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Traps in Space-Time

Black holes are a permanent fixture in science fiction literature. In reality, there is hardly a more extreme location in the universe. These mass monsters swallow everything that ventures too close to them: light, gas, dust and even entire stars. It sounds quite simple, but the nature of black holes is complex. Maria Rodriguez, Minerva Group Leader at the Max Planck Institute for Gravitational Physics in Golm, wants to solve some of the puzzles these exotic cosmic bodies present.

TEXT FELICITAS MOKLER

or a long time it seemed that with 62 solar masses. Only a few months work of Newtonian gravitational theo- they existed only in the minds later, the researchers registered gravi- ry and the corpuscular theory of light. of theoretical physicists – black tational waves of source GW151226 At the beginning of the 20th cen- holes. But since at least a year from a similar system. These events tury, Albert Einstein revolutionized our ago now, we finally have clari- gave the space-time structure a violent understanding of gravitation – and thus ty: theyF really do exist. On September shake – and provided impressive con- also of matter, space and time – with his 14, 2015, gravitational waves caused firmation of the existence of the mass general theory of relativity. His idea re- space-time to oscillate to a measurable monsters. (MaxPlanckResearch 2/2016, placed the classical concept of extent in the American LIGO detectors page 78 ff.) as the direct interaction between two for the first time. masses that move through rigid, Euclid- The detection of the undulation of EINSTEIN’S THEORY REPLACES ian space. Instead, it held that three-di- space-time predicted 100 years earlier THE CLASSICAL CONCEPT mensional space and time are united to by Albert Einstein (1879 to 1955) is si- form a four-dimensional space-time multaneously deemed to be experimen- Naturalists John Mitchell (1724 to 1793) and are themselves now deformable tal proof of the physical existence of and Pierre Simon de Laplace (1749 to and dynamic. A mass such as the Sun black holes. The first measured signal 1827) were already speculating in the bends space-time in its vicinity – the GW150914 originated from two black late 18th century about dark stars or larger and, in particular, the denser a holes with 36 and 29 solar masses, re- dark astrophysical bodies whose gravi- mass, the stronger the effect. spectively, that used to orbit one anoth- ty was so strong that light couldn’t es- The motion of a second, smaller er in a kind of binary star system until cape them. The ideas of the two re- mass, such as a planet, then follows this they finally merged into one object searchers were still within the frame- curvature. If the local curvature chang-

Under the spell of gravity: Black holes have been keeping astrophysicists busy for more than a century. None has yet been observed directly, but the discovery of gravitational waves at least shows that these bizarre structures really do exist. Graphic: Alain r/CC-BY-SA 2.5

26 MaxPlanckResearch 1 | 17 Graphic: Alain r/CC-BY-SA 2.5 FOCUS_Extreme Space

es because a mass accelerates across this the ,” says the Minerva Group (1873 to 1916) in the metric that bears space, this change propagates at the Leader at the Max Planck Institute for his name. The so-called speed of light as a gravitational wave in Gravitational Physics in Golm. that shields the interior of the black the space-time structure. There is no escape for either matter hole from the outside world is defined Einstein used Riemannian geome- or light. This is what makes it so diffi- by the , which de- try as the mathematical basis for dy- cult for astronomers to observe these pends on the mass. “Its shape is a per- namic space-time. Black holes emerge objects. The explanation is simple: in fect sphere for conventional black holes, from the field equations, which de- order to leave a conventional celestial which don’t rotate and have no electric scribe the curvature of space brought body such as Earth, objects require a charge,” says Rodriguez. The researcher about by matter and, conversely, the minimum kinetic energy that depends investigates the boundary surfaces of effect of curvature on matter, as a nat- on the body’s mass. The velocity that black holes with different properties. ural solution for matter concentrated rockets require, for example, is called But black holes with no angular at one point. The gravity there is in- the escape velocity. For a black hole, momentum are probably very rare in finitely large, and space-time has an this velocity corresponds to the speed nature. This is because these objects infinitely large curvature: mathemati- of light. are formed, for instance, when partic- cally, it is a singularity. ularly massive stars have exhausted “Physically, however, such infinities GRAVITY EVENTUALLY GAINS the supply of fusionable material in don’t tell us anything,” says Maria Ro- THE UPPER HAND their interior toward the end of their driguez. “What is relevant is the separa- life. The temperature there then drops tion from the point mass below which How space-time behaves under these and thermal and radiation pressure are gravity becomes so strong that nothing conditions was first described in 1916 no longer sufficient to counteract the can escape from it and can only fall into by astrophysicist Karl Schwarzschild star’s gravitation. The stellar interior implodes and the once free electrons are pushed into the positively charged atomic nuclei. Event horizon In such a , the neutrinos re- leased in this process transport a large portion of the energy away and hurl the outer stellar shell into space. The matter in the core, in contrast, con- tracts more and more under its own gravity. If the original mass of the star was more than eight solar masses, the ultimate result is a black hole. Since stars usually rotate about their own axis and the is con- served, they pass it on to the black hole. Astronomers are still puzzled by the birth of the particularly massive black Inner horizon holes – with a few million to a billion solar masses – that are presumed to lie at the centers of galaxies. They may pos- sibly have formed from the first gener- Clear structures: The physics might be complex, but the explanation of the structure is simple. ation of extremely heavy stars that, The graphic shows a with a ring singularity in the center and the inner having become a black hole, rapidly ac- horizon. The event horizon is something like the surface of the black hole; when something disappears behind it, it is truly out of this world. The ergosphere marks the region in which creted more and more mass and thus

