Exploring Quantum Black Holes: Dual Dynamics and Brane Evaporation

 
the dual dynamics of
quantum black holes
 
Marija Toma
šević
CPHT, Ecole polytechnique
 
w/ Emparan, Luna, Suzuki and Way
2301.02587
problem
 
history
 
new method
 
results
2
 
brane black
hole
evaporation
history, motivation
 
Quantum dynamics in gravity is hard, and we still do not fully
understand black hole evaporation
We only have some perturbative idea about what’s going on, and
our understanding is best in models with low dimensions
 
An idea emerged ~20 yrs ago when Tanaka and Emparan 
et al.
thought about looking at the 
dual
 of the problem at hand
In essence: put a black hole on a brane and look at its higher-
dimensional, classical picture
Such a classicalization of the problem gives a new perspective on
the problem, letting us ask questions we could not ask before
3
 
Tanaka ‘02
Emparan, Fabbri, Kaloper ‘02
history, motivation
 
In a bit more detail,
 
classical dynamics in an AdS
d+1 
bulk with a d-dim brane
holographically encodes the quantum dynamics of the dual
d-dim CFT coupled to a d-dim gravity on the brane
 
This means that we can view this setup from two
perspectives:
1)
either as an object in the bulk w/ some boundary
conditions or
2)
as a higher-curvature gravity coupled to a cutoff CFT on
the brane
4
 
[de Haro, Skenderis, Solodukhin ’00]
history, motivation
 
So, how does that look like for brane black holes?
A brane bh evaporating can be represented in several ways
One can construct a 
droplet
, or a 
funnel
—these are the principal representations
The brane bh is coupled to a strongly-coupled, large N CFT
BH evaporation would then simply mean sliding off the brane
5
history, motivation
 
But bear in mind that we don’t have the usual quantum fields à la Birrell and Davies
 
We have a large N CFT,  so the evaporation time should be much shorter than for a
few quantum fields
 
The intuition is that we have many more channels into which the black hole can
evaporate, and the rate is enhanced by large N
 
This would suggest that we 
cannot 
find stable time-independent solutions of
droplets and funnels: they would always evaporate quickly off the brane!
 
 
6
history, motivation
 
The story turned out to be quite different though
People did find stable droplets on Randall-Sundrum branes which were time-
independent!
 
How come an AF black hole surrounded by quantum fields does not
evaporate? Where did we make a mistake?
 
7
 
Fitzpatrick, Randall, Wiseman ‘06
Gregory, Ross, Zegers ‘08
Figueras, Lucietti, Wiseman ‘11
history, motivation
 
The answer lies in the second feature of brane CFTs: they are strongly-coupled
Just as plasma balls emit only color-neutral “glueballs”, so does a black hole
immersed in a strongly-coupled CFT
But then, its Hawking radiation would have an energy of        , and so would be
invisible to the classical bulk geometry, which only encodes energies of           --
we cannot see the brane bh evaporating!
In other words, if we have access only to 
confined dofs 
then we don’t know how
the bh evaporates
 
 
8
Fitzpatrick, Randall, Wiseman ‘06
Gregory, Ross, Zegers ‘08
Figueras, Lucietti, Wiseman ‘11
history, motivation
 
In order to evaporate properly, the bh would need
access to the 
deconfined
 degrees of freedom
 
What is the bulk dual of this statement?
The deconfined dofs ~ black hole in the bulk
Access ~ the bulk bh must be connected to the brane bh
 
This suggests that funnels and rattles should allow for
evaporation!
 
9
history, motivation
 
And what would be the driving mechanism behind this
evaporation from the bulk point of view?
 
We will need the horizons on the brane to pinch-off – this
is exactly the physics of the 
Gregory-Laflamme (GL)
instability
!
 
