Kerr Taub NUT Research Articles

Kerr/CFT correspondence for the extremal accelerating Kerr–Taub–NUT black hole

In this paper, we explore the application of Kerr/CFT correspondence to the accelerating Kerr–Taub–NUT spacetime. We demonstrate that the correspondence can be maintained if the near-horizon angular coordinate is appropriately rescaled. This rescaling allows the Cardy formula to accurately reproduce the extremal Bekenstein–Hawking entropy, a departure from the typical direct recovery of extremal Bekenstein–Hawking temperature in Kerr/CFT literature. This discrepancy is attributed to the presence of multiple sources of conic singularity in the spacetime, specifically the acceleration and NUT parameters. To support the Kerr/CFT holography, we investigate the hidden conformal symmetry in the near-horizon region of the extremal black hole geometry. Our findings confirm that the angular coordinate rescaling does not introduce inconsistencies within the Kerr/CFT framework, as evidenced by the preserved hidden conformal symmetry and consistent entropy matching calculations in the near-horizon geometry of the extremal accelerating Kerr–Taub–NUT black hole.

Time evolution of the Von Neumann entropy for a Kerr–Taub–NUT black hole

In this work, we study the evolution of an evaporating black hole, described by the Kerr–Taub–NUT metric, which emits scalar particles. We found that allowing the black hole to radiate massless scalar particles increases the angular momentum loss rate while decreasing the loss rate of the NUT parameter and black hole mass. In fact, it means that angular momentum will disappear faster than the other black hole parameters (mass and NUT parameter) during the evaporation process. We also calculate the time evolution of the mass, angular momentum, and NUT parameter in order to get the evolution of the Von Neumann entropy of the black hole. We found that the entropy follows approximately the so-called Page curve, where the β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} parameter, which quantifies the amount of radiation, affects the evaporation process. Implying that high β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} values accelerate the evaporation process of a Kerr–Taub–NUT black hole.

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).

Meissner effect and holographic dual for the Melvin–Kerr–Newman–Taub–NUT spacetimes

We investigate correspondence between the Melvin–Kerr–Newman–Taub–NUT spacetime, and the conformal field theory. The near horizon geometry of extremal Melvin–Kerr–Newman–Taub–NUT spacetime possesses the SLleft( 2,{{mathbb {R}}}right) times Uleft( 1right) isometry, which allows one to employ the asymptotic symmetry group method, in establishing the holographic correspondence for the spacetime. We also use the alternative way of the stretched horizon method, to compute the extremal entropy of the black hole. We find perfect agreement between the results of asymptotic symmetry group and the stretched horizon methods, to establish the holography for the extremal Melvin–Kerr–Newman–Taub–NUT black hole. The black hole Meissner effect for the Melvin–Kerr–Taub–NUT black hole is also discussed.

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.

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.

Study of relativistic accretion flow around KTN black hole with shocks

We present the global solutions of low angular momentum, inviscid, advective accretion flow around Kerr-Taub-NUT (KTN) black hole in presence and absence of shock waves. These solutions are obtained by solving the governing equations that describe the relativistic accretion flow in KTN spacetime which is characterized by the Kerr parameter (a k) and NUT parameter (n). During accretion, rotating flow experiences centrifugal barrier that eventually triggers the discontinuous shock transition provided the relativistic shock conditions are satisfied. In reality, the viability of shocked accretion solution appears more generic over the shock free solution as the former possesses high entropy content at the inner edge of the disc. Due to shock compression, the post-shock flow (equivalently post-shock corona, hereafter PSC) becomes hot and dense, and therefore, can produce high energy radiations after reprocessing the soft photons from the pre-shock flow via inverse Comptonization. In general, PSC is characterized by the shock properties, namely shock location (rs ), compression ratio (R) and shock strength (S), and we examine their dependencies on the energy (ξ) and angular momentum (λ) of the flow as well as black hole parameters. We identify the effective domain of the parameter space in λ-ξ plane for shock and observe that shock continues to form for wide range of flow parameters. We also find that a k and n act oppositely in determining the shock properties and shock parameter space. Finally, we calculate the disc luminosity (L) considering free-free emissions and observe that accretion flows containing shocks are more luminous compared to the shock free solutions.

