Newman Unti Research Articles

Bekenstein–Hawking entropy products for NUT class of black holes in AdS space

In this paper, we derive the entropy product rule for Taub–Newman–Unti–Tamburino (Taub–NUT)–de Sitter black hole (BH) and Taub–NUT–anti-de Sitter BH. We show that the entropy products in terms of both the physical horizons are mass-independent. Both perturbative approximation and direct method have been considered. By introducing the cosmological horizon, we show that for Taub–NUT–de Sitter BH, there exists a mass-independent entropy functional relation in terms of three horizons namely event horizon (EH), Cauchy horizon (CH) and cosmological horizon (CHH) which depends on cosmological parameter ([Formula: see text]) and the NUT parameter (N). For Taub–NUT–anti-de Sitter BHs, we determine the mass-independent entropy functional relations in terms of two physical horizons (namely EH and CH) which depends on only NUT parameter. Sometimes some complicated functions of EH entropy and CH entropy are also strictly mass-independent. This is plausible only due to the new formalism developed in [S. Wu and D. Wu, Phys. Rev. D 100, 101501(R) (2019)] for NUT class of BHs. The formalism states that a generic four dimensional Taub–NUT spacetime should be described completely in terms of three or four different types of thermodynamic hairs. They could 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]. Finally, we could say that this universality is mainly due to the presence of new conserved charges [Formula: see text] which is closely analogue to the Kerr-like angular momentum [Formula: see text].

First law of black hole thermodynamics and the weak cosmic censorship conjecture for Kerr–Newman Taub–NUT black holes

Stimulated by the recent researches of black hole thermodynamics for black hole with Newman–Unti–Tamburino (NUT) parameter, we investigate the thermodynamics and weak cosmic censorship conjecture for a Kerr–Newman Taub–NUT black hole. By defining the electric charge as a Komar integral over the event horizon, we construct a consistent first law of black hole thermodynamics for a Kerr–Newman Taub–NUT black hole through Euclidean action. Having the first law of black hole thermodynamics, we investigate the weak cosmic censorship conjecture for the black hole with a charged test particle and a complex scalar field. We find that an extremal black hole cannot be destroyed by a charged test particle and a complex scalar field. For a near-extremal black hole with small NUT parameter, it can be destroyed by a charged test particle but cannot be destroyed by a complex scalar field.

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).

On the unit component of the Newman–Unti group

In this short note we identify the unit component of the Newman–Unti (NU) group in the fine very strong topology. In previous work, this component has been endowed with an infinite-dimensional Lie group structure, while the full NU-group does not support such a structure.

The partial Bondi gauge: Further enlarging the asymptotic structure of gravity

We present a detailed analysis of gravity in a partial Bondi gauge, where only the three conditions g_{rr}=0=g_{rA}grr=0=grA are fixed. We relax in particular the so-called determinant condition on the transverse metric, which is only assumed to admit a polyhomogeneous radial expansion. This is sufficient in order to build the solution space, which here includes a cosmological constant, time-dependent sources in the boundary metric, logarithmic branches, and an extra trace mode at subleading order in the transverse metric. The evolution equations are studied using the Newman–Penrose formalism in terms of covariant functionals identified from the Weyl scalars, and we build the explicit dictionary between this formalism and the tensorial Einstein equations. This provides in particular a new derivation of the (A)dS mass loss formula. We then study the holographic renormalisation of the symplectic potential, and the transformation laws under residual asymptotic symmetries. The advantage of the partial Bondi gauge is that it allows to contrast and treat in a unified manner the Bondi–Sachs and Newman–Unti gauges, which can each be reached upon imposing a further specific gauge condition. The differential determinant condition leads to the \LambdaΛ-BMSW gauge, while a differential condition on g_{ur}gur leads to a generalized Newman–Unti gauge. This latter gives access to a new asymptotic symmetry which acts on the asymptotic shear and further extends the \LambdaΛ-BMSW group by an extra abelian radial translation. This generalizes results which we have recently obtained in three dimensions.

Lie theory for asymptotic symmetries in general relativity: The NU group

We study the Newman–Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this topology. To obtain a manifold structure we consider a finer Whitney-type topology. This turns the unit component of the NU group into an infinite-dimensional Lie group. We then study the Lie theoretic properties of this group. Surprisingly, the group operations of the full NU group become discontinuous, whence the NU group does not support a Lie group structure. The NU group contains the Bondi–Metzner–Sachs (BMS) group as a subgroup, whose Lie group structure was constructed in a previous article. It is well known that the NU Lie algebra splits into a direct sum of Lie ideals of the Lie algebras of the BMS group and conformal rescalings of scri. However, the lack of a Lie group structure on the NU group implies that the BMS group cannot be embedded as a Lie subgroup therein.