Recall, the GL instability occurs for extended black
objects, like black strings, leading to the creation of two
or more separate black objects, like black holes
 
10
history, motivation
 
So let us try to show the pinching/evaporation
explicitly
In order to do so, we would need dynamical
evolution of the bulk configurations
In general, this requires a difficult numerical
procedure
 
But we will resort to a different method:
the large 
d
 effective theory
11
 
Emparan et al. ‘13
The large 
d
 method
 
The large 
d
 limit effectively separates scales and isolates the dynamics of
the horizon
 
In other words, the spacetime away from the black hole is effectively flat –
the large number of dimensions suppresses the effect of the gravitational
potential far from the black hole
 
This suppression simplifies the equations and one can perform
complicated dynamical simulations in a matter of seconds/minutes
12
The large 
d
 method
 
One caveat we should keep in mind:
The large 
d
 method can only study one type of black holes at a time
This means that we first 
have to fix the 
brane black hole to be either large or
small, and then we can study them
 
In this talk, our examples will mostly constitute 
small AdS brane 
black
holes, which are the natural ones for the analysis of evaporation
13
funnels
14
In pictures and videos
Funnels
 
Now that we have the
funnel, we can perturb
it to see when the
black holes on branes
will evaporate
In pictures and videos
Funnels 1.0
The black holes
evaporate on the
brane, forming a
bigger black hole in
the bulk
In pictures and videos
Funnels 2.0
One of the black holes
evaporates, making
the other one bigger
funnels
 
These two examples show full evaporation on either one or both branes
But this holographic setup allows us to have another interesting possibility
 
Namely, if the funnel is thin enough, the evaporation can start as before, but the
Gregory-Laflamme instability can kick in fast enough *in the bulk*, severing the
connection between the brane bh and the rest
In this case, the naked singularity that occurs in the bulk leads to some sort of
disentangling between the brane bh and the CFT modes
 
There is no known analogue of this phenomena for bhs w/ weakly-coupled matter
18
 
Emparan, Licht, Suzuki,
Tomaševi
ć
, 
Way ‘21
rattles
 
Now let us try to evaporate rattles
To obtain them, we can start with a funnel solution and perturb it in such a
way so as to obtain twin droplets
Then we perturb the droplets in various ways and try to find a perturbation
that would lead to evaporation of the brane black holes
Note first that we confirm that droplets which are only moderately
perturbed do not lead to evaporation
 
19
 
In pictures and videos
 
 
Rattles
 
Small/moderate
perturbations do not
lead to an evaporating
black hole on the
brane!
 
The situation is the
same even if we have
only one droplet
 
In pictures and videos
 
 
Small rattles
 
Small/moderate
perturbations do not
lead to an evaporating
black hole on the
brane!
 
The situation is the
same even if we have
only one droplet
In pictures and videos
Big rattles
 
But big perturbations
do!
questions
 
How come small rattles don’t lead to evaporation, but big ones do?
Both allow the access to the deconfined dofs, so why is there this
distinction?
 
The answer lies in the 
second law of thermodynamics
, that is
 
 “heat flows from a hotter system to a colder one”
23
back to thermo-basics
 
Recall, large black holes in AdS have T = M, while small black holes behave
as in AF space and T = 1/M
If we start with a small droplet, it’s hot, so it needs a colder system into
which to evaporate
A small rattle is a small black hole in the bulk – hotter than the droplet!
Need instead a bigger black hole in the bulk so that it’s colder – this way
the droplet will want to flow its heat into it
24
colder
hotter
r
0
< L
AdS
small AdS black hole
hotter when smaller
colder
hotter
With funnels
The large 
d
 method: large brane bhs
 
Let us just quickly show what happens with large brane black holes
26
summary, questions
 
We can study the evaporation of brane black holes using the large 
d
 limit of
General Relativity
Evaporation on the brane is only possible when we have a colder black
connection in the bulk – either as a funnel or in the form of a big rattle
Otherwise, the droplets become stable
Can be best understood through the laws of thermodynamics – heat will
flow from a hotter system to a colder one
But the more pressing question is how to understand all of these phases
through the CFT lens
27
 
Thank you!
 
