NUT Black Hole Research Articles

CFT duals on extremal rotating NUT black holes

We investigate the Kerr–Newman–NUT black hole solution obtained from Plebański–Demiański solutions with several assumptions. The origin of the microscopic entropy of this black hole is investigated using the conjectured Kerr/CFT correspondence which is originally proposed for extremal Kerr black holes. The isometry of the near-horizon extremal Kerr–Newman–NUT black hole shows that the asymptotic symmetry group may be implemented to compute the central charge of the Virasoro algebra. Furthermore, by assuming the Frolov–Thorne vacuum, the conformal temperatures can be obtained. Then by using the Cardy formula, the microscopic entropy is gained which matches the Bekenstein–Hawking entropy. We also employ the Cardy prescription to find the logarithmic correction of the entropy. Then at limit [Formula: see text], the extremal Reissner–Nordström–NUT solution is recovered and by enhancing with the fibered coordinate we find the five-dimensional (5D) solution. The second dual CFT is applied to this black hole to gain the entropy. Finally, the microscopic entropy is still in agreement with the area law of 5D black hole solution. Hence, the extremal Reissner–Nordström–NUT solution is holographically dual to the CFT.

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.

The fingerprints of black holes—shadows and their degeneracies

We show that, away from the axis of symmetry, no continuous degeneration exists between the shadows of observers at any point in the exterior region of any Kerr–Newman black hole spacetime of unit mass. Therefore, except possibly for discrete changes, an observer can, by measuring the black holes shadow, determine the angular momentum and the charge of the black hole under observation as well as the observer’s radial position and angle of elevation above the equatorial plane. Furthermore, his/her relative velocity compared to a standard observer can also be measured. However, the black hole shadow does not allow for a full parameter resolution in the case of a Kerr–Newman–Taub–NUT black hole, as a continuous degeneration relating specific angular momentum, electric charge, Taub–NUT charge and elevation angle exists in this case.

Circular orbits in the Taub–NUT and massless Taub–NUT spacetime

In this work, we study the equatorial causal geodesics of the Taub–NUT (TN) spacetime in comparison with massless TN spacetime. We emphasized both on the null circular geodesics and time-like circular geodesics. From the effective potential diagram of null and time-like geodesics, we differentiate the geodesics structure between TN spacetime and massless TN spacetime. It has been shown that there is a key role of the NUT parameter to changes the shape of pattern of the potential well in the NUT spacetime in comparison with massless NUT spacetime. We compared the innermost stable circular orbit (ISCO), marginally bound circular orbit (MBCO) and circular photon orbit (CPO) of the said spacetime with graphically in comparison with massless cases. Moreover, we compute the radius of ISCO, MBCO and CPO for extreme TN black hole (BH). Interestingly, we show that these three radii coincides with the Killing horizon, i.e. the null geodesic generators of the horizon. Finally in Appendix A, we compute the center-of-mass (CM) energy for TN BH and massless TN BH. We show that in both cases, the CM energy is finite. For extreme NUT BH, we found that the diverging nature of CM energy. First, we have observed that a non-asymptotic flat, spherically symmetric and stationary extreme BH showing such feature.

Thermodynamic product formula for a Taub–NUT black hole

We derive various important thermodynamic relations of the inner and outer horizon in the background of Taub-NUT(Newman-Unti-Tamburino) black hole in four dimensional \emph{Lorentzian geometry}. We compare these properties with the properties of Reissner Nordstr{\o}m black hole. We compute \emph{area product, area sum, area minus and area division} of black hole horizons. We show that they all are not universal quantities. Based on these relations, we compute the area bound of all horizons. From area bound, we derive entropy bound and irreducible mass bound for both the horizons. We further study the stability of such black hole by computing the specific heat for both the horizons. It is shown that due to negative specific heat the black hole is thermodynamically unstable. All these calculations might be helpful to understanding the nature of black hole entropy both \emph{interior} and exterior at the microscopic level.

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.

Universal BPS structure of stationary supergravity solutions

We study asymptotically flat stationary solutions of four-dimensional supergravity theories via the associated G/H ∗ pseudo-Riemannian non-linear sigma models in three spatial dimensions. The Noether charge C associated to G is shown to satisfy a characteristic equation that determines it as a function of the four-dimensional conserved charges. The matrix C is nilpotent for non-rotating extremal solutions. The nilpotency degree of C is directly related to the BPS degree of the corresponding solution when they are BPS. Equivalently, the charges can be described in terms of a Weyl spinor |C i of Spin ∗ (2N), and then the characteristic equation becomes equivalent to a generalisation of the Cartan pure spinor constraint on |C i . The invariance of a given solution with respect to supersymmetry is determined by an algebraic ‘Dirac equation’ on the Weyl spinor |C i . We explicitly solve this equation for all pure supergravity theories and we characterise the stratified structure of the moduli space of asymptotically Taub–NUT black holes with respect to their BPS degree. The analysis is valid for any asymptotically flat stationary solutions for which the singularities are protected by horizons. The H ∗ -orbits of extremal solutions are identified as Lagrangian submanifolds of nilpotent orbits of G, and so the moduli space of extremal spherically symmetric black holes is identified as a Lagrangian subvariety of the variety of nilpotent elements of g. We also generalise the notion of active duality transformations to an ‘almost action’ of the three-dimensional duality group G on asymptotically flat stationary solutions.

Taub–NUT black holes in third order Lovelock gravity

We consider the existence of Taub–NUT solutions in third order Lovelock gravity with cosmological constant, and obtain the general form of these solutions in eight dimensions. We find that, as in the case of Gauss–Bonnet gravity and in contrast with the Taub–NUT solutions of Einstein gravity, the metric function depends on the specific form of the base factors on which one constructs the circle fibration. Thus, one may say that the independence of the NUT solutions on the geometry of the base space is not a robust feature of all generally covariant theories of gravity and is peculiar to Einstein gravity. We find that when Einstein gravity admits non-extremal NUT solutions with no curvature singularity at r=N, then there exists a non-extremal NUT solution in third order Lovelock gravity. In 8-dimensional spacetime, this happens when the metric of the base space is chosen to be CP3. Indeed, third order Lovelock gravity does not admit non-extreme NUT solutions with any other base space. This is another property which is peculiar to Einstein gravity. We also find that the third order Lovelock gravity admits extremal NUT solution when the base space is T2×T2×T2 or S2×T2×T2. We have extended these observations to two conjectures about the existence of NUT solutions in Lovelock gravity in any even-dimensional spacetime.

MODIFICATIONS TO BEKENSTEIN–HAWKING ENTROPY DUE TO ARBITRARY SPIN FIELDS

The modified entropy, due to massless quantum fields of arbitrary spin s≤2, of the Kerr–Taub–NUT black hole is evaluated. The appearance of logarithmic terms is demonstrated. The modified entropy can be reduced to the form proportional to the area of the event horizon. However, modified coefficient not only depend on the characteristics of the black hole but also on the spin of the fields.

Algebraically special frequencies of NUT black holes

The algebraically special frequencies of Taub–NUT black holes are investigated in detail in comparison with known results concerning the Schwarzschild case. The periodicity of the time coordinate, required for regularity of the solution, prevents algebraically special frequencies to be physically acceptable. In the more involved Kerr–Taub–NUT case, the relevant equations governing the problem are obtained.