every object is forced to co-rotate. more and more angular momentum. Graphic: designergold, based on original material from the MPI for Gravitational Physics

28 MaxPlanckResearch 1 | 17 Engine at the center: Centaurus A is around 15 million light-years away, making it the nearest radio galaxy, but it also emits intense X-ray and gamma radiation. The jet structure visible in this image is apparently caused by the activity of the central black hole with around 55 million solar masses.

The hypothesis of so-called is called its ergosphere and high-energy jets in around 20 active black holes, according to which these is ellipsoid in shape. Matter from out- galaxies or . These objects prob- cosmic heavyweights formed shortly side that gets caught up in it doesn’t ably have an extremely massive, rapid- after the Big Bang together with the necessarily plunge directly into the ly rotating black hole at their center,” first galaxies, is also being discussed. As- space-time trap, but rather initially says the Max Planck researcher. tronomers also speculate about the ex- co-rotates with it. Nevertheless, it is un- To be able to correctly interpret istence of medium-weight black holes, able to escape from it. these phenomena, the researchers are with 100 to one million solar masses, “Unless the matter is electrically attempting to compute the behavior that could be present at the centers of charged,” says Rodriguez, because the of rotating black holes and the physi- large globular clusters. co-rotating charged matter causes a cal processes in their immediate vicin- magnetosphere to form. Some of the ity according to the laws of the gener- PARTICLES ARE EJECTED charged particles are deflected along al theory of relativity. Analytically, they the magnetic field lines. Depending on have initially succeeded in doing this When a black hole rotates, its event the sign of the charge and the orienta- only for very slowly rotating black horizon deforms slightly. Furthermore, tion of the field lines, the particles then holes, but Maria Rodriguez is interest- the space-time of its immediate vicini- fall more rapidly into the black hole – ed in the very opposite: objects that ty and the matter located there rotate or are ejected along the rotational axis. rotate about their own axis at almost

Graphic: designergold, based on original material from the MPI for Gravitational Physics Photo: ESO/WFI (optical); MPIfR/ESO/APEX/A.Weiss et al. (submillimeter); NASA/CXC/ CfA/R.Kraft et al. (X-ray) with it. This sphere of influence of the “Astronomers have since observed very the speed of light. >

1 | 17 MaxPlanckResearch 29 30 itation withtheotherthreefundamen inordertounifygrav- to stringtheory strong force. be moresuitablefordescribing the modynamics ultimatelyturned outto electromagnetic force. Quantum chro- neutrons, withtheweakforce andthe quarks togethertoformprotonsand the strongforce, whichkeepsthe tounify tempted tousestringtheory composed of quarks. Thescientists at- of anatomicnucleusarethemselves ered thatthebuildingblocks(nucleons) At thattime,particlephysicistsdiscov- string theory.” Rodriguez. “We usedamethodfrom adopting asystematicapproach,”says be foundeitherbytrialanderroror the same formalism. “Thesolution can ofrelativityonthebasisoneand ry the fieldequationsofgeneraltheo- electrodynamics and, simultaneously, To thisend,shesolvestheequationsof of the configurations from five to two and three dimensions. three projections and the two are to five Depicted from momentum). (angular rotation configurations and the of mass on depend shapes diagram Their The dimensions. dimensions. spatial five for three than solutions more in analytical holes black depicts of horizons event of AEI), Institute, configurations Einstein surface (Albert possible Physics computed Gravitational for Rodriguez Maria Institute Planck Max the at postdoc a as time her During mathematics: Advanced MaxPlanckResearch 1 MaxPlanckResearch However, scientistslaterreturned This theory originated in the 1960s. originatedinthe1960s. This theory | 17 - ible) tube. describe thecableasalong, thin(flex al dimensionsarerequired in orderto sional,” saysRodriguez.Two addition- experience itsworldasone-dimen - only thedirectionstraight ahead and crawls throughacablewillregister large. “Anant,forexample,that either particularlytinyor really doexist–couldbethattheyare ditional dimensions–ifindeedthey The reason we can’t perceive these ad- ONLY ONEDIMENSION AN ANTINACABLEKNOWS basis,” saysMariaRodriguez. of space-timeformapurelyheuristic dimensions atall.Thefour doesn’t specifythenumber ofspatial ofrelativity,the generaltheory sinceit quite compatiblewiththeconceptof six furtherspatialdimensions.“This is mensions of space-time,it introduces tal forces. Inadditionto thefourdi

