NUT Charge Research Articles

Optical properties of an axially symmetric black hole in the Rastall gravity

This work is devoted to the study of the optical properties of the charged-rotating-NUT-Kiselev (CRNK) black hole in the Rastall theory of gravity. By investigating the motion of photons in the CRNK black hole spacetime in the Rastall gravity, we show that the deflection angle of photons due to the gravitational lensing is mostly influenced by the NUT charge, parameter of the equation of state for the quintessence and the quintessential intensity. We observe that the effects of the rest of the spacetime parameters are negligible on the deflection angle. We present the shape of the shadow cast by the CRNK black hole in the Rastall gravity for various values of the spacetime parameters. We demonstrate that spin parameter a of the black hole changes the position and size of the shadow of the black hole very little, while changing the values of the rest of the spacetime parameters can alter the shape and the size of the observed shadow of the black hole significantly. We observe that the radius of the black hole shadow and the deflection angle of photon are bigger for the CRNK black hole in the Rastall gravity, as compared with the case of the Kerr black hole. Lastly, we show how the spacetime parameters can change the observables $$R_s$$ and $$\delta _s$$ , being the average radius of the shadow and the distortion parameter that measures the deviation of the shape of the shadow from a perfect circle with radius $$R_s$$ , respectively. Our results show that in most scenarios, for bigger values of $$R_s$$ , we get smaller values of the parameter $$\delta _s$$ .

Pure Gauss–Bonnet NUT black hole solution: I

We obtain an exact Lambda -vacuum solution in the pure Gauss–Bonnet gravity with NUT charge in six dimension, with horizon having the product topology of S^{(2)} times S^{(2)}. We discuss its horizon and singularity structure, and consequently arrive at parameter windows for its physical viability. It turns out that for the curvatures to remain function of r alone for NUT black hole spacetime, horizon topology has to be product of S^{(2)} spheres. This is true for Einstein as well as for pure Gauss–Bonnet gravity, and perhaps would hold good for higher order pure Lovelock as well.

On-shell electric-magnetic duality and the dual graviton

Using on-shell amplitude methods, we explore four-dimensional electric-magnetic duality and its double copy. We show explicitly that the on-shell scattering amplitudes know about ``dual'' photons (and dual gravitons), that the off-shell photon propagator double-copies to the graviton propagator, and that the magnetic part of the propagator is essential for the double copy to hold. We also show that there is an equivalent gravitomagnetic part of the graviton propagator, which is essential in giving rise to solutions with either angular momentum or NUT charge. Furthermore, we comment on the so-called Weinberg paradox, which states that scattering amplitudes involving the mixing of electric and magnetic monopoles cannot be Lorentz invariant, and would seem to preclude the existence of the 't Hooft--Polyakov (topological) monopole. We trace this paradox to the magnetic part of the propagator, showing that it can be eliminated if one restricts the scenario to proper orthochronous Lorentz transformations. Finally, we compute the fully relativistic cross section for arbitrary spin dyons using the recently formulated on-shell duality transformation, and we show that this is always fully Lorentz invariant.

Strong gravitational lensing by Kerr–Newman-NUT-Quintessence black hole

We investigate the strong gravitational lensing on equatorial plane as well as quasi-equatorial plane by the Kerr–Newman-NUT-Quintessence (KNNQ) black hole (BH) with the equation of state (EoS) parameter of the quintessence [Formula: see text] and the quintessence density [Formula: see text]. Our results show that the strong gravitational lensing in the KNNQ black hole space–time has some distinct behaviors from those in the backgrounds of the four dimension Kerr black hole. Also, we investigate the strong gravitational lensing on equatorial plane as well as quasi-equatorial plane by the KNNQ BH with the effects of Nut charge, spin parameter and quintessence parameter. First, we calculate the null geodesic equations using the Hamilton–Jacobi separation method. Then we investigate the equatorial lensing by KNNQ black hole. We obtain the deflection angle and deflection coefficients in the equatorial plane, which is affected by EoS parameter of the quintessence [Formula: see text], quintessence density [Formula: see text], Nut parameter [Formula: see text], spin parameter [Formula: see text] and quintessence parameter [Formula: see text] [Formula: see text]. Next, we discuss the lens equation and the observables in the equatorial plane. Finally, we investigate gravitational lensing by the KNNQ black hole in the quasi-equatorial plane. In this work, the quintessence density [Formula: see text], the EoS parameter of the quintessence [Formula: see text], Nut parameter [Formula: see text], spin parameter [Formula: see text] and quintessence parameter [Formula: see text] [Formula: see text] have significant effects on the strong gravitational lensing both in equatorial plane as well as quasi-equatorial plane.

