How the Tiger got its Stripes

By Nicolas Yunes, Stephon Alexander, and Kent Yagi

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Nature is sometimes lazy and messy, like a 4 year-old that likes to play with all of the toys and put none of them away, always increasing the degree of disorder. In physics, we quantify disorder through the concept of entropy. The tendency of systems to always increase their entropy is encoded in the second law of thermodynamics. Aside from a kid’s disorganised bedroom, another place in the universe with a tremendous amount of entropy is a black hole. Bekenstein and Hawking [1-4] proved that the entropy of a black hole in General Relativity is proportional to its area. For astrophysical black holes of stellar-mass, this yields a value of entropy of about 10⁵⁶ Joules per Kelvin. The reason for this large value is their incredibly small temperature, about 10^-9 Kelvin for a stellar-mass black hole, which in fact cannot be any smaller for an object of its size due to Heisenberg’s uncertainty principle.

Yunes is an Associate Professor of Physics at Montana State University and co-founder of the eXtreme Gravity Institute.

Alexander is a Professor of Physics at Brown University.

Yagi is an Assistant Professor of Physics at the University of Virginia.

The entropy area scaling is surprising because the entropy of extensive systems in statistical mechanics is proportional to their volume, not their area. In fact, Bekenstein’s and Hawking’s observation was a strong motivator for the concept of holography. The typical rationalisation of the area result is that black holes are special objects because, by definition, they possess a horizon. The argument is then that the entropy is proportional to the area because somehow the internal degrees of freedom of a black hole are imprinted on the surface area associated with its horizon. The consequence of this argument is that the only objects in nature whose entropy scales with their surface area are those with event horizons. In particular, the entropy of stars, be them compact or not, should scale with their volume and not their area.

Quantum imprints of a black hole’s shape

Can quantum fields tell us about the curvature of a black hole event horizon?

By Tom Morley,  Peter Taylor, Elizabeth Winstanley

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The event horizon of a black hole completely surrounds a singularity. It seems obvious that the event horizon takes the form of a (possibly distorted) sphere, a surface with positive curvature. If the space-time far from the black hole is flat, this must be the case. Suppose instead that the space-time in which the black hole is situated itself has negative curvature (this is known as anti-de Sitter space-time and arises in string theory). Then the event horizon does not have to have positive curvature; it can have zero or negative curvature.

How do these different horizon shapes affect black hole physics? If we look at our reflection in a flat mirror, it is undistorted, but a mirror with positive or negative curvature distorts our reflection, as might be experienced in a “hall of mirrors” at a fairground (see image below for some similar effects).

Tom Morley is a PhD student at the University of Sheffield.

Peter Taylor is Assistant Professor of Mathematical Sciences at the Centre for Astrophysics and Relativity, Dublin City University.

Elizabeth Winstanley is Professor of Mathematical Physics at the University of Sheffield.

Gravitational waves measure colour of black holes

By Enrico Barausse, Richard Pires Brito, Vitor Cardoso, Irina Dvorkin, and Paolo Pani

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Black holes predicted by Einstein are, well, black. In classical physics, nothing can escape their event horizon, not light, not matter, and neither gravitational waves.

There is a deep reason for this absolute blackness. If the event horizon were not a perfectly absorbing surface, but rather a partially reflective one, spinning black holes would become unstable and would shed most of their rotational energy into gravitational waves. This process is known as superradiant instability [1], and is tightly linked to the presence of an ergoregion, a region of spacetime just outside the event horizon, where modes of negative energy are allowed to exist. Negative energy-modes can form in the ergoregion of normal humdrum black holes, but are eventually doomed to fall in the event horizon.

Enrico Barausse

Richard Pires Brito

Professor Vitor Cardoso

Irina Dvorkin

Paolo Pani

If (what look like) black objects had a surface, such modes would be partially reflected by it, and they would bounce back and forth between the horizon and the boundary of the ergoregion (which they cannot cross, since negative energy modes cannot travel to infinity). Each time they reach the ergoregion boundary, they come out as positive energy-modes, thus inside the ergoregion they would keep growing in amplitude (i.e. their energy would keep decreasing and becoming more negative) eventually producing an instability. Indeed, these ‘bounces’ produce ‘echoes’ in the gravitational wave signal [2] from the remnant black hole forming from binary mergers, and there are claims [3] (albeit controversial [4]) that they may have been seen in the LIGO data.

