A Visual Journeyintointo

General RelativityOne Century after Einstein

Werner BengerCenter for Computation & Technology

AtAt Louisiana State University

Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut - AEI)

&Zuse Institut Berlin (ZIB)

AbstractEinstein was convinced about his concepts when he conceived his theory of general relativity. At his time, it was purely theoretical and his ideas were esoteric. Only later they could be proven to be not only to be consistent with nature, but to even provide a description superiorto be consistent with nature, but to even provide a description superior to any alternatives. But while this is still the case, many aspects of relativity had to be left unexplored due to their sheer complexity. Now, nearly a century after its fundaments have been invented, high performance computing technology helps to tackle the last riddles ofperformance computing technology helps to tackle the last riddles of this advanced theory of gravity. One of the leading groups in this area is homed at Louisiana State University, at the Center for Computation and Technology. In this talk, the progress and work of this group and its ancestors will be presented, and illustrated with visualizations of the s a ces o s w be p ese ed, a d us a ed w v sua a o s o eresults of numerical simulations that have burned hundreds of thousands of CPU hours to delve into the last hidden realm of one of the most successful physical theories ever.

AbstractEinstein was convinced about his concepts when he conceived his theory of general relativity. At his time, it was purely theoretical and his ideas were esoteric. Only later they could be proven to be not only to be consistent with nature, but to even provide a description superiorto be consistent with nature, but to even provide a description superior to any alternatives. But while this is still the case, many aspects of relativity had to be left unexplored due to their sheer complexity. Now, nearly a century after its fundaments have been invented, high performance computing technology helps to tackle the last riddles ofperformance computing technology helps to tackle the last riddles of this advanced theory of gravity. One of the leading groups in this area is homed at Louisiana State University, at the Center for Computation and Technology. In this talk, the progress and work of this group and its ancestors will be presented, and illustrated with visualizations of the s a ces o s w be p ese ed, a d us a ed w v sua a o s o eresults of numerical simulations that have burned hundreds of thousands of CPU hours to delve into the last hidden realm of one of the most successful physical theories ever.

Finite Speed of Propagation

• Problem with Newtonian Gravity: • assumes infinite speed of gravityassumes infinite speed of gravity

• But: Gravity can propagate with speed of light at maximumlight at maximum• If the sun would vanish all of a sudden, we

won’t be able to recognize this until 8minuteswon t be able to recognize this until 8minutes later (light runtime – we don’t see the sun where it is, but where it was 8min before))

Gravitational Waves

• Accelerated Masses radiate gravitational energy (similar to radio waves emitted from gy (an antenna)

• 2-body system looses energy – can no2 body system looses energy can no longer be stationary

Extreme gravity around Black Holes

Gravitational waves

Gravitational wave detectors

GEO600, Hannover

LIGO, Livingston

LIGO, Hanford

Measuring Gravitational wavesMeasuring Gravitational waves (GEO600)

Relative distance change:

1 : 10-22

10-17cm (Diameter of an electron, 1/100000 of an

atomic nucleus) by 600m600

LIGO

1999: Grazing Collision of 2 BH’s

Gravitational wave astronomy

National Science Board, 2006, Science and Engineering Indicators 2006 ( ol me 1 NSB 06(volume 1, NSB 06-01; volume 2, NSB 06-01A)06 01A)

NSF Submits Its Fiscal 2006 Budget Request of $5.6 Billion

Gravitational Waves: 70% Orbit

The 2-body-problem

• Newtonian Gravity: Kepler-Ellipses (stable)• 1915: Relativistic Gravitational field of a1915: Relativistic Gravitational field of a

point mass (Schwarzschild-solution)• Analytical attempts to solve the two body• Analytical attempts to solve the two-body

problem failed due to complexity of the Einstein equationsEinstein equations

2-body problem: ca. 1960

• Larry Smarr: semi-numerical approaches• Motivated the foundaton of the National Center

f l ( ) ifor Supercomputing Applications (NCSA) in Champaign/Illinois• NCSA later got famous via NCSA Mosaic the firstNCSA later got famous via NCSA Mosaic, the first

Web-Browser that was used worldwide, and origin of netscape (now mozilla/firefox) and Microsoft Internet ExplorerExplorer

• NCSA httpd is also origin of the most used webserver Apache

US Grand ChallengeUS Grand ChallengeNCSA, 1995

• Axially symmetric problems in 2D• Headon-collisions of

black holes• Oscillating black holes• Oscillating black holes

Event Horizon Merger

Gravitational Waves

1999

• Ed Seidel, AEI & NCSA: grazing collision of black holes

• 200GB raw data• 100 000 CPU hours SGI Origin 2000 256• 100 000 CPU-hours SGI Origin 2000, 256

CPU’sC d 10 i i• Corresponds to 10years computation time on desktop PC

Merger of neutron stars (1999)Birth of a black hole from a headon-collision (WashU,

St. Louis, Wai-Mo-Suen et.al.)

