Gary Horowitz UCSB Weak Cosmic Censorship Generic smooth initial data cannot evolve to regions of arbitrarily large curvature that are visible to distant observers Many of us hope this is false so we might directly observe effects of quantum gravity ID: 760294
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Slide1
Connecting the Cosmic Censorship and Weak Gravity Conjectures
Gary HorowitzUCSB
Slide2(Weak) Cosmic Censorship
Generic smooth initial data
cannot evolve to
regions of arbitrarily large curvature that are visible to distant observers.
Many of us hope this is false, so we might directly observe effects of quantum gravity.
In D > 4, there are unstable black holes which violate this when the horizon pinches off. (But the pinch-off only involves a small amount of mass.)
Slide3Plan for talk
Describe a new counterexample to cosmic censorship in AdS
4
involving a Maxwell field
Discuss the weak gravity conjecture (in
AdS
)
Show that if the weak gravity conjecture is satisfied, one can’t violate cosmic censorship this way
Punchline: The bound on the charge required to preserve cosmic censorship is precisely the weak gravity bound!
Discussion
Slide4The counterexample
Consider D = 4 Einstein-Maxwell with Λ < 0.Fix the metric and vector potential on the AdS boundary to beStart by finding the static (T = 0) solutions. Simple solutions known for μ = 0 (AdS) and μ = const (planar RN AdS). We will demand μ -> 0as r -> ∞. (Iqbal, Santos, Way, G.H. 1412.1830)(Related work by Blake, Donos, and Tong, 1412.2003.)
Slide5We consider the following profiles:Solutions describe static, self-gravitating electric fields. Smooth solutions exist only for a < amax:For n > 1, they approach AdS4 in the interior and have a smooth Poincare horizon.
Slide6Now consider Start with a = 0 and slowly increase to a(∞) > amax. Bulk can’t settle down to a smooth solution. Expect the curvature to grow without bound violating cosmic censorship. (Santos, Way, G.H. 1604.06465)This has recently been confirmed by a full time dependent numerical relativity calculation. (Crisford and Santos, 1702.05490)
Slide7They consider n = 1 profile with
amax = .678Numerically, one can change a(t) quickly.Focus on Fab Fab (v) on the horizon, on the axis.
V = 0
Slide8a
max
= .678
Slide9When
a(∞)
<
a
max
, solution converges to static one.
Slide10When a(∞) > amax, if F2 = A vb, then b = d(ln F2) / d(ln v)
Slide11Comments
Since F
2
blows up, the curvature
also
blows up on the horizon.
The blow-up is not just on the axis, but all along the horizon.
T
he growing curvature remains visible to distant observers, so one can violate cosmic censorship in AdS
4
with only a Maxwell field.
This violation is much stronger than seen in D > 4.
Slide12Weak gravity conjecture
(Arkani-Hamed, Motl, Nicolis, and Vafa, hep-th/0601001)
Any consistent quantum theory of gravity must contain charged particles with q/m > 1.
This implies that
extremal
charged black holes are not stable, but will decay by emitting charged particles.
Vafa
(2016): Will this save cosmic censorship?
Slide13Epiphany
(
Crisford
,
Santos,
G.H., 2017)
:
We can study this by adding a classical scalar field
φ
with mass m and charge q.
For large enough q, our previous Einstein-Maxwell solutions should become unstable to turning on the scalar field.
(Similar to the holographic superconductor.)
Key Questions: With nonzero scalar, is there still a maximum amplitude for static solutions? If not, what is the minimum charge you need to preserve cosmic censorship?
Slide14Weak gravity conjecture in AdS
What should the condition be in AdS?To make contact with the asymptotically flat case, we demand that small spherical extreme BHs evaporate.This requires
Slide15To see when our Einstein-Maxwell solutions become unstable, look for zero mode of scalar field.
Crisford
, Santos, G.H.,
1709.07880
Slide16If you change the mass, the smallest zero mode charge is always below the weak gravity bound:
(n = 8, a =
amax)
Our previous solutions always become unstable if q >
q
W
.
Slide17We construct the solutions with nonzero φ numerically and find that they exist for all amplitude.
z
ero mode
a
max
Cannot violate cosmic censorship!
f
or n
= 8,
q
=
q
W
Slide18So the weak gravity conjecture saves cosmic censorship in
AdS
.
But it might appear that slightly smaller charges would also work.
Slide19Solutions with
φ
≠ 0 become singular if you lower q.
φ ≠ 0
φ
=
0
Slide20The weak gravity conjecture appears to be both necessary and sufficient to avoid this class of counterexamples to cosmic censorship.
Slide21A caveat:
This was all based on static solutions, i.e., an ``adiabatic approximation”.
Crisford
and Santos are currently constructing the full time dependent solution.
This is nontrivial since you might form a
hovering black hole
:
a static, spherical,
extremal
BH hovering above the Poincare horizon.
Slide22Hovering black holes with
φ = 0 have been found numerically
z = 0
infinity
z = ∞
horizon
r = 0
Properties
Still have standard Poincare horizon in IR
Near horizon geometry is exactly RN
AdS
A
BH
-> 0 as
a
->
a
*
,
and grows monotonically as amplitude increases
BH bigger than the
AdS
radius have been found
Slide23These could not form in Einstein-Maxwell evolution since there was no charged matter. Now there is a slight chance that they will.
If so, the minimum charge might be lower.
Slide24Can This Happen in Vacuum?
Consider a vacuum solution (with Λ < 0) having a boundary metric with differential rotation: ds2 = -dt2 + dr2 + r2[d𝜑+ω(r)dt]2 where ω(r) = a p(r). There is again a maximum amplitude beyond which smooth stationary solutions do not exist.It appears one can again violate cosmic censorship.
(Santos and G.H., in progress)
Slide25But before one reaches
a
max
,
g
tt
> 0 somewhere on the boundary and the solution is unstable to
superradiance
of
nonaxisymmetric
modes.
The endpoint of
superradiance
in
AdS
is not know, but it won’t be the massive violation of cosmic censorship that we have without it.
Slide26But before one reaches
a
max
,
g
tt
> 0 somewhere on the boundary and the solution is unstable to
superradiance
of
nonaxisymmetric
modes.
The endpoint of
superradiance
in
AdS
is not know, but it won’t be the massive violation of cosmic censorship that exists without it.
P
ure GR has a built in mechanism for implementing the vacuum analog of the weak gravity conjecture.
(Recall
:
Extremal
rotating black holes evaporate due to a quantum version of
superradiance
.)
Slide27Summary
One can violate cosmic censorship with a Maxwell field in AdS
4
.
Adding a charged scalar field (with sufficient charge) removes this violation.
The bound on the charge is precisely the weak gravity bound (in
AdS
).
To Do: Understand why
a
close connection exists between these two conjectures.