28
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Exploring the dual dynamics of quantum black holes reveals new perspectives on black hole evaporation. By placing black holes on branes, we can study their classical picture in higher dimensions. This approach provides insights that were previously unattainable, leading to a better understanding of black hole evaporation processes. The interaction between classical dynamics in an AdS bulk and gravity on the brane encodes the quantum dynamics of the dual CFT, shedding light on the intriguing connection between gravity and quantum field theory. The evaporation of brane black holes can be represented in various ways, highlighting the impact of large N CFT on the evaporation process and the instability of time-independent solutions.


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  1. the dual dynamics of quantum black holes Marija Toma evi CPHT, Ecole polytechnique w/ Emparan, Luna, Suzuki and Way 2301.02587

  2. history problem new method brane black hole evaporation results 2

  3. history, motivation Tanaka 02 Emparan, Fabbri, Kaloper 02 Quantum dynamics in gravity is hard, and we still do not fully understand black hole evaporation We only have some perturbative idea about what s going on, and our understanding is best in models with low dimensions An idea emerged ~20 yrs ago when Tanaka and Emparan et al. thought about looking at the dual of the problem at hand In essence: put a black hole on a brane and look at its higher- dimensional, classical picture Such a classicalization of the problem gives a new perspective on the problem, letting us ask questions we could not ask before 3

  4. history, motivation [de Haro, Skenderis, Solodukhin 00] In a bit more detail, classical dynamics in an AdSd+1 bulk with a d-dim brane holographically encodes the quantum dynamics of the dual d-dim CFT coupled to a d-dim gravity on the brane This means that we can view this setup from two perspectives: 1) either as an object in the bulk w/ some boundary conditions or 2) as a higher-curvature gravity coupled to a cutoff CFT on the brane 4

  5. history, motivation So, how does that look like for brane black holes? A brane bh evaporating can be represented in several ways One can construct a droplet, or a funnel these are the principal representations The brane bh is coupled to a strongly-coupled, large N CFT BH evaporation would then simply mean sliding off the brane 5

  6. history, motivation But bear in mind that we don t have the usual quantum fields la Birrell and Davies We have a large N CFT, so the evaporation time should be much shorter than for a few quantum fields The intuition is that we have many more channels into which the black hole can evaporate, and the rate is enhanced by large N This would suggest that we cannot find stable time-independent solutions of droplets and funnels: they would always evaporate quickly off the brane! 6

  7. Fitzpatrick, Randall, Wiseman 06 Gregory, Ross, Zegers 08 Figueras, Lucietti, Wiseman 11 history, motivation The story turned out to be quite different though People did find stable droplets on Randall-Sundrum branes which were time- independent! How come an AF black hole surrounded by quantum fields does not evaporate? Where did we make a mistake? 7

  8. Fitzpatrick, Randall, Wiseman 06 Gregory, Ross, Zegers 08 Figueras, Lucietti, Wiseman 11 history, motivation The answer lies in the second feature of brane CFTs: they are strongly-coupled Just as plasma balls emit only color-neutral glueballs , so does a black hole immersed in a strongly-coupled CFT But then, its Hawking radiation would have an energy of , and so would be invisible to the classical bulk geometry, which only encodes energies of -- we cannot see the brane bh evaporating! ? 1 ? ?2 In other words, if we have access only to confined dofs then we don t know how the bh evaporates 8

  9. history, motivation In order to evaporate properly, the bh would need access to the deconfined degrees of freedom What is the bulk dual of this statement? The deconfined dofs ~ black hole in the bulk Access ~ the bulk bh must be connected to the brane bh This suggests that funnels and rattles should allow for evaporation! 9

  10. history, motivation And what would be the driving mechanism behind this evaporation from the bulk point of view? We will need the horizons on the brane to pinch-off this is exactly the physics of the Gregory-Laflamme (GL) instability! Recall, the GL instability occurs for extended black objects, like black strings, leading to the creation of two or more separate black objects, like black holes 10