In this paper we do not look at the black holes that form from binary mergers, but rather at isolated ones. These black holes can have a wide range of masses (from stellar masses for stellar-origin black holes up to millions or billions solar masses for supermassive black holes) and a variety of spins (on which we have some knowledge thanks to electromagnetic observations). Normally, isolated black holes do not emit gravitational waves, but if their event horizon had some reflectivity (that is, if these objects were not totally black), they would turn into black-hole bombs due to superradiance, and they would shed almost all their angular momentum in gravitational waves. These gravitational wave signals would be too weak to be detected singularly, but because there are in general many more black holes in isolation than in binaries, they can produce a very large stochastic background. Indeed, this background would be orders of magnitude larger than the current upper bounds from LIGO/Virgo. Similar results also apply to supermassive black holes, in the yet-unexplored LISA band.

So in conclusion, the existing stochastic background constraints from LIGO and Virgo show that black holes are very black, although some shades of grey may still be allowed. Indeed, while 100% reflection from the horizon is ruled out, smaller reflection coefficients may still be possible depending on the spin of the object [5].

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References:
[1] W. H. Press and S. A. Teukolsky, “Floating Orbits, Superradiant Scattering and the Black-hole Bomb“. Nature. 238 (5361): 211-212 (1972);
Brito, Cardoso, Pani; “Superradiance“, Springer (2015)
[2] Cardoso, Franzin, Pani, “Is the gravitational-wave ringdown a probe of the event horizon?“, Phys. Rev. Lett. 116, 171101 (2016)
[3] Abedi & Afshordi, “Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons“, Phys. Rev. D 96, 082004 (2017)
[4] Ashton+ https://arxiv.org/abs/1612.05625; Abedi, Dykaar, Afshordi, https://arxiv.org/abs/1701.03485 and https://arxiv.org/abs/1803.08565;
Westerweck+, “Low significance of evidence for black hole echoes in gravitational wave data“, Phys. Rev. D 97, 124037 (2018)
[5] Maggio, Pani, Ferrari “Exotic Compact Objects and How to Quench their Ergoregion Instability“, Phys. Rev. D 96, 104047 (2017); Maggio, Cardoso, Dolan, Pani, http://arxiv.org/abs/arXiv:1807.08840

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Read the full article in Classical and Quantum Gravity:
The stochastic gravitational-wave background in the absence of horizons
Enrico Barausse et al 2018 Class. Quantum Grav. 35 20LT01

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Finding order in a sea of chaos

By Alejandro Cárdenas-Avendaño, Andrés F. Gutiérrez, Leonardo A. Pachón, and Nicolás Yunes

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Hunting for constants of the motion in dynamical systems is hard. How can one find a combination of dynamical variables that remains unchanged during a complicated evolution? While it is true that answering this question is not trivial, symmetries can sometimes come to the rescue. The motion of test particles around a spinning (Kerr) black hole, for example, has a conserved mass, energy and angular momentum. Nevertheless, simple symmetries can only go so far. Given the complexity of the radial and polar sector of Kerr geodesics, it came as a complete surprise when Carter found, in 1968, a fourth constant of the motion, which was later found to be associated with the existence of a Killing tensor by Walker and Penrose. This fourth constant then allowed the complete separability of the geodesic equations, thus proving the integrability of the system, and as a consequence, that the motion of a test particle around a Kerr black hole is not chaotic in General Relativity (GR).

 

● Alejandro Cárdenas-Avendaño is a graduate student at Montana State University and holds a junior researcher position at Fundación Universitaria Konrad Lorenz.

● Andrés F. Gutierrez is a graduate student at Universidad de Antioquia.

● Leonardo A. Pachón is an associate professor at Universidad de Antioquia.

● Nicolás Yunes is an associate professor at Montana State University, and co-founder of the eXtreme Gravity Institute.

The Sound of Exotic Astrophysical “Instruments”

by Sebastian Völkel and Kostas Kokkotas

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Could you distinguish the sound of a wormhole from an ultra compact star or black hole?

Such an exotic, though quite fundamental question, could be asked to any physicist after the groundbreaking and Nobel Prize winning discoveries of gravitational waves from merging black holes and neutron stars. Gravitational waves provide mankind with a novel sense, the ability to hear the universe. This analogy, between sound waves and gravitational waves, will bring to the minds of many physicists Mark Kac’s famous  question: “Can One hear the Shape of a Drum?” [1], and not just to the drummers amongst us. The possibility of this analogy is one of the ways in which gravitational waves are very distinct from the usual tool of astronomy, light.

To answer the question for our exotic instruments, we will rephrase it in a more technical form. In the simplest version one can describe linear perturbations of spherically symmetric and non-rotating models of wormholes and ultra compact stars. It is well known that the perturbation equations for these cases can simplify to the study of the one-dimensional wave equation with an effective potential. The solutions, which are usually given as a set of modes, represent the characteristic sound of the object. The so-called quasi-normal mode (QNM) spectrum is the starting point for our discussion.