On the Counter-Rotation of Closed Time-like Curves

While it is tempting to think of closed time-like curves (CTCs) around rotating bodies, such as a black hole, as being “caused” by the rotation of the source, Andréka et al. pointed out that the underlying physics are not as straightforward as this, since such CTCs are “counter-rotating”, i.e., the time orientation (the opening of the local light cones) of the CTCs is opposite to the direction in which the singularity or the ergosphere rotates. It was also suggested that this is a generic phenomenon that calls for a deeper intuitive physical understanding. In this short note, we point out—with Kerr–Taub–NUT as an example—that CTCs are counter-rotating with respect to the local angular velocity of the spacetime, not the global angular momentum, nor the angular velocity of the black hole horizon, which makes the physical interpretation of CTCs being “caused” by a rotating source even more problematic.

On generic rotating regular black hole solutions

In the present paper, we study rotating regular black hole (RBH) in the model of nonlinear electrodynamics (NED) in the framework of General Relativity (GR). The paper explores derivation of the generic form of rotating RBH solutions which can be written in Kerr-like form in Boyer–Lindquist coordinates. It is shown that RBH solutions depend on NED Lagrangian. Lastly, we also showed that Kerr–Newman–Taub–NUT spacetime, which is solution of Einstein–Maxwell equations, can be a candidate for one of exact analytical rotating RBH solution by calculating curvature invariants at origin r=0, as well as, Kerr–Taub–NUT and Taub–NUT spacetimes.

Investigating the existence of gravitomagnetic monopole in M87*

We examine the possibility for the existence of gravitomagnetic monopole (n_*) in M87* by using the results obtained from its first Event Horizon Telescope image. By numerically deducing the shadow sizes in Kerr-Taub-NUT (KTN) spacetime, we show that the shadow size increases with increasing |n_*| for a fixed Kerr parameter |a_*| in case of the KTN black hole, whereas for a KTN naked singularity it increases with increasing n_* for a fixed a_* > 0 if n_* > -cot 17^{circ } . In general, the asymmetry of shadow shape increases if the central dark object in M87 is a KTN/Kerr naked singularity instead of a KTN/Kerr black hole. We find that a non-zero gravitomagnetic monopole is still compatible with the current EHT observations, in which case the upper limit of n_* cannot be greater than 1.1, i.e., n_* lesssim 1.1 for the prograde rotation (a_* > 0), and the lower limit of n_* cannot be less than -1.1, i.e., n_* gtrsim -1.1 for the retrograde rotation (a_* < 0). Moreover, if the circularity of the shadow can be measured on a precision of lesssim 1%, the Kerr and KTN naked singularities can be falsified for M87*.

Study of relativistic accretion flow in Kerr-Taub-NUT spacetime

We study the properties of the relativistic, steady, axisymmetric, low angular momentum, inviscid, advective, geometrically thin accretion flow in a Kerr-Taub-NUT (KTN) spacetime which is characterized by the Kerr parameter ($a_{\rm k}$) and NUT parameter ($n$). Depending on $a_{\rm k}$ and $n$ values, KTN spacetime represents either a black or a naked singularity. We solve the governing equations that describe the relativistic accretion flow in KTN spacetime and obtain all possible global transonic accretion solutions around KTN black hole in terms of the energy $({\cal E})$ and angular momentum $(\lambda)$ of the flow. We identify the region of the parameter space in $\lambda-{\cal E}$ plane that admits the flow to possess multiple critical points for KTN black hole. We examine the modification of the parameter space due to $a_{\rm k}$ and $n$ and find that the role of $a_{\rm k}$ and $n$ in determining the parameter space is opposite to each other. This clearly indicates that the NUT parameter $n$ effectively mitigates the effect of black hole rotation in deciding the accretion flow structure. Further, we calculate the maximum disc luminosity ($L_{\rm max}$) corresponding to the accretion solutions around the KTN black hole and for a given set of $a_{\rm k}$ and $n$. In addition, we also investigate all possible flow topologies around the naked singularity and find that there exists a region around the naked singularity which remains inaccessible to the flow. We study the critical point properties for naked singularities and find that the flow possesses maximum of four critical points. Finally, we obtain the parameter space for multiple critical points for naked singularity and find that parameter space is shrunk and shifted to lower $\lambda$ and higher ${\cal E}$ side as $a_{\rm k}$ is increased which ultimately disappears.

