Going NUTs

By Paul I. Jefremov and Volker Perlick.

Among all known solutions to Einstein’s vacuum field equation the (Taub-)NUT metric is a particularly intriguing one. It is that metric that owing to its counter-intuitive features was once called by Charles Misner “a counter-example to almost anything”. In what follows we give a brief introduction to the NUT black holes, discuss what makes them interesting for a researcher and speculate on how they could be detected should they exist in nature.

paul jefremov-and-volker

Volker Perlick and Pavel (Paul) Ionovič Jefremov from the Gravitational Theory group at the University of Bremen in Germany. Volker is a Privatdozent and his research interests are in classical relativity, (standard and non-standard) electrodynamics and Finsler geometry. He is an amateur astronomer and plays the piano with great enthusiasm and poor skills. Paul got his diploma in Physics at the National Research Nuclear University MEPhI in Moscow, 2014. Now he is a PhD Student in the Erasmus Mundus Joint Doctorate IRAP Programme at the University of Bremen. Beyond the scientific topics in physics his interests include philosophy in general, philosophy of science, Eastern and ancient philosophy, religion, political and social theories and last but not the least organic farming.

The NUT (Newman–Unti–Tamburino) metric was obtained by Newman, Unti and Tamburino (hence its name) in 1963. It describes a black hole which, in addition to the mass parameter (gravito-electric charge) known from the Schwarzschild solution, depends on a “gravito-magnetic charge”, also known as NUT parameter. If the NUT metric is analytically extended, on the other side of the horizon it becomes isometric to a vacuum solution of Einstein’s field equations found by Abraham Taub already in 1951. However, for an observer who is prudent enough to stay outside the black hole, the Taub part is irrelevant.

At first sight, the existence of the NUT metric seems to violate the uniqueness (“no-hair”) theorem of black holes according to which a non-spinning uncharged black hole is uniquely characterised by its mass. Actually, there is no contradiction because Continue reading

Black holes without special relativity

By Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou.

Black holes are perhaps the most fascinating predictions of General Relativity (GR). Yet, their very existence (conventionally) hinges on Special Relativity (SR), or more precisely on local Lorentz symmetry. This symmetry is the local manifestation of the causal structure of GR and it dictates that the speed of light is finite and the maximal speed attainable. Accepting also that light gravitates, one can then intuitively arrive at the conclusion that black holes should exist — as John Michell already did in 1783!

One can reverse the argument: does accepting that black holes exist, as astronomical observations and the recent gravitational wave direct detections strongly suggest, imply that Lorentz symmetry is an exact symmetry of nature? In other words, is this ground breaking prediction of GR the ultimate vindication of SR?

Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou from the School of Mathematical Sciences, University of Nottingham.

Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou from the School of Mathematical Sciences, University of Nottingham.

These questions might seem ill-posed if one sees GR simply as a generalisation of SR to non-inertial observers. On the same footing, one might consider questioning Lorentz symmetry as a step backwards altogether. Yet, there is an alternative perspective. GR taught us that our theories should be expressible in a covariant language and that there is a dynamical metric that is responsible for the gravitational interaction. Universality of free fall implies that Continue reading

Can astrophysical black holes have “hair”?

by Carlos Herdeiro and Eugen Radu, Guest Editors of Focus Issue: Hairy Black Holes.


Carlos A. R. Herdeiro (left) got his PhD from Cambridge University (U.K.) in 2002. He is currently an assistant professor at Aveiro University, Portugal, and an FCT principal researcher. He is also the founder and coordinator of the Gravitation group at Aveiro University (gravitation.web.ua.pt). Eugen Radu (right) got his PhD from Freiburg University (Germany) in 2002. He is currently an FCT principal researcher at Aveiro University (Portugal).

One of the most recognizable statements about black holes is that they have “no-hair”. Close inspection, however, shows that this is a belief rather than a mathematically proven theorem. Moreover, decades of research on this topic have shown that, depending on what one precisely means, this statement may be simply wrong. That is, as solutions of Einstein’s equations, in a generic context, black holes are not necessarily “bald”. Then, less ambitious, but perhaps more relevant questions are: “Can astrophysical black holes have hair?” and “Can we test the existence of black hole hair with present and future astrophysical observations?”.