FIG. 1. Sebastian Völkel (right) is a PhD student in the Theoretical Astrophysics group of Professor Kostas Kokkotas at the University of Tübingen, located in the south of Germany. Among his research interests is the study of compact objects along with the associated gravitational wave emissions. More information about his research can be found here.
Professor Kostas Kokkotas (left) is leading the group of Theoretical Astrophysics at the University of Tübingen. The focus of his research is on the dynamics of compact objects (neutron stars & black-holes) as sources of gravitational waves in general relativity and in alternative theories of gravity. More information about the group can be found here.
Photo by Severin Frank.

COSMOLOGICAL CONS(tant → erved charge)

The road to black hole thermodynamics with Λ

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by  Dmitry Chernyavsky and Kamal Hajian

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What are volume and pressure in black hole thermodynamics? That is the question!

What do the gas in a balloon and a black hole have in common? For a regular CQG reader the answer should be obvious; both can be described within the framework of thermodynamics. However we know that the gas in balloon is characterised by volume and pressure, as well as other  thermodynamic quantities. So, a natural question arises about analogues of the volume and pressure for a black hole.
Answering this question, black hole physicists have noticed that if the universe is filled with a non-zero cosmological constant Λ, this mysterious entity can be absorbed in the energy-momentum tensor of matter, and its contribution resembles a perfect fluid with a pressure proportional to Λ. Continuing with this analogy, one can also introduce a ‘thermodynamic volume’ for a black hole. For instance, the appropriate volume which satisfies the first law of thermodynamics for the Schwarzschild black hole is equal to the volume of a ball with the same radius, but in flat space! Using the notions of the black hole pressure P and volume V, it is standard to vary the cosmological constant generalising the first law of black hole thermodynamics by V δP.

Dmitry Chernyavsky and Kamal Hajian Sevan lake in Armenia where we started to think about the cosmological conserved charge instead of cosmological constant.

Black and White Hole Twins Connected by Quantum Gravity

By Javier Olmedo, Sahil Saini and Parampreet Singh

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Black holes are perhaps the most exotic objects in our Universe with very intriguing properties. The event horizon does not allow light and matter to escape, and hides the central singularity. As in the case of the big bang singularity, the central singularity is a strong curvature singularity where all in-falling objects are annihilated irrespective of their strength. Since singularities point out pathologies of general relativity, a more fundamental description obtained from quantum gravity must resolve the problem of singularities. Singularity resolution is also important for resolving many of the paradoxes and conundrums that plague the classical theory such as the cosmic censorship conjecture, black hole evaporation, black hole information loss paradox, etc.

Dr. Javier Olmedo is a postdoctoral researcher at Pennsylvania State University

Sahil Saini is a graduate student at Louisiana State University

Dr. Parampreet Singh is an associate professor at Louisiana Stare University

Black holes have mirror versions too. Known as white holes, these are solutions of general relativity with the same spacetime metric.  If the black holes do not allow even the light to escape once it enters the horizon, thus nothing can enter the white hole horizon. Light and matter can only escape from the white hole. It has sometimes been speculated that black hole and white hole solutions can be connected, providing gateways between different universes or travelling within the same universe, but details have been sparse. The reason is due to the presence of the central singularity which does not allow a bridge between the black and white holes.

Tails of gravitational waves and mechanics of compact binaries

by Luc Blanchet and Alexandre Le Tiec

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The first law of binary black hole mechanics can be extended to include non local tail effects.

Ever since Kepler’s discovery of the laws of planetary motion, the “two-body problem” has always played a central role in gravitational physics. In Einstein’s general theory of relativity, the simplest and most “universal,” purely gravitational, two-body problem is that of a binary system of black holes. The inspiral and merger of two compact objects (i.e. bodies whose radius is comparable to their mass, in “geometric” units where G = c = 1) produces copious amounts of gravitational radiation, as was recently discovered by LIGO’s multiple detections of gravitational waves from black hole binary systems.

Alexandre Le Tiec (left) celebrates the detection of gravitational waves and Luc Blanchet (right) thinks about gravitational waves in Quy Nhon, Vietnam

In general relativity, the inspiral and onset of the merger of two compact objects is indeed universal, as it does not depend on the nature of the bodies, be they black holes or neutron stars, or possibly more exotic objects like boson stars or even naked singularities. However, the gravitational waves generated during the post-merger phase depend on the internal structure of the compact objects, and in the case of neutron stars should reveal many details about the scenario for the formation of the final black hole after merger, and the equation of state of nuclear matter deep inside the neutron stars

Going NUTs

By Paul I. Jefremov and Volker Perlick.

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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.

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

Black holes without special relativity

By Jishnu Bhattacharyya, Mattia Colombo and Thomas Sotiriou.

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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.

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