  11. history, motivation Emparan et al. 13 So let us try to show the pinching/evaporation explicitly In order to do so, we would need dynamical evolution of the bulk configurations In general, this requires a difficult numerical procedure But we will resort to a different method: the large d effective theory 11

  12. The large d method The large d limit effectively separates scales and isolates the dynamics of the horizon In other words, the spacetime away from the black hole is effectively flat the large number of dimensions suppresses the effect of the gravitational potential far from the black hole This suppression simplifies the equations and one can perform complicated dynamical simulations in a matter of seconds/minutes 12

  13. The large d method One caveat we should keep in mind: The large d method can only study one type of black holes at a time This means that we first have to fix the brane black hole to be either large or small, and then we can study them In this talk, our examples will mostly constitute small AdS brane black holes, which are the natural ones for the analysis of evaporation 13

  14. funnels Let us start with the funnel case first: We start with a solution for a black string in global AdS, whose metric can be written as ?2 ??2= cos2???2+??2?? ???? 1 We will analyze perturbations of the black string in gAdS, which correspond to different brane-CFT physics, that is, different radiation physics And we will look for such perturbations which could lead to the brane black holes sliding off 14

  15. In pictures and videos Funnels Now that we have the funnel, we can perturb it to see when the black holes on branes will evaporate

  16. In pictures and videos Funnels 1.0 The black holes evaporate on the brane, forming a bigger black hole in the bulk

  17. In pictures and videos Funnels 2.0 One of the black holes evaporates, making the other one bigger

  18. funnels Emparan, Licht, Suzuki, Toma evi , Way 21 These two examples show full evaporation on either one or both branes But this holographic setup allows us to have another interesting possibility Namely, if the funnel is thin enough, the evaporation can start as before, but the Gregory-Laflamme instability can kick in fast enough *in the bulk*, severing the connection between the brane bh and the rest In this case, the naked singularity that occurs in the bulk leads to some sort of disentangling between the brane bh and the CFT modes There is no known analogue of this phenomena for bhs w/ weakly-coupled matter 18

  19. rattles Now let us try to evaporate rattles To obtain them, we can start with a funnel solution and perturb it in such a way so as to obtain twin droplets Then we perturb the droplets in various ways and try to find a perturbation that would lead to evaporation of the brane black holes Note first that we confirm that droplets which are only moderately perturbed do not lead to evaporation 19

  20. In pictures and videos Rattles Small/moderate perturbations do not lead to an evaporating black hole on the brane! The situation is the same even if we have only one droplet

  21. In pictures and videos Small rattles Small/moderate perturbations do not lead to an evaporating black hole on the brane! The situation is the same even if we have only one droplet

  22. In pictures and videos Big rattles But big perturbations do!

  23. questions How come small rattles don t lead to evaporation, but big ones do? Both allow the access to the deconfined dofs, so why is there this distinction? The answer lies in the second law of thermodynamics, that is heat flows from a hotter system to a colder one 23

  24. back to thermo-basics Recall, large black holes in AdS have T = M, while small black holes behave as in AF space and T = 1/M If we start with a small droplet, it s hot, so it needs a colder system into which to evaporate A small rattle is a small black hole in the bulk hotter than the droplet! Need instead a bigger black hole in the bulk so that it s colder this way the droplet will want to flow its heat into it 24

  25. With funnels colder colder hotter hotter r0< LAdS small AdS black hole hotter when smaller

  26. The large d method: large brane bhs Let us just quickly show what happens with large brane black holes 26

  27. summary, questions We can study the evaporation of brane black holes using the large d limit of General Relativity Evaporation on the brane is only possible when we have a colder black connection in the bulk either as a funnel or in the form of a big rattle Otherwise, the droplets become stable Can be best understood through the laws of thermodynamics heat will flow from a hotter system to a colder one But the more pressing question is how to understand all of these phases through the CFT lens 27

  28. Thank you! 28

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