This CQG focus issue brings together a set of papers describing models in which black holes do have “hair”, as well as observational efforts that have the potential to assess if this is (or not) the case for astrophysical black hole candidates. This collection of research papers is by no means a faithful and complete description of all possible alternatives to the Kerr paradigm in the literature. Rather, the selected papers focus on Continue reading

Setting space on fire

by Yasaman K. Yazdi and Niayesh Afshordi.

Niayesh Afshordi and Yasaman Yazdi discover that firewalls have consequences

Niayesh Afshordi and Yasaman Yazdi discover that firewalls have consequences. Yasaman K. Yazdi is a PhD candidate at the University of Waterloo and the Perimeter Institute for Theoretical Physics. Niayesh Afshordi is an associate professor at the University of Waterloo and the Perimeter Institute for Theoretical Physics.

Thought experiments highlight the edge of our understanding of our theories.  Sometimes, however, we can get so caught up in heated debates about the solution to a thought experiment, that we may forget that we are talking about physical objects, and that an actual experiment or observation may give the answer.  In this Insight we discuss a proposed solution to the black hole information puzzle, and a possible observational signal that might confirm it.


The black hole information puzzle and a potential solution

The black hole information loss problem is a decades old problem that highlights the tensions between some of the pillars of modern theoretical physics. It has evolved from being Continue reading

CQG+ Insight: More Classical Charges for Black Holes

Written by Geoffrey Compère, a Research Associate at the Université Libre de Bruxelles. He has contributed to the theory of asymptotic symmetries, the techniques of solution generation in supergravity, the Kerr/CFT correspondence and is generally interested in gravity, black hole physics and string theory.

Why mass and angular momentum might not be enough to characterize a stationary black hole

Geoffrey Compère

Geoffrey Compère having family time in the park Le
Cinquantenaire in Brussels.

“Black hole have no hair.” This famous quote originates from John Wheeler in the sixties. In other words, a stationary black hole in general relativity is only characterized by its mass and angular momentum. This is because multipole moments of the gravitational field are sources for gravitational waves which radiate the multipoles away and only the last two conserved quantities, mass and angular momentum, remain. That’s the standard story.

Now, besides gravitational waves, general relativity contains another physical phenomenon which does not exist in Newtonian theory: the memory effect. It was discovered beyond the Iron Curtain by Zeldovich and Polnarev in the seventies and rediscovered in the western world and further extended by Christodoulou in the nineties. While gravitational waves lead to spacetime oscillations, the memory effect leads to a finite permanent displacement of test observers in spacetime. The effect exists for any value of the cosmological constant but in asymptotically flat spacetimes, it can be understood in terms of an asymptotic diffeomorphism known as a BMS supertranslation.

In order to understand that, let’s go back to the sixties where the radiative properties of sources were explored in general relativity; it was found by Bondi, van der Burg, Mezner and Sachs that there is a fundamental ambiguity in the coordinate frame at null infinity. Most expected that Continue reading

CQG+ Insight: Spacetime near an extreme black hole

Written by James Lucietti, a Lecturer in Mathematical Physics in the School of Mathematics at the University of Edinburgh; and Carmen Li, previously a graduate student in the School of Mathematics at the University of Edinburgh and now a postdoc in the Institute of Theoretical Physics at the University of Warsaw.

How many extreme black holes are there with a given throat geometry?


James Lucietti, University of Edinburgh

The classification of equilibrium black hole states is a major open problem in higher dimensional general relativity. Besides being of intrinsic interest, it has numerous applications in modern approaches to quantum gravity and high energy physics. Two key questions to be answered are: What are the possible topologies and symmetries of a black hole spacetime? What is the ‘moduli’ space of black hole solutions with a given topology and symmetry? For vacuum gravity in four spacetime dimensions, these questions are answered by the celebrated no-hair theorem which reveals a surprisingly simple answer: the Kerr solution is the only possibility. However, since Emparan and Reall’s discovery of the black ring — an asymptotically flat five dimensional black hole with ‘doughnut’ topology — it has become clear that there is a far richer set of black hole solutions to the higher dimensional Einstein equations.


Carmen Li, University of Warsaw, at the top of Ben Nevis in the UK.

