numerical relativity in fundamental physics · 2019. 11. 15. · numerical relativity in...
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Numerical Relativity in Fundamental Physics
Ulrich Sperhake
DAMTP University of Cambridge
Gravity@Malta COST action University of Malta, 23 Jan 2018
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This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 690904, from H2020-ERC-2014-CoG Grant No. ”MaGRaTh"
646597, from NSF XSEDE Grant No. PHY-090003 and from STFC Consolidator Grant No. ST/L000636/1.
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Overview⚫ Motivation
⚫ Particle Laboratories in Outer Space
⚫ Boson Stars
⚫ Compact Objects in Modified Gravity
⚫ High-Energy Collisions of Black Holes
⚫ Fundamental Properties of Spacetimes
⚫ Concluding Remarks
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Motivation
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A Tale of Two Pillars
⚫ Successful: pp Collisions, Solar System, Cosmology, GWs,…
Rotation Curves, Grav.Lensing, CMB, X-Ray Obs. of Halos
Not explained by Gravity of visible Matter
Dark Energy, Dark Matter and/or Modified Gravity
Cosm.Constant Problem: Why is so small and why
Hierarchy Problem: Why is Gravity so feeble?
!
⇤ ⇢dark ⇠ ⇢mat
SM of Particle Physics General Relativity
⚫ And yet: QM and Gravity not compatible + Problems or Gaps:
!
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Particle Laboratories in Outer Space
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Dark Matter Searches⚫ DM Candidates: Primordial BHs, LIGO BHs, WIMPs, WISPs,…
⚫ Many particle searches under way at LHC,…
⚫ Ultralight fields (WISPs):
Axions, Dark Photons, Q-balls, Bosonic Condensations,…
Compton Wavelength:
⚫ No-hair theorems limit BH-fund.field interaction, but:
Long-lived states of scalar/vector fields, Hairy BHs, super radiance
Okawa et al 1401.1548, Herdeiro & Radu 1403.2757, Zel’dovich 1971
Runaway instabilities: e.g. BH bomb Press & Teukolsky 1972
⚫ BH as atom
⚫ Search for DM through GW observations!
m ⌧ 1 eV
m ⇠ 10�10 . . . 10�20 eV ! � ⇠ 1 km . . . 102 AU
!
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Superradiance⚫ Amplification of field if
akin to Penrose process
⚫ BH spins Constraints on photon mass
Pani & Cardoso 1209.0465
⚫ Superradiance also amplifies GWs East et al 1312.4529
⚫ Floating orbits Press & Teukolsky 1972
⚫ Nonlinear study of Proca field East & Pretorius 1704.04791
of BH mass extracted; saturation when
⚫ TODO: GW signature of fundamental fields in BH mergers?
⚫ Fund.fields can also pile up at centre of stars Brito et al 1508.04773
! < m⌦BH
!
! > 9% m⌦BH & !
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Boson Stars
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Basic properties⚫ EM solitons: Geons Wheeler 1955 but unstable!
⚫ Self-gravitating complex scalar field: Klein-Gordon Geons
Kaup 1968 Now called Boson Stars
⚫ Mini Boson Stars:
diagram; cf. Neutron Stars
Scaling with :
⚫ Self-interaction wider range of models
E.g. :
⚫ Rotating BSs: angular mom. per particle number = Integer
Quantum nature
⚫ Oscillatons: localized, oscillating real scal.fields
� / ei!t , V (�) = m |�|2
Eby et al 1511.04474
M �RM
max
= 0.633M2Planck
/mm
!
� |�|4/4 Mmax
⇡ (0.1GeV2)M��1/2/m2 Colpi et al 1986
!
Seidel & Suen 1991
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Boson star inspirals⚫ Potential (“nontopological solitonic BSs”):
⚫ Superpose two single BS solutions; conformal
⚫ Phase shift : Stars almost completely annihilate
Otherwise: Rotating bar relaxing to a non-rotating BS
Bezares et al 1705.01071
⚫ Inspiral waveforms
⚫ TODO: systematic
waveform modeling
V (�) = m|�|2 + �|�|4
BH formation or…
Oscillating BSs
Palenzuela 1710.09432
Z4
⇡
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Compact objects in modified gravity
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Range of theories⚫ Classify theories through Lovelock’s theorem
⚫ Prerequisite: Well-posed initial value formulation!
