Working Group 3: Black holes and fundamental physics€¦ · Testing a new regime Gravity Parameter...

Working Group 3: Black holes and fundamental physics

Thomas P. Sotiriou

Testing a new regime Gravity Parameter Space 5

10-62 10-58 10-54 10-50 10-46 10-42 10-38 10-34 10-30 10-26 10-22 10-18 10-14 10-10

Curv

atur

e, ξ

(cm

-2)

10-12 10-10 10-8 10-6 10-4 10-2 100

Potential, ε

BBN

Lambda

Last scattering

WD MS

PSRs

NS

Clusters Galaxies

MW

M87S stars

R

MSS

BH

SMBH

P(k)| z=0 Accn. scale

Satellite

CMB peaks

Fig. 1.— A parameter space for gravitational fields, showing the regimes probed by a wide range of astrophysical and cosmologicalsystems. The axes variables are explained in §2 and individual curves are detailed in §3. Some of the label abbreviations are: SS = planetsof the Solar System, MS = Main Sequence stars, WD = white dwarfs, PSRs = binary pulsars, NS = individual neutron stars, BH = stellarmass black holes, MW = the Milky Way, SMBH = supermassive black holes, BBN = Big Bang Nucleosynthesis.

in Fig. 1 (orange, dashed). Systems below-left of thisacceleration scale cannot be modelled without adding acontribution to the gravitational field from unseen mat-ter. This region of the parameter space is then prob-lematic12 for testing gravity theories, since here thereis a degeneracy between two uncertain components of acosmological model: dark matter and an e↵ective darkenergy (which could be due to real fields or correctionsto General Relativity).One final trend is worth noting before we move on to

describing specific systems. The gravitational field inside

12 But not impossibly so, due to the di↵erent properties of darkenergy and dark matter.

an isothermal sphere with a density profile

⇢(r) = ⇢0

⇣r0

r

⌘2

(19)

corresponds to a vertical line on the parameter space,since the potential (x-axis) parameter

✏iso

=GM(< r)

rc2(20)

=G⇢

0

rc2

Z r

0

4⇡⇣r

0

r̃

⌘2

r̃2dr̃

=4⇡G⇢

0

r20

c2(21)

taken from T. Baker, D. Psaltis, C. Skordis, ApJ 802, 63 (2015)

Untested combination of curvature and potential!

Thomas P. Sotiriou - COST Meeting, Malta, January 24th 2017

Key question

So, why have 4 BBH & 1 BNS detections not ruled out everything?

Existing constraints are already strong

Degeneracies of various types

Lack of concrete predictions


Lovelock and GR

Lovelock’s theorem leads to GR under assumptions:

4 dimensions

Covariance

Second order equations

No extra fields

Locality

Not all of them are equally important for phenomenology!


Propagation effects

E2 = m2g ±M1p+ c2gp

2 ± p3

M3± p4

M24

+ . . .

Strong bound on the mass of the graviton, , But marginally interesting from a theory perspective Weak bounds on in eV range Strong constraint from BNS and EM

M1 M3

M4

This rules out several dark energy models that predict cg 6= c

But we can do better in constraining Lorentz violations by looking for other polarisations!

T.P.S., PRL, too appear, arXiv:1709.00940 [gr-qc]; A. E. Gumrukcuoglu, M. Saravani and T.P.S., PRD too appear, arXiv:1711.08845[gr-qc]

�2⇥ 10�15 � �cg/c � 7⇥ 10�16


Waveform

taken from B. P. Abbott et al. (LIGO -Virgo) PRL 116, 061102 (2016)


WG3: Topics

Strong field parametrizations Kento Yagi

Black holes beyond General Relativity Enrico Barausse

Black hole perturbation theory and fundamental physics Paolo Pani

Binaries in alternative theories of gravity Carlos Palenzuela

Testing the black hole hypothesis Carlos Herdeiro


Binary pulsar

Very strong constraints, it the same regime as the early inspiral!


Extracting new physics

Step-by-step guide for your favourite candidate:

Study compact objects and determine their properties

Model the inspiral (post-Newtonian); model the ringdown (perturbation theory)

Do full-blown numerics to get the merger (requires initial value formulation!)


WG3: Topics







Scalar fields in BH spacetimes

S.W. Hawking, CMP 25, 152 (1972).

⇤� = 0

stationary, as the endpoint of collapse asymptotically flat, i.e. isolated

The equation

admits only the trivial solution in a BH spacetime that is

⇤� = U 0(�)

The same is true for the equation

with the additional assumption of local stability

U 00(�0) > 0

T. P. S. and V. Faraoni, PRL 108, 081103 (2012)


No difference from GR?

Actually there is...

Perturbations are different!

They even lead to new effects, e.g. superradiance

In general, relaxing the symmetries of the scalar can lead to “hairy” solutions.

Cosmic evolution or matter could also lead to scalar “hair”

E. Barausse and T.P.S., PRL 101, 099001 (2008).

A. Arvanitaki and S. Dubovksy, PRD 83, 044026 (2011) R. Brito, V. Cardoso and P. Pani, Lect.Notes Phys. 906, 1 (2015)

T. Jacobson, PRL 83, 2699 (1999); M. W. Horbatsch and C. P. Burgess, JCAP 1205, 010 (2012). V. Cardoso, I. P. Carucci, P. Pani and T. P. S., PRL 111, 111101 (2013)

C. A. R. Herdeiro and E. Radu, PRL 112, 221101 (2014).


Black hole hair

P. Kanti et al., PRD 54, 5049 (1996).

We already know that more general couplings lead to “hairy” solutions! Such solutions have been found for couplings of the type

For a shift-symmetric (a.k.a. massless) field, the coupling

is the only one that leads to hair!

e�(R2 � 4Rµ⌫Rµ⌫ +Rµ⌫�Rµ⌫�)

�G

T.P.S. and S.-Y. Zhou, PRL 112, 251102 (2014); PRD 90, 124063 (2014).


WG3: Topics







Working Group 3: Black holes and fundamental physics€¦ · Testing a new regime Gravity Parameter...

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