Circular orbits in Kerr-Taub-NUT spacetime and their implications for accreting black holes and naked singularities

It has recently been proposed that the accreting collapsed object GRO J1655–40 could contain a non-zero gravitomagnetic monopole, and hence could be better described with the more general Kerr-Taub-NUT (KTN) spacetime, instead of the Kerr spacetime. This makes the KTN spacetime astrophysically relevant. In this paper, we study properties of various circular orbits in the KTN spacetime, and find the locations of circular photon orbits (CPOs) and innermost-stable-circular-orbits (ISCOs). Such orbits are important to interpret the observed X-ray spectral and timing properties of accreting collapsed objects, viz., black holes and naked singularities. Here we show that the usual methods to find the ISCO radius do not work for certain cases in the KTN spacetime, and we propose alternate ways. For example, the ISCO equation does not give any positive real radius solution for particular combinations of Kerr and NUT parameter values for KTN naked singularities. In such a case, accretion efficiency generally reaches 100% at a particular orbit of radius r=r0, and hence we choose r=r0 as the 'ISCO' for practical purposes.

Can test fields destroy the event horizon in the Kerr–Taub–NUT spacetime?

In this work we investigate if the interaction of the Kerr–Taub–NUT spacetime with test scalar and neutrino fields can lead to the destruction of the event horizon. It turns out that both extremal and nearly extremal black holes can be destroyed by scalar and neutrino fields if the initial angular momentum of the spacetime is sufficiently large relative to its mass and NUT charge. This is the first example in which a classical field satisfying the null energy condition can actually destroy an extremal black hole. For scalar fields, the modes that can lead to the destruction of the horizon are restricted to a narrow range due to superradiance. Since superradiance does not occur for neutrino fields, the destruction of the horizon by neutrino fields is generic, and it cannot be fixed by backreaction effects. We also show that the extremal black holes that can be destroyed by scalar fields correspond to naked singularities in the Kerr limit, in accord with the previous results which imply that extremal Kerr black holes cannot be destroyed by scalar test fields.

New entropy formula for Kerr black holes

We introduce a new entropy formula for Kerr black holes inspired by recent results for 3-dimensional black holes and cosmologies with soft Heisenberg hair. We show that also Kerr–Taub–NUT black holes obey the same formula.

Surface area products for Kerr-Taub-NUT space-time

We examine properties of the inner and outer horizon thermodynamics of Taub-NUT (Newman-Unti-Tamburino) and Kerr-Taub-NUT (KTN) black hole (BH) in four-dimensional Lorentzian geometry. We compare and contrasted these properties with the properties of Reissner Nordstrøm (RN) BH and Kerr BH. We focus on “area product”, “entropy product”, “irreducible mass product” of the event horizon and Cauchy horizons. Due to mass dependence, we speculate that these products have no nice quantization feature. Nor do they have any universal property. We further observe that the first law of BH thermodynamics and Smarr-Gibbs-Duhem relations do not hold for Taub-NUT (TN) and KTN BH in Lorentzian regime. The failure of these aforementioned features are due to the presence of the non-trivial NUT charge which makes the space-time be asymptotically non-flat, in contrast with RN BH and Kerr BH. Another reason for the failure is that Lorentzian TN and Lorentzian KTN geometries contain Dirac-Misner–type singularity, which is a manifestation of a non-trivial topological twist of the manifold. The black-hole mass formula and Christodoulou-Ruffini mass formula for TN and KTN BHs are also computed. These thermodynamic product formulae give us further understanding of the nature of inner as well as outer BH entropy at the microscopic level.