Few thermodynamical features of charged accelerating rotating black holes

It is generally remarkable to discuss black hole thermodynamics by considering the phenomenon of phase transition for a most general class of static spacetime. For this purpose, we consider the charged Newman–Unti–Tamburino accelerating and rotating pair of black holes. Then, we check the validation of the first law of thermodynamics as well as calculated some thermodynamic quantities like Bekenstein–Hawking entropy area relationship, specific heat, effective temperature, and effective pressure at critical points. We also examine the physical behavior of such thermodynamic potentials and check the global and local stability with the help of Gibbs free energy and specific heat. Moreover, we investigate the difference in the behavior of phase transition for acceleration horizons, inner and outer horizons. Finally, using Ehrenfest’s equations, we describe the existence of phase transition by Prigogine–Defay ratio at the critical points.

Lie theory for asymptotic symmetries in general relativity: The BMS group

We study the Lie group structure of asymptotic symmetry groups in general relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi–Metzner–Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Finally, we verify the Trotter property as well as the commutator property. As an outlook, we comment on the situation of related asymptotic symmetry groups. In particular, the much more involved situation of the Newman–Unti group is highlighted, which will be studied in future work.

Effects of thermal fluctuations on the Kerr–Newman–NUT–AdS black hole

This paper is devoted to studying the impact of thermal fluctuations on thermodynamics of rotating as well as charged anti-de Sitter black holes with the Newman–Unti–Tamburino (NUT) parameter. To this end, we derive the analytic expression of thermodynamic variables, namely the Hawking temperature, volume, angular velocity, and entropy within the limits of extended phase space. These variables meet the first law of thermodynamics as well as the Smarr relation in the presence of new NUT charge. To analyze the effects of quantum fluctuations, we derive the exact expression of corrected entropy, which yields modification in other thermodynamical equations of state. The local stability and phase transition of the considered black hole are also examined through specific heat. It is found that the NUT parameter increases the stability of small black holes, while the logarithmic corrections induce instability in the system.

Multipole expansion of gravitational waves: from harmonic to Bondi coordinates

We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a functional of the mass and current multipole moments of the source, valid all-over the exterior region of the source. Imposing appropriate boundary conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual symmetry group. To quadratic order, in the case of the mass-quadrupole interaction, we determine the contributions of gravitational-wave tails in the NU metric, and prove that the expansion of the metric in terms of the radius is regular to all orders. The mass and angular momentum aspects, as well as the Bondi shear, are read off from the metric. They are given by the radiative quadrupole moment including the tail terms.

Cosmic footballs from superrotations

Superrotations arise from singular vector fields on the celestial sphere in asymptotically flat space, and their finite integrated versions have been argued by Strominger and Zhiboedov to insert cosmic strings into the spacetime. In this work, we argue for an alternative definition of the action of superrotations on Minkowski space that avoids introducing any defects. This involves realizing the finite superrotation not as a diffeomorphism between spaces, but as a mapping of Minkowski space to itself that may be multivalued or non-surjective. This eliminates any defects in the bulk spacetime at the expense of allowing for defects in the boundary celestial sphere metric. We further explore the geometry of the spatial surfaces in the superrotated spaces, and note that they intersect null infinity at the singularity of the superrotation, causing a breakdown in the large r asymptotic expansion there. To determine how these surfaces embed into Minkowski space, a derivation of the finite superrotation transformation is presented in both Bondi and Newman–Unti gauges. The latter is particularly interesting, since the superrotations are shown to preserve the hyperbolic slicing of Minkowski space in Newman–Unti gauge, and this gauge also provides a means for extending the geometry beyond the Bondi coordinate patch. We argue that the new interpretation for the action of superrotations on spacetime motivates consideration of a wider class of celestial sphere metrics and asymptotic symmetry groups.

Black Holes and Naked Singularities in an Infinite Momentum Frame

The problem of the construction of shock waves by the boosting method for metrics of black holes and naked singularities is considered. It is noted that singular terms may arise under the boosting, which prevents the generation of shock waves (in particular, in the case of the absence of quasi-Cartesian coordinates). We find that if the Fisher metric of a black hole with a scalar charge and a singular horizon is boosted, then the scalar field disappears (unlike the case of black holes with electric and magnetic charges). It is noted that boosted metrics are solutions of the linearized Einstein equations, while the original metrics are exact nonlinear solutions of these equations. The event horizon disappears under the boosting. Thus, the boosting of naked singularities leads to the same result as the boosting of black holes. This is confirmed by the example of gamma-metrics (Zipoy–Vourhees solution) as well. Finally, it is shown that if a linearized metric is boosted with the Newman–Unti–Tamburino parameter (NUT) along the Misner string, then a shock wave with a nondiagonal structure of the gyraton is obtained.

Geometrothermodynamics of a gravitating system with axially symmetric metric

Theory of the first-order phase transition in contact statistical manifold is proposed to describe interface systems. The theory has not limitations of known Van der Waals-like phase transition theories. Based on this approach, geometrothermodynamics of gravitating systems with axially symmetric metrics is investigated. It has been shown that such geometrothermodynamics occurs in space-time with Newman–Unti–Tamburino-like metric.