Surface of the event horizon - - the center of our Milky Way. Its vicini- are generated. also somecasesinwhichno jetsatall tions,” saysMariaRodriguez. Thereare tions naturefavorsunderwhich condi- still havetofindoutwhichofthesolu- ly focusedorbroadlyfannedout.“We energy involved:theycanbeextreme- ly fromeachotherintermsofformand cate thatthejetscandiffersignificant- stellar explosion. counterparts thatweregeneratedbya spiral galaxiesandtotheirlessmassive heavyweights aspresumablyexistinall to such extremely massivecosmic lar momentum;itcanbeappliedboth holes isindependentofmassandangu- el togeneratejetsforrotatingblack unified inonetheory. Rodriguez’mod- ent dependenciesondistance,canbe mental forces act,aswell astheirdiffer gy regimesinwhichthefourfunda With thisextension,thedifferentener One example here is the object at The researcher’s computationsindi Angular momentum

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Photo: Private collection; graphic: Maria Rodriguez Photo: Private collection; graphic: Maria Rodriguez

Graphic: UCLA Galactic Center Group – W.M. Keck Observatory Laser Team had speculatedshortlybefore thisthat him. TheoreticianJacobBekenstein – theHawkingradiationnamed after could emit a specific form of radiation the mid-1970sthatblackholes really Stephen Hawking already proposed in momentum andcharge,isincomplete. such asmassand–possiblyangular fewproperties, mation aboutonlyvery jects canbepersuadedtorevealinfor- view thatsaysthesecompactob- ferent way. Perhapstheconventional their presencefeltinacompletelydif- million solarmasses. mers todayassumeithasaround4.5 ments onotherstellarorbits,astrono- hole. Thanks tomoreaccurate measure spatial area,itcouldonlybeablack lar masses.Limitedtosuchanarrow tral objecttobearound3.7millionso searchers estimated the mass of the cen- 15.2years. of riod compact radiosource, which hasape- liptical orbit of the star S2 about the pletely reconstructedtheextremelyel his colleagues,amongothers,com the aid of earlier images, Genzel and to travelfromtheSunPluto.With parison, lighttakesaroundfivehours tance of just 17 light-hours. By com- ittarius A*.Thiscorrespondstoadis- milli-arcseconds fromthe source ofSag star S2cametowithinadistanceof12 howthe (ESO)inChiletoobserve ry - at theEuropeanSouthernObservato ferometers oftheVery LargeTelescope when theastronomersusedinter- of thegalaxy. Sagittarius A*radiosource atthecenter orbits ofindividualstarsaroundthe the for ExtraterrestrialPhysicsobserved leagues from theMaxPlanck Institute work, ReinhardGenzelandhiscol- no high-energyjets.Inyearsofhard ty emitsradioemissions,butthereare The breakthroughcamein2002, Using Kepler’s thirdlaw, there But maybeblackholescouldmake ------namic entropy. represent a measure for thethermody- the surface of the event horizon could Bekenstein and Hawking were the first Bekenstein andHawkingwerethefirst information is contained in the system. tem: thehigherentropy, themore sure oftheinformationcontentasys- Entropy canbeconsideredtoamea- BE PRESERVED INFORMATION MAY POTENTIALLY the Milky Way. The gravity of the object forces nearby stars onto more or less elliptical orbits. orbits. elliptical less or Between more onto stars nearby forces object the of gravity The Way. Milky the around with hole black A center: the Around Keck telescope in Hawaii. in telescope Keck 1995 0.1" and and 2014 , astronomers measured these motions very accurately using the the using accurately very motions these measured astronomers , 4.5 million solar masses lurks at the heart of to compute the entropy of a black hole, to computetheentropyofablackhole, tum physics. String theory also tackles alsotackles tum physics.Stringtheory contradicted bytheconceptsofquan- destroyed inthehole;this,however, is ofrelativity,ory informationcouldbe black hole.Within thescopeof with entropyandinformationina been abletofullyclarifywhathappens was formed.Scientistshavestillnot the precursorstarfromwhichhole but itdidn’t matchatallwiththatof the problem of entropy and provides the problemofentropyandprovides 1 FOCUS_Extreme Space | MaxPlanckResearch 17MaxPlanckResearch S102 S38 S20 S19 S16 S5 S2 S1