Supersymmetric black holes with spiky horizons

We use the recipe of [1] to find half-BPS near-horizon geometries in the t3 model of N = 2, D = 4 gauged supergravity, and explicitely construct some new examples. Among these are black holes with noncompact horizons, but also with spherical horizons that have conical singularities (spikes) at one of the two poles. A particular family of them is extended to the full black hole geometry. Applying a double-Wick rotation to the near-horizon region, we obtain solutions with NUT charge that asymptote to curved domain walls with AdS3 world volume. These new solutions may provide interesting testgrounds to address fundamental questions related to quantum gravity and holography.

Aspects of holography of Taub-NUT- AdS4 spacetimes

In this paper we consider aspects of the holographic interpretation of Taub-NUT-${\mathrm{AdS}}_{4}$. We review our earlier results which show that ${\mathrm{TNAdS}}_{4}$ gives rise to a holographic three-dimensional conformal fluid having constant vorticity. We then study the holographic relevance of the Misner string by considering bulk scalar fluctuations. The scalar fluctuations organize naturally into representations of the $SU(2)\ifmmode\times\else\texttimes\fi{}\mathbb{R}$ isometry algebra. If we require the string's invisibility we obtain a Dirac-like quantization relating the frequency of the scalar field modes to the NUT charge. As the latter quantity determines the total vorticity flux of the boundary fluid, we argue that such an assumption allows for a holographic interpretation of ${\mathrm{TNAdS}}_{4}$ as a nondissipative superfluid whose excitations are quantized vortices. Alternatively, if we regard the Misner string as a physical object, as has recently been advocated for thermodynamically, the aforementioned quantization conditions are removed, and we find that ${\mathrm{TNAdS}}_{4}$ corresponds to a holographic fluid whose dissipative properties are probed as usual by the complex quasinormal modes of the bulk fluctuations. We show that such quasinormal modes are, perhaps surprisingly, organized into infinite-dimensional nonunitary representations of the isometry algebra.

NUT charge weak gravity conjecture from dimensional reduction

We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole weak gravity conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.

Pure Gauss\u2013Bonnet NUT black hole with and without non-central singularity

It is known that NUT solution has many interesting features and pathologies like being non-singular and having closed timelike curves. It turns out that in higher dimensions horizon topology cannot be spherical but it has instead to be product of 2-spheres so as to retain radial symmetry of spacetime. In this letter we wish to present a new solution of pure Gauss–Bonnet Lambda -vacuum equation describing a black hole with NUT charge. It has three interesting cases: (a) black hole with both event and cosmological horizons with singularity being hidden behind the former, (b) a regular spacetime free of both horizon and singularity, and (c) black hole with event horizon without singularity and cosmological horizon. Singularity here is always non-centric at r ne 0.

Hairy Taub-NUT/bolt-AdS solutions in Horndeski theory

We present different Taub-NUT/Bolt-anti de Sitter (AdS) solutions in a shift-symmetric sector of Horndeski theory of gravity possessing nonminimal kinetic coupling of scalar fields to the Einstein tensor. In four dimensions, we find locally and asymptotically locally AdS solutions possessing nontrivial scalar field. In higher dimensions, analytical Taub-NUT/Bolt-AdS p-branes and solitons are obtained, supported by the existence of p Horndeski scalar fields with axionic profile. The thermodynamical properties are studied through Euclidean methods and it is found that the first law of thermodynamics is satisfied. Moreover, constraints on the parameter space of Horndeski gravity and NUT charge are obtained by demanding positivity of the mass, entropy, and specific heat of the p-branes and soliton. We briefly comment on future applications in holography.

NUT charges and black hole shadows

We study the nontrivial effects of the NUT charges on the shadows of the Kerr-Taub-NUT black holes seen by zero-angular-momentum-observers. Inclination angles with which the observers gain maximal, locally extreme or minimal shadow sizes and distortions are investigated for the black holes with different NUT charges and distributions of string singularities. Typically, we discover that when the observer approaches the string singularity, the shadow size can be relatively very small while the shadow distortion being relatively quite large. And exceptionally, we find that when the string singularity locates only at the south pole axis of the black hole with large enough NUT charge, the shadow size is maximal for a north pole observer.

