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 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
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
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 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
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 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
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
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 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
According to Einstein’s theory of general relativity (GR), black holes are ferocious beasts able to swallow and destroy everything within their reach. Their strong gravitational pull deforms the space-time causal structure in such a way that nothing can get out of them once their event horizon is crossed. The fate of those incautious observers curious enough to cross this border is to suffer a painful spaghettification process due to the strong tidal forces before being destroyed at the center of the black hole.
For a theoretical physicist, the suffering of observers is admissible (one might even consider it part of an experimentalist’s job) but their total destruction is not. The destruction of observers (and light signals) is determined by the fact that the affine parameter of their word-line (its geodesic) stops at the center of the black hole. Their clocks no longer tick and, therefore, there is no way for them to exchange or acquire new information. This implies the breakdown of the predictability of the laws of physics because physical measurements are no longer possible at that point. For this reason, when a space-time has incomplete geodesics — word-lines whose affine parameter does not cover the whole real line — we say that it is singular.
In order to overcome the conceptual problems raised by singularities, a careful analysis of what causes the destruction of observers is necessary. Our intuition may get satisfied by blaming the enormous tidal forces near the center, but the problem is much subtler. This is precisely what we explore in our paper. Continue reading
Tim Johannsen is a postdoctoral fellow at Perimeter Institute for Theoretical Physics and the University of Waterloo specializing in black-hole astrophysics and tests of general relativity.
Black holes have no hair – so they say. Formally, this statement refers to several famous theorems in general relativity that were established mostly from the late 1960s to the early 1970s and are collectively known as the no-hair theorem. According to this theorem, a black hole only depends on its mass, angular momentum (or spin), and electric charge and is uniquely described by the Kerr-Newman metric. So, just about everyone would expect that astrophysical black holes are indeed the Kerr black holes of general relativity understanding that any net electric charge would quickly Continue reading
Following from the seminal work of Dain, a great deal is now known concerning geometric inequalities relating the area, charge, and angular momentum of axisymmetric black hole horizons in (possibly dynamical) spacetimes. A key feature of these results is that they are quasi-local: they depend on spacetime only near the horizon itself and so are not sensitive to the asymptotic behaviour of the geometry.
For Einstein-Maxwell theory the celebrated uniqueness theorems tell us under certain conditions, that the Kerr-Newman (KN) family of solutions are the only stationary, axisymmetric and asymptotically flat black hole spacetimes. These are the model geometries that originally motivated the inequalities. However if we relax the condition of asymptotic flatness there are many other families of black hole solutions. While in general these will not contain event horizons (whose standard definitions require flat or AdS asymptotics) they still contain singularities and Killing horizons. In this paper we focussed Continue reading
Helvi and Paolo visiting Toronto during the International Conference on Black Holes at the Fields Institute last year.
Helvi is Research Fellow in the School of Mathematical Sciences at the University of Nottingham. Paolo is Assistant Professor at Sapienza University of Rome and Research Scientist at the Instituto Superior Técnico in Lisbon.
We are proud to present the completed Focus Issue on “Black holes and Fundamental Fields” one year after its first contribution has been published online.
This issue appears serendipitously at the same time as LIGO’s historic detection of gravitational waves which, simultaneously, provided us with the first direct observational evidence for the existence of black holes (BHs). We wish to take this opportunity to congratulate the LIGO/VIRGO Scientific Collaboration and everyone involved on their breakthrough discovery!
The true excitement around this discovery arises from the fact that it marks the beginning of the long-sought-for era of gravitational-wave astronomy. As Kip Thorne recently put it, “Recording a gravitational wave […] has never been a big motivation for LIGO, the motivation has always been to open a new window to the Universe”. The outstanding observation of a BH binary coalescence — and the expectation of Continue reading