive particle falls into the black hole; a massless particle collides with a massive particle, then the massless daughter particle escapes from the black hole to infinity, and the massive daughter particle falls into the black hole (Compton scattering); a massive particle collides with a massless particle, the massive daughter particle escapes from the black hole to infinity and the massless daughter particle falling into the horizon (inverse Compton scattering). We find that for these cases, regardless of whether particles are spinning or not, the maximum energy extraction efficiency of the collisional Penrose process always decreases as the NUT charge increases, and the energy extraction efficiency in the spinning case is always higher than that in the non-spinning case.

Quasinormal modes of NUT-charged black branes in the AdS/CFT correspondence

We study the scalar, electromagnetic and gravitational perturbations of planar AdS4 black holes with NUT charge. In the context of the AdS/CFT correspondence, these solutions describe a thermal quantum field theory embedded in a Gödel-type Universe with closed time-like curves. For a given temperature and NUT charge, two different planar Taub–NUT solutions exist, but we show that only the one with a positive specific heat contributes to the Euclidean saddle point in the path integral. By using the Newman–Penrose formalism, we then derive the master equations satisfied by scalar, electromagnetic and gravitational perturbations in this background, and show that the corresponding equations are separable. Interestingly, the solutions pile up in the form of Landau levels, and hence are characterized by a single quantum number q. We determine the appropriate boundary conditions satisfied by the master variables and using these we compute the quasinormal modes of scalar and gravitational perturbations. On the other hand, electromagnetic perturbations depend on a free parameter whose determination is problematic. We find that all the scalar and gravitational QNM frequencies lie in the lower half of the complex plane, indicating that these Taub–NUT spacetimes are stable. We discuss the implications of these results in the light of the AdS/CFT correspondence.

Dual charges for AdS spacetimes and the first law of black hole mechanics

We apply the recent derivations of dual charges in asymptotically flat spacetimes to asymptotically locally AdS spacetimes. In contrast to the results in the flat case, in the AdS case with a Dirichlet boundary the dual charge contribution vanishes at the leading order. However, by focusing on the Taub-NUT-AdS solution, we show that nevertheless, more generally, the dual charge is non-vanishing and corresponds to the NUT parameter. We propose a complex first law of black mechanics in the presence of NUT charges that is inspired by the naturally complex nature of the charges derived using Hamiltonian methods.

Lorentzian Taub-NUT spacetimes: Misner string charges and the first law

Motivated by recent activities in Lorentzian Taub-NUT space thermodynamics, we calculate conserved charges of these spacetimes. We find additional mass, nut, angular momentum, electric and magnetic charge densities distributed along Misner string. These additional charges are needed to account for the difference between the values of the above charges at horizon and at infinity. We propose an unconstrained thermodynamical treatment for Taub-NUT spaces, where we introduce the nut charge $n$ as a relevant thermodynamic quantity with its chemical potential \phi_n. The internal energy in this treatment is M-n\phi_n rather than the mass M. This approach leads to an entropy which is a quarter of the area of the horizon and all thermodynamic quantities satisfy the first law, Gibbs-Duhem relation as well as Smarr's relation. We found a general form of the first law where the quantities depend on an arbitrary parameter. Demanding that the first law is independent of this arbitrary parameter or invariant under electric-magnetic duality leads to a unique form which depends on Misner string electric and magnetic charges. Misner string charges play an essential role in the first law, without them the first law is not satisfied.

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

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.