Relativistic Neutron Stars

• Extraction of gravitational waves• Distortion of spacetimeDistortion of spacetime

Newtonian Neutron Star Merger• Newtonian Simulations (Phillip Gressman, WashU)Newtonian Simulations (Phillip Gressman, WashU)

covering multiple orbits (1999)

Nonlinearity of Gravity

• Einstein: Energy distribution is source of Gravity• Gravity itself has energyy gy

• Gravity itself is source to gravity as welly g y• Doubling matter is more than twice the gravity:

Gravity(2 x Mass) > 2 x Gravity (Mass)

Consequence of non-linearity

• Gravity can “hold itself”• Black holesBlack holes• Collapse of pure gravitational energy to a black

hole theoretically possible (“Brillwaves”)y p ( )

Brill-Wave

• Initial condition: energy in a torus (Dieter Brill, 1959), )

• Gravitational energy collapses• “bounces back” and dissipates (subcritical)• bounces back and dissipates (subcritical)• “gets stuck” and forms black hole

(supercritical)(supercritical)

2-body problem 2002

• First time ever ¾ Orbit of last orbit• 650 Gigabyte raw data650 Gigabyte raw data• Linux Cluster with 512 CPU’s Itanium64bit

Features

Discovery Channel:Discovery Channel:Broadcasting: 3rd June 2002

3D structure

Heightfield

GEO600

Lorentz-Transformation

• Light has same speed for all observers• Moving observer becomes contractedMoving observer becomes contracted• Time of moving objects will be dilated

Twin paradoxonSituation:

Astronaut travels with relativistic speed away

from earth and turns back

Result:

Time passes slower for the moving astronaut, thus he is younger on return than

his twin.s w .

Rotation in SR• View fast rotating disc• Tangential co-moving

measure shorter relative tomeasure shorter relative to measure at rest

• Circumference of the t ti di lrotating disc appears longer

when measured with co-moving measure than with

t tmeasure at rest• However: radial distance is

not affectedπ>Umfang π>Radius

Acceleration & SR

…leads to

Non euclidean GeometryNon-euclidean Geometry

(Riemann, 1848)(Riemann, 1848)

Umfang π≠RadiusUmfang

General Equivalence Principlei iEinstein:

• Gravity is property of spacetime and i di ti i h bl f l tiindistinguishable from acceleration

• Any existing matter distribution causes non-Euclidean GeometryEuclidean Geometry

•Newtonian theory of gravity, “absolute” space and “absolute” time is wrongp g

Non-Euclidean Geometry

• Pythagoras theorem• Generalization: Cosine-Generalization: Cosine

theorem• Most general: metric

αcos2222 abbac −+=

• Most general: metric• Einstein-Equation of

i i d i higravitation determines this metric

Metric

• Metric determines the distance from one point to its neighboursp g

Eg.: distance |A-B| 10m

di t |C A| 100

Vi li ti lli

distance |C-A| 100m

Visualization as ellipse

Metric FieldGravitational field of a

static black hole

Radial distances are stretched, tangential ones unchanged

π<Umfang π<Radius

Metrische Verzerrung

Beispiel: Metrische Verzerrung anhand eines Raumschiffes der Gala ClassGalaxy Class (USS NCC1701 Enterprise caEnterprise, ca. 2400 n.Chr.)

Raumverzerrung amRaumverzerrung am Schwarzen Loch

Raumverzerrung amRaumverzerrung amSchwarzen Loch

Wie man Schwarze LoecherWie man Schwarze Loecher sehen kann

Photon Orbit

• Beim 1½-fachen des Schwarzschild-Radius kann Licht auf einer (instabilen) Kreisbahn la fenlaufen

• Innerhalb wirkt “Zentrifugalbarierre”Zentrifugalbarierre nach innen

Wie ein Schwarzes LochWie ein Schwarzes Loch wirklich aussieht

• Licht wird gekrümmt• Nordpol und Südpol

l i h ß i h bgleichermaßen sichtbar