Over the last decade, a number of general results have been derived which Continue reading

Inspiral into Gargantua; where science meets science-fiction

Niels Warburton from the Massachusetts Institute of Technology shares an insight into his latest work with Sam Gralla and Scott Hughes published in Classical and Quantum Gravity.

Niels Warburton

Niels Warburton is a Marie Curie postdoctoral fellow currently working at the Kavli Institute for Astrophysics and Space Research at the Massachusetts Institute of Technology. He works on calculating gravitational waveforms from the capture of compact objects by black holes ranging from hundreds to millions of solar masses. Outside of research he often encounters other types of waves on the waters around Boston where he is a keen sailor. Niels co-authored the article recently published in CQG with Sam Gralla of the University of Arizona and Scott Hughes at the Massachusetts Institute of Technology.

The first merging black holes recently detected by LIGO were strange objects indeed. Torturing reality so that even light cannot escape from their interiors, as they whirled around each other at over half the speed of light, the disturbances they induced in space and time propagated outwards as gravitational waves. The measured characteristic chirp, an upsweep in frequency and amplitude of the waves, signaled that the two black holes had merged into a single, larger black hole. Amazingly, though this remnant was more than sixty times as massive as our sun it could be described by just two numbers – its mass and its spin. This is an unusual property for any macroscopic object as they usually require Continue reading

Waves, stability and exotic black holes

Jake Dunn and Dr Claude Warnick from the Pure Mathematics group at Imperial College, London tell us all about their research using the Klein-Gordon equation to study black holes.

Jake Dunn

Jake Dunn is a PhD student at Imperial College, London.
Claude Warnick is a Lecturer in Pure Mathematics at Imperial College, London.

There is a long standing conjecture in the theory of general relativity that the final state of the gravitational collapse of a star should be a stationary black hole modelled by the Kerr solution. To this date there remains no mathematical proof of this statement, and it seems that we may have to wait a while before this result can be established. Even the simpler problem of black hole stability is a considerable mathematical challenge.

We may think of a stationary black hole as Continue reading

What does numerical relativity have to do with detecting gravitational waves?

Heather Fong — a PhD candidate in Physics at the University of Toronto, who also loves travelling and gastronomy photography — gives us an insight into her group’s work on using numerical relativity simulations for the detection of gravitational waves.


Heather Fong, a PhD candidate in Physics at the University of Toronto.

Answer: quite a lot! Numerical relativity (NR) provides the most accurate solutions to the binary black hole problem, which is exactly the type of source LIGO wants to detect — and has succeeded at! Most of the time, LIGO’s data streams are overwhelmed with noise, and so we use a technique called matched-filtering to identify gravitational-wave signals. Finding and characterizing signals requires a massive amount of accurate waveforms, and we use semi-analytic waveform models as filters which are built using the results of NR simulations.

Why don’t we use NR alone to identify signals? It certainly would be ideal if the theoretical template waveforms were generated entirely from NR; not only would we be using the most accurate waveforms available, it would also allow us to Continue reading

Fractals and black hole shadows

Jake Shipley and Dr Sam Dolan work in the Particle Astrophysics and Gravitation group at the University of Sheffield, focusing on general relativity, wave propagation and black hole physics. Here they provide us with an insight into their research. 

Jake Shipley

Jake Shipley is a Ph.D student in the School of Mathematics and Statistics at the University of Sheffield. If Jake were a black hole, you would also see a lensed version of Dr Sam Dolan, standing behind the camera.

This has been a “miracle year” for relativity.

LIGO detected gravitational waves. The LISA Pathfinder mission demonstrated near-perfect freefall in space. And the era of gravitational-wave astronomy began in some style.

A century after black holes and gravitational waves were first predicted, we have learnt something truly mind-boggling: When two black holes collide, they shake the fabric of space-time with more power than is radiated by all the stars in the known universe put together!

The “chirps” from distant black hole collisions will travel for millions of years, at the speed of light, to reach our growing network of gravitational-wave detectors on Earth … and one day, out in space.

Next year, attention will turn to the Event Horizon Telescope (EHT): a global network of radio telescopes linked together to form an Earth-sized virtual telescope, using the technique of Very Long Baseline Interferometry. The EHT will Continue reading