Most NR work restricted to scalar-tensor theory
Berti 1501.07274
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Scalar tensor theory⚫ Spontaneous scalarization:
Consider equilibrium NS models
Abrupt increase of scalar charge for some parameter range
Palenzuela 1710.09432
Damour & Esposito Farese 1993, 1996
⚫ Generates scalar GWs in stellar collape
Novak+ 1990s, Gerosa et al 2016
⚫ Constrains massless ST theory!
�6 �4 �2 0 2 4 6�0
10�4
10�3
10�2
↵0
PSRJ0348+0432
PSR J1738+0333
Cassini
Runs
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Massive ST theories⚫ Massive fields: short range!
constraints only valid up to
⚫ Quasi-monochromatic signals lasting months to centuries
US et al 1708.03651
⚫ Suitable for LIGO
⚫ Historic SNe!
� =h
mcm . 10�16 eV
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Compact binaries⚫ BH binaries in ST theory: Constrained by no-hair theorems!
But: scalar radiation for non-trivial BCs or potentials
Berti et al 1304.2836, Healy et al 1112.3928
⚫ NS binaries in ST theory: Dynamical scalarization
Palenzuela 1310.4481
⚫ BH binaries in dyn.Chern-Simons theory
⚫ TODO: smoking guns; parametric models
Well-posedness questionable
Delsate et al 1407.6727
Pert.approach around GR
Scalar signal
Okounkouva et al 1705.07924
)
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High-energy collisions of BHs
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Motivation: TeV Gravity
⚫ Particle collisions may form BHs E.g. Dimopoulos & Landsberg ‘01, Giddings & Thomas ’01
⚫ Provide data for LHC event generators
⚫ Collide BHs in dimensions
⚫ Gravity other forces
⚫ Gravity not measured below . Diluted due to
Large extra dimensions Arkani-Hamed, Dimopoulos, Dvali ‘98
Extra dimensions with warp factor Randall & Sundrum ‘99
⇡ 10�39⇥
Cross section for BH formation
Loss of energy and any.momentum in GWs
D > 4
⇠ 0.1 mm
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Does matter matter?⚫ Hoop conjecture kinetic energy triggers BH formation
⚫ Einstein + minimally coupled, massive complex scalar field
“Boson stars” Choptuik & Pretorius 0908.1780
⚫ BH formation threshold
⚫ Model point particle collision by BH collisions
⚫ Similar results for collisions of perfect fluid balls
Rezzolla & Takami 1209.6138, East & Pretorius 1312.4529
)
�thr
= 2.9± 10% ⇠ 1/3 �hoop
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Grazing collisions in D=4⚫ Spins: aligned, zero, anti aligned US et al 1211.6114
⚫ : spin effects washed out as bscat, Erad v ! c
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Scattering threshold in D=5⚫ Numerical stability still an issue…
Okawa, Nakao & Shibata 1105.3331
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Head-on collisions from rest in D=4…10⚫ strongly suppresses in higher
Cook et al 1709.10514
Erad D
4 5 6 7 8 9 10
D
10-5
10-4
10-3
Era
d /
M
Data
Fit: a0 (2π)
β/ Γ(β), β = (D-a
1) / a
2
Fit: b0 2 π
β/ Γ(β), β = (D-b
1) / b
2
⚫ But: No suppression for high mass ratios!
likely due to new length scales in high
⚫ TODO: High velocity in
D Emparan et al 1302.6382
D > 4
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Fundamental properties of BHs
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Motivation: Fundamental BH properties⚫ Cosmic censorship Lehner & Pretorius ’10, Figueras, Kunesch, Tunyasuvunakool et al. ’16, ’17
⚫ Stability of AdS Bizon & Rostworowski ’11
⚫ Stability of Hairy BH solutions of
Herdeiro & Radu 1403.02757
Herdeiro et al 1603.02687 ???
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Summary of main open tasks⚫ Simulate signature of ultra-light fields in BH waveforms
⚫ GW templates from Boson Stars and other ultra-compact objects
⚫ Smoking gun signatures and waveform catalogues for GW sources
in alternative theories of gravity
⚫ High-energy collisions of BHs in
⚫ Stability and dynamics of Hairy BHs
⚫ Numerical relativity in other areas
> D
Nonlinear cosmology
AdS/CFT
Critical phenomena without spherical symmetry
…