Anomalous Lense–Thirring precession in Kerr–Taub–NUT spacetimes

Exact Lense-Thirring (LT) precession in Kerr-Taub-NUT spacetime is reviewed. It is shown that the LT precession does not obey the general inverse cube law of distance at strong gravity regime in Kerr-Taub-NUT spacetime. Rather, it becomes maximum just near the horizon, falls sharply and becomes zero near the horizon. The precession rate increases again and after that it falls obeying the general inverse cube law of distance. This anomaly is maximum at the polar region of this spacetime and it vanishes after crossing a certain `critical' angle towards equator from pole. We highlight that this particular `anomaly' also arises in the LT effect at the interior spacetime of the pulsars and such a signature could be used to identify a role of Taub-NUT solutions in the astrophysical observations or equivalently, a signature of the existence of NUT charge in the pulsars. In addition, we show that if the Kerr-Taub-NUT spacetime rotates with the angular momentum $J=Mn$ (Mass$\times$Dual Mass), inner horizon goes to at $r=0$ and only {\it event horizon} exists at the distance $r=2M$.

Inner-most stable circular orbits in extremal and non-extremal Kerr–Taub-NUT spacetimes

We study causal geodesics in the equatorial plane of the extremal Kerr-Taub-NUT spacetime, focusing on the Innermost Stable Circular Orbit (ISCO),and compare its behaviour with extant results for the ISCO in the extremal Kerr spacetime. Calculation of the radii of the direct ISCO, its Kepler frequency, and rotational velocity show that the ISCO coincides with the horizon in the exactly extremal situation. We also study geodesics in the strong {\it non}-extremal limit, i.e., in the limit of vanishing Kerr parameter (i.e., for Taub-NUT and massless Taub-NUT spacetimes as special cases of this spacetime). It is shown that the radius of the direct ISCO increases with NUT charge in Taub-NUT spacetime. As a corollary, it is shown that there is no stable circular orbit in massless NUT spacetimes for timelike geodesics.

The Dirac equation in Kerr-Taub-NUT spacetime

We study the Dirac equation in the Kerr–Taub–NUT spacetime. We use Boyer–Lindquist coordinates and separate the resulting equations into radial and angular parts. We obtain some exact analytical solutions of the angular equations for some special cases. We also obtain the radial wave equations with an effective potential. Finally, we discuss the potentials by plotting them as a function of radial distance in a physically acceptable region.

Asymptotic flatness, Taub-NUT metric, and variational principle

Using hyperbolic temporal and spatial cutoffs to define four-dimensional asymptotically flat spacetimes, we show that supertranslation ambiguities in the asymptotic fields can all be removed even in the presence of gravitational magnetic charges. We then show that configurations with different electric and magnetic four-momenta can be consistently considered in the Mann-Marolf variational principle. This generalizes the previous result where variations over asymptotically flat configurations with fixed magnetic four-momenta were considered. We also express the Kerr Taub-NUT metric to the leading and next-to-leading order in the Beig-Schmidt form, and compare the asymptotic form with the tensor harmonics on three-dimensional de Sitter space.

SEPARABILITY OF THE MASSIVE DIRAC EQUATION AND HAWKING RADIATION OF DIRAC PARTICLES IN THE CHARGED AdS–KERR–TAUB–NUT BLACK HOLE

We investigate the separability of massive Dirac equation in the charged AdS–Kerr–Taub–NUT black hole. It is shown that the Dirac equation can be separated by variables into purely radial and purely angular parts in this background spacetime. From the separated solutions for massive Dirac equation, a first-order symmetric operator that commutes with the Dirac operator is constructed and expressed in terms of Killing–Yano tensor admitted by the charged AdS–Kerr–Taub–NUT spacetime. Then the Hawking radiation of Dirac particles in the background of charged AdS–Kerr–Taub–NUT black hole is investigated via the Damour–Ruffini–Sannan method. It is shown that quantum thermal effect of the Dirac particles in the charged AdS–Kerr–Taub–NUT black hole has the same character with that of the scalar particles.