Upper limit on NUT charge from the observed terrestrial Sagnac effect

The exact Sagnac delay in the Kerr–Taub–NUT (Newman–Unti–Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin , the delay does not vanish. This fact is similar to the non-vanishing of Lense–Thirring precession under even though the two effects originate from different premises. Assuming a reasonable input that the Kerr–Taub–NUT corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge n. It is found that the upper limits on n are far larger than the Earth’s gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain n to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known ‘twin paradox’ of special relativity.

Circular motion in NUT space-time

We consider circular motion in the NUT (Newman–Unti–Tamburino) space-time. Among other things, we determine the location of circular time-like geodesic orbits, in particular of the innermost stable circular orbit (ISCO) and of the marginally bound circular orbit. Moreover, we discuss the von Zeipel cylinders with respect to the stationary observers and with respect to the zero angular momentum observers (ZAMOs). We also investigate the relation of von Zeipel cylinders to inertial forces, in particular in the ultra-relativistic limit. Finally, we generalise the construction of thick accretion tori (‘Polish doughnuts’) which are well known on the Schwarzschild or Kerr background to the case of the NUT metric. We argue that, in principle, an NUT source could be distinguished from a Schwarzschild or Kerr source by observing the features of circular matter flows in its neighbourhood.

Asymptotically flat space–times: an enigma

We begin by emphasizing that we are dealing with standard Einstein or Einstein–Maxwell theory—absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein–Maxwell theory are transformed to a new coordinate system with surprising and (seemingly) inexplicable results. We begin with the standard description of (Null) asymptotically flat space–times described in conventional Bondi-coordinates. After transforming the variables (mainly the asymptotic Weyl tensor components) to a very special set of Newman-Unti (NU) coordinates, we find a series of relations totally mimicking standard Newtonian classical mechanics and Maxwell theory. The surprising and troubling aspect of these relations is that the associated motion and radiation does not take place in physical space–time. Instead these relations takes place in an unusual inherited complex four-dimensional manifold referred to as H-space that has no immediate relationship with space–time. In fact these relations appear in two such spaces, H-space and its dual space .

Area product and mass formula for Kerr–Newman–Taub–NUT spacetime

We derive area product, entropy product, area sum and entropy sum of the event horizon and Cauchy horizons for Kerr–Newman–Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. We observe that these thermodynamic products are not universal (mass-independence) for this black hole (BH), whereas for Kerr–Newman (KN) BH such products are universal (mass-independence). We also examine the entropy sum and area sum. It is shown that they all depend on mass, charge and NUT parameter of the background spacetime. Thus, we can conclude that the universal (mass-independence) behavior of area product and entropy product, area sum and entropy sum for Kerr–Newman–Taub–NUT (KNTN) BH fails and which is also quite different from KN BH. We further show that the KNTN BH do not possess first law of BH thermodynamics and Smarr–Gibbs–Duhem relations, and that such relations are unlikely in the KN case. The failure of these aforementioned features are due to presence of the nontrivial NUT charge which makes the spacetime to be asymptotically non-flat, in contrast with KN BH. The other reason of the failure is that Lorentzian KNTN geometry contains Dirac–Misner type singularity, which is a manifestation of a nontrivial topological twist of the manifold. The BH mass formula and Christodoulou–Ruffini mass formula for KNTN BHs are also derived. Finally, we compute the area bound which is just Penrose like inequality for event horizon. From area bound we derive entropy bound. These thermodynamic products on the multi-horizon play a crucial role in BH thermodynamics to understand the microscopic nature of BH entropy.

Circular geodesics in the Kerr–Newman–Taub–NUT spacetime

In this paper we investigate the equatorial causal (time-like and null) circular geodesics of the Kerr–Newman–Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. The special characteristics of this black hole are that it is of Petrov–Pirani type-D and the photon trajectories are doubly degenerate principal null congruence. We derive the conditions for the existence of the innermost stable circular orbit, marginally bound circular orbit and circular photon orbit in the background of Kerr–Newman–Taub–NUT (KNTN) spacetime. The effective potential for both time-like and null cases have been studied. It is shown that the presence of the NUT parameter deforms the shape of the effective potential in contrast with the zero NUT parameter. We further investigate the energy extraction by the Penrose process for this spacetime. It is shown that the efficiency of this black hole depends on both the charge and NUT parameter. It is observed that the energy gain is maximum when the NUT parameter goes to zero value and for the maximum spin value. When the value of the NUT parameter is increasing, the energy gain is decreasing.

Conformal Carroll groups

Conformal extensions of Lévy–Leblondʼs Carroll group, based on geometric properties analogous to those of Newton–Cartan space-time are proposed. The extensions are labeled by an integer k. This framework includes and extends our recent study of the Bondi–Metzner–Sachs (BMS) and Newman–Unti (NU) groups. The relation to conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by ‘Carrollian photons’. Motion both in the Newton–Cartan and Carroll spaces may be related to that of strings in the Bargmann space.

Conformal Carroll groups and BMS symmetry

The Bondi–Metzner–Sachs group is shown to be the conformal extension of Lévy-Leblond’s ‘Carroll’ group. Further extension to the Newman–Unti group is also discussed in the Carroll framework.