Henriette Elvang- Dynamics and phases of multi-black hole configurations

8/3/2019 Henriette Elvang- Dynamics and phases of multi-black hole configurations

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Dynamics and phases

ofmulti-black hole

configurations

Henriette Elvang, MIT

Prestrings - Granada, June 18, 2007


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Surprises in higher-D gravity

Black Holes, Strings, Rings

Their combinations give multi-black hole configurations:

Black Saturns, Di-Rings, multiple concentric rings

Different kinds ofblackthings:

Supersymmetric AND non-supersymmetric.


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This talk:

Einstein vacuum gravity Einsteins equation(Einstein-Hilbert action- no matter fields)

Boundary conditions: Asymptotically flat

Minkowski space

Equilibrium Stationary (time-independent)

Review 4+1d BH phase diagram Physics of Black Saturn

Newest news

Dynamics and phases of vacuum black holes in 4+1d


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Finding solutions

How to solve ?

- exact / approximations / numerical methods

- develop techniques!

- solutions discussed in this talk constructed by

an exactsolution generating technique:

the inverse scattering method

see talk by Pau Figueras


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What to do with solutions?

Analyze and extract physics!

- Dynamical properties: how do they work?

e.g. how does black ring balance work?

- stability?

- interactions between black holes,

e.g. shape, deformations, etc

- thermodynamics, phase diagram

- microscopic description


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This talk:

Einstein vacuum gravity Einsteins equation(Einstein-Hilbert action- no matter fields)

Boundary conditions: Asymptotically flat

Minkowski space

Equilibrium Stationary (time-independent)

Review 4+1d BH phase diagram Physics of Black Saturn

Newest news

Dynamics and phases of vacuum black holes in 4+1d


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sub0

Review of phase diagram

(angular momentum only in one plane)


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Phase diagram for 4+1d BHs

Horizon area vs angular momentum for fixed mass

Myers-Perryblack hole


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Phase diagram

Horizon area vs angular momentum for fixed mass

thin black rings

fat black rings


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How black ring balance works

Newtonian mechanics for very thinblack rings

Black rings have string-like tension

Thin black rings are balanced bytension vs. centrifugal force.

Note:gravitational attraction is subleading

Rotating rubberband:T TensionM Mass Angular velocity

R Radius

[Hovdebo & Myers (2005)][Emparan, Virmani, H.E. (2006)]

R

T

MT


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Black ring balance in an external potential?

R

TM


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Black ring around a spherical black hole

External potential = gravitational field of spherical black hole

R

T

M


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Black ring around a spherical black hole

External potential = gravitational field of spherical black hole

R

T

M

Black Saturn


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Black Saturn

Using the inverse scattering method we haveconstructed an exactsolution to the Einsteinvacuum equations describing a black ringbalancedaround a spherical black hole

[P. Figueras, H.E., hep-th/0701035]

Properties

Non-uniqueness Interactions

Counter-rotation

The new phase diagram


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Black Saturn

Using the inverse scattering method we haveconstructed an exactsolution to the Einsteinvacuum equations describing a black ringbalancedaround a spherical black hole

[P. Figueras, H.E., hep-th/0701035]

Properties


Counter-rotation



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Non-uniqueness

4 parameters, only 2 conserved asymptotic observables

ADM mass

ADM angular momentum

2-fold continuous non-uniqueness!


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Non-uniqueness

4 parameters, only 2 conserved asymptotic observables

ADM mass

ADM angular momentum

2-fold continuous non-uniqueness!

asymptotic observer

black hole

???


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Black Saturn

Properties


Counter-rotation



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Vocabulary

Rotation: A black hole is rotatingwhen it has non-zero angular velocity.

Co- and counter-rotation:Co-rotation: angular velocities have samesigns.Counter-rotation: angular velocities have oppositesigns.

Intrinsic spin:The angular momentum of a black hole.

Measured by the Komar integral evaluated onthe black hole horizon.


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Adding a MP BH withoutintrinsic spinat the center of a rotating black ring

Total mass fixed

BR area fixed


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Angular velocity

The spherical black hole has

follows

Spherical black hole has no intrinsic spin,at the center

Nonetheless it is rotating: !