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Max Planck Innovation is responsible for the technology transfer of the Max Planck Society and, as such, the link between industry and basic research. With our inter- disciplinary team we advise and support scientists in evaluating their inventions, Drama in three acts: A star is torn apart by the tidal effect of a black hole (left). It then devours a portion of the stellar debris, heating up strongly in the process (center). This, in turn, leads to a gigantic outburst of radiation, which subsides again in time (right). filing patents and founding companies. We offer industry a unique access to the innovations of the Max Planck Institutes. solutions for a finite entropy content. thought to be the site of an extremely itational wave signals from black holes. The information from the event hori- massive black hole with 6.6 billion so- Most recent estimates have shown that Thus we perform an important task: the zon would then possibly become avail- lar masses. In this way, the researchers the sensitivity of the LIGO detectors transfer of basic research results into able to an external observer. hope to find out whether jets really are during the recently launched measure- In this context, earlier work that formed in the ergosphere of a black ment campaign should be high enough products, which contribute to the economic Maria Rodriguez produced during her hole, or in a disk of matter further out to either confirm or exclude them. and social progress. postdoc phase at the Max Planck Insti- after all. Gravitational wave astronomy will thus tute in Golm, in the research group of Certain effects of quantum gravita- one day shed some further light on the Director Hermann Nicolai, could also tion, in contrast, should affect the grav- nature of black holes. become interesting again. At that time,

she developed a whole catalog of solu- tions for black holes in higher dimen- sions based on string theory. In the TO THE POINT three-dimensional representation we l The gravity inside a black hole is infinitely large, and space-time has an infinitely are familiar with, they look like a large curvature. However, this mathematical singularity has no meaning from a Connecting Science sphere, a donut-like ring, either on its physical point of view. own or orbiting a sphere, similar to the l What is crucial is the separation from the point mass below which gravity be- comes so strong that nothing more can escape from it. This boundary is identified ringed planet Saturn; or like two en- by the event horizon. This is a perfect sphere for black holes that aren’t rotating twined rings. In the higher dimensions, and have no electric charge. all these surfaces are interconnected to l But static black holes are very rare in nature. The researchers are therefore and Business give a solution. attempting to compute the behavior of rotating black holes and the physical If black holes really do emit a spe- processes in their immediate vicinity according to the laws of the general theory cific type of radiation, it will probably of relativity. be extremely difficult to measure it l Analytically, such computations have been successful only for very slowly rotating even at some time in the future. But black holes. Maria Rodriguez, on the other hand, investigates objects that rotate about their own axis at almost the speed of light. She uses string theory methods maybe it will soon be possible to check for this purpose. specific effects from Rodriguez’ models for conventional black holes with the aid of observations. GLOSSARY A network of radio telescopes spread LIGO: The Laser Interferometer Gravitation Wave Observatory consists of two detectors all over the world is currently being set sited in the US states of Louisiana and Washington. This is where gravitational waves up, the so-called Event Horizon Tele- were first discovered on September 14, 2015. Although the installation, which is called scope. The astronomers want to use Advanced LIGO in its present upgrade stage, is located in the US, Max Planck researchers made a significant contribution to the discovery through hardware, computer programs this and the Very Long Baseline Array and models. to image the galactic center with much Riemannian space: An object from the branch of mathematics known as Riemannian better resolution. In addition, they geometry with special properties. For instance, the shortest connections between want to look more closely at the heart different points aren’t necessarily straight lines, but can be curved lines. And the angular of the active galaxy known as M 87, sum of triangles can be greater or less than 180 degrees.

which has a high-energy jet. This is Computer graphic: NASA/CXC/MPI for Extraterrestrial Physics

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Probedruck Computer graphic: NASA/CXC/MPI for Extraterrestrial Physics Probedruck mi_anzeige_1/1_englisch_1#29C8F 17.02.201113:53UhrSeite1 Connecting Science and Business C M Y CM and social progress. products, which contribute to the economic transfer ofbasicresearch resultsinto task:the animportant Thus we perform innovations ofthe MaxPlanck Institutes. auniqueaccesstoWe the industry offer patentsfiling andfounding companies. scientists inevaluating their inventions, team we adviseandsupport disciplinary andbasicresearch. With ourinter-industry Society and,assuch, the linkbetween the technology transfer ofthe MaxPlanck Max Planck Innovation isresponsiblefor MY CY CMY K