The gravimagnetic dipole

We investigate a previously constructed stationary solution of the vacuum Einstein equations, which represents a system of two non-extreme black holes with equal masses and opposite NUT charges, connected by a Misner string with tension. For large separations, the inverse square law force measured by this tension is attractive or repulsive, according to the relative values of the masses and NUT charges. For small separations, the force is always repulsive, so that the system cannot collapse to a single black hole. For given values of the black hole masses and NUT charges, there is a unique configuration such that the Misner string is tensionless. This behaves asymptotically as the Kerr solution, but can be overspinning while remaining free from a ring singularity, thus evading the usual black hole uniqueness theorems. All double black hole and string configurations satisfy a generalized first law of black hole mechanics where the two black holes and the Misner string are treated on an equal footing.

Scalarized Nutty Wormholes

We construct scalarized wormholes with a NUT charge in higher curvature theories. We consider both Einstein-scalar-Gauss-Bonnet and Einstein-scalar-Chern-Simons theories, following Brihaye, Herdeiro and Radu, who recently studied spontaneously scalarised Schwarzschild-NUT solutions. By varying the coupling parameter and the scalar charge we determine the domain of existence of the scalarized nutty wormholes, and their dependence on the NUT charge. In the Gauss-Bonnet case the known set of scalarized wormholes is reached in the limit of vanishing NUT charge. In the Chern-Simons case, however, the limit is peculiar, since with vanishing NUT charge the coupling constant diverges. We focus on scalarized nutty wormholes with a single throat and study their properties. All these scalarized nutty wormholes feature a critical polar angle, beyond which closed timelike curves are present.

Multipole moments of compact objects with NUT charge: Theoretical and observational implications

We derive the multipole moments of the Kerr-NUT black hole spacetime using the Geroch-Hansen formalism, even though the spacetime is not asymptotically flat. Intriguingly, in the presence of the NUT charge, the absence of reflection symmetry about the equatorial plane, leads to mass and spin multipole moments of all orders, in stark contrast to Kerr-like spacetimes. This leads to a drastic departure of the multipolar structure of a compact object with NUT charge, whose implications for gravitational wave observations have been explored. Our analysis of multipole moments for the Kerr-NUT spacetime is also in tune with the Thorne's approach.

Strong cosmic censorship conjecture with NUT charge and conformal coupling

Strong cosmic censorship conjecture is central to the deterministic nature of general relativity, since it asserts that given any generic initial data on a spacelike hypersurface, the future can be uniquely predicted. However, recently it has been found that for charged black holes in asymptotically de Sitter spacetimes, the metric and massless scalar fields can be extended beyond the Cauchy horizon. This spells doom on the strong cosmic censorship conjecture, which prohibits precisely this scenario. In this work we try to understand the genericness of the above situation by studying the effect of NUT charge and conformally coupled scalar field on the violation of strong cosmic censorship conjecture for charged asymptotically de Sitter black holes. We have shown that even in the presence of the NUT charge and a conformally coupled scalar field strong cosmic censorship conjecture in indeed violated for such black holes with Cauchy horizon. Moreover, the presence of conformal coupling makes the situation even worse, in the sense that the scalar field is extendible across the Cauchy horizon as a C 1 function. On the other hand, the strong cosmic censorship conjecture is respected for conformally coupled scalar field in rotating black hole spacetimes with NUT charge. This reinforces the belief that possibly for astrophysical black holes, strong cosmic censorship conjecture is respected, irrespective of the nature of the scalar field.

Gravitational Wu-Yang monopoles

We show that in an asymptotically flat space where an S-Matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct super-selection sectors, labeled by their dual supertranslation charges. These results suggest that dual supertranslation may be interpreted as a redundant gauge symmetry of asymptotically flat spacetimes. This would allow to recast general relativity as a theory of diffeomorphisms possessing an additional asymptotic gauge symmetry. We then use the conjectured dual supertranslation gauge symmetry to construct a gravitational equivalent of the Wu-Yang monopole solution. The metric describing the solution is defined using two overlapping patches on the celestial sphere. The solution is regular on each one of the patches separately and differentiable in the overlap region, where the two descriptions are identical by virtue of a dual supertranslation gauge transformation. Our construction provides an alternative to Misner's interpretation of the Taub-NUT metric. In particular, we find that using our approach the Taub-NUT metric can be made regular everywhere on the celestial sphere and at the same time it is devoid of closed timelike curves, provided that the bound $\frac{m}{\ell} \leq \sqrt{\frac{5}{27}}$ on the ratio of mass to NUT charge is obeyed.