How can that be??

Note:


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Frame-dragging

The rotating black ring drags the surrounding spacetime

The black hole is rotating because it -- and thesurrounding spacetime -- is being dragged by the black ring.


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Testing frame-dragging

The effect of draggingdecreases as theproper distancebetween the twoblack objects increases

Supports frame-dragginginterpretation.


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Black Saturn

Properties


Counter-rotation



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Co- and counter-rotationGenerally the black ring and black hole in Black Saturn carry

independent intrinsic spins.

For fixed and fixed total mass.

co-rotation

counter-rotation

Intrinsic spin of BH cancels

effect of frame-dragging

Example of a saturn phase in the phase diagram:


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Co- and counter-rotationGenerally the black ring and black hole in Black Saturn carry

independent intrinsic spins.

Example of a saturn phase in the phase diagram:

There are blacksaturns with zero total

angular momentum!

For fixed and fixed total mass.


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Phases with

Theorem: The Schwarzschild black hole is the uniqueasymptoticallyflat staticblack hole in vacuum gravity. [Gibbons, Ida and Shiromizu (2002)]

BUT:There are non-static (but stationary) black hole solutionswith , namely black saturns with counter-rotation.


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Black Saturn

Properties


Counter-rotation



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New phase diagram

For any , we find black saturn solutions with total area

arbitrarily close to the bound

4+1 dimensions vacuum gravity asymptotic flatness single ang mom

The whole open strip multiply covered by black saturns!

[Emparan, Figueras, H.E., hep-th/0702111]


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Equilibrium phase diagram

4+1 dimensions vacuum gravity asymptotic flatness single ang mom equilibrium

Equilibrium: Planet and Ring of Saturn have same temperature same angular velocity

[Emparan, Figueras, H.E., hep-th/0702111]


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Black Saturn

Properties

Outlook

Interactions: rotational frame-dragging

Counter-rotation

Non-uniqueness and the new phase diagram

Multiple rings of saturn.Doubly spinning rings [Pomeransky & Senkov (2006); H. Kudoh (2006)]

and saturns

n objects give 2(n-1)-fold continuous non-uniqueness.

n doubly spinning objects give 3(n-1)-fold continuous non-uniqueness.


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sub6

The newest news


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Balanced orthogonal double ring systems

exact solution in vacuum gravity

[Rodriquez, Emparan, H.E., in progress]


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Different from Di-Rings

[Iguchi & Mishima (2007); Krishnan & Evslin (2007)]


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Bi-Rings: Dragging


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Phase diagram

Plot total area againstangular momentum in 34-plane

10,000 random Bi-Ring configurations

standard black ring

MP BH


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Model

Simply superimpose two black rings(ignore interactions). Ring 1 (12-plane) very largeand thin. Curves of fixed mass m1 of ring 1, andfixedj12=10.

standard black ring


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Compare


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Compare with area of ring 2


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Outlook


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Outlook

Stability?

Phase transitions?

Interpretations in string theory

vacuum black rings have instabilities. Saturns and Bi-Rings probably inherit these.

Critical phenomena in gravity.

Charged black saturns, di-rings and bi-rings!

Dipole ring black saturns constructed [Yazadjiev (2007)] Supersymmetric saturns: already known [Gauntlett & Gutowski (2004)]

Supersymmetric concentric black rings AdS black holes, rings (and saturns!) as duals of plasma-lumps [Lahiri & Minwalla (2007)]


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Many options!

??

?


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Extra slides


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How to solve ?

Symmetries: Metric does notdepend on:

Stationarity time

Rotation in two planes angles and


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Example of phase structure

Take a black ring of FIXED horizon area, e.g.

Add a spherical black hole with no intrinsic spin,at the center.


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Exploring the phase diagram

Black saturn has 2-fold continuous non-uniqueness:How much of the phase diagram is covered?

Scatter plot: 100.000 random saturn configurations in thephase diagram.


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Just one of the rings:


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and the other ring

Henriette Elvang- Dynamics and phases of multi-black hole configurations

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