Topological dyonic Taub-Bolt/NUT-AdS solutions: Thermodynamics and first law

Motivated by the absence of Misner string in the Euclidean Taub-Bolt/NUT solutions with flat horizons, we present a new treatment for studying the thermodynamics of these spactimes. This treatment is based on introducing a new charge, $N=\sigma \, n$ (where $n$ is the nut charge and $\sigma$ is some constant) and its conjugate thermodynamic potential $\Phi_N$. Upon identifying one of the spatial coordinates, the boundary of these solutions contains two annulus-like surfaces in addition to the constant-r surface. For these solutions, we show that these annuli surfaces receive electric, magnetic and mass/energy fluxes, therefore, they have nontrivial contributions to these conserved charges. Calculating these conserved charges we find, $Q_e = Q^{\infty}_e-2N\Phi_m$, $Q_m =Q^{\infty}_m+2N\Phi_e$ and $\mathfrak{M} =M-2N\Phi_N$, where $Q^{\infty}_e$, $Q^{\infty}_m$, $M$ are electric charge, magnetic charge and mass in the $n=0$ case, while $\Phi_e$ and $\Phi_m$ are the electric and magnetic potentials. The calculated thermodynamic quantities obey the first law of thermodynamics while the entropy is the area of the horizon. Furthermore, all these quantities obey Smarr's relation. We show the consistency of these results through calculating the Hamiltonian and its variation which reproduces the first law.

NUT charge in linearized infinite derivative gravity

We study the gravitational field of the NUT-like source in the linearized (ghost-free) infinite derivative gravity. Such a source is equivalent to the spinning semi-infinite cosmic string with no tension. In general relativity, the linearized (massless) Taub-NUT solution has a curvature singularity as well as a topological defect corresponding to distributional curvature on one half of the symmetry axis called the Misner string. We find the NUT-charged spacetime in the linearized infinite derivative gravity. We show that it is free from curvature singularities as well as Misner strings. We also discuss an asymptotic limit along the symmetry axis that leads to the spacetime of a spinning cosmic string of infinite length.

Holographic description of M-branes via AdS2

We study AdS2× S4× S2× Σ2 solutions in type IIB string theory arising from D1-D3-NS5 brane intersections. These backgrounds enjoy sixteen supercharges and the corresponding internal geometry is non-compact due to the specific form of the warping w.r.t. the Riemann surface Σ2. Even though a direct computation of the holographic free energy of the would-be dual CFT1 yields a divergent behaviour, it reveals the typical N3 scaling of a 6d theory upon introducing a hard cut-off. We claim that such geometries may be interpreted as the gravity duals of M(atrix) models describing an IR phase of the (2, 0) theory of M5 branes, in presence of momentum and NUT charges. We discuss parallel AdS2 geometries describing longitudinal M2 branes in the UV, where the counting of the number of degrees of freedom correctly reproduces the expected N3/2 behaviour of the dual field theory. These geometries provide explicit examples where deconstructed extra dimensions yield well-defined UV descriptions in terms of higher-dimensional CFTs.

Weak cosmic censorship conjecture for a Kerr-Taub-NUT black hole with a test scalar field and particle

Motivated by the recent researches of black holes with NUT charge, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black hole with a test massive scalar field and a test particle, respectively. For the scalar field scattering gedanken experiment, we consider an infinitesimal time interval process. The result shows that both extremal and near-extremal Kerr-Taub-NUT black holes cannot be over-spun. For the test particle thought experiment, the study suggests that extremal Kerr-Taub-NUT black hole cannot be over-spun; while near-extremal Kerr-Taub-NUT black hole can be over-spun. By comparing the two methods, the results indicate the time interval for particles crossing the black hole horizon might be important for consideration of the weak cosmic censorship conjecture.

Enhanced Ehlers transformation and the Majumdar-Papapetrou-NUT spacetime

The transformation which adds (or removes) NUT charge when it is applied to electrovacuum, axisymmetric and stationary space-times is studied. After analysing the Ehlers and the Reina-Treves transformations we propose a new one, more precise in the presence of the Maxwell electromagnetic field. The enhanced Ehlers transformation proposed turns out to act as a gravitomagnetic duality, analogously to the electromagnetic duality, but for gravity: it rotates the mass charge into the gravomagnetic (or NUT) charge. As an example the Kerr-Newman-NUT black hole is obtained with the help of this enhanced transformation. Moreover a new analytical exact solution is built adding the NUT charge to a double charged black hole, at equilibrium. It describes the non-extremal generalisation of the Majumdar-Papapetrou-NUT solution. From the near-horizon analysis, its microscopic entropy, according to the Kerr/CFT correspondence, is found and the second law of black hole thermodynamics is discussed.