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Quantum corpuscular corrections to the Newtonian potential
Andrea Giugno
Arnold Sommerfeld Center, Ludwig Maximilians Universität, Theresienstraße 37, 80333, Munich
in collaboration with R.Casadio, A.Giusti and M.Lenzi
3rd Karl Schwarzschild Meeting, “Gravity and the Gauge/Gravity duality”
Frankfurt am Main, July 27, 2017
Based on arXiv:1702.05918, to appear in PRD
Motivation: Black Holes & the road to QG
Matter matters! (Baryons & gravitons)
Classical & Quantum corrections to the Newtonian potential
Outlook
Outline of the talk
Motivation: Black Holes & the road to QG
Motivation: Black Holes & the road to QG
Horizon
Staticity
Trapped surface
gij ∇ ir ∇ j r=0
r=RH=2GN M (t , r)
Misner-Sharp mass
Strong gravity scale
Motivation: Black Holes & the road to QG
Horizon
Staticity
Trapped surface
gij ∇ ir ∇ j r=0
r=RH=2GN M (t , r)
Misner-Sharp mass
… but nature is quantum!!!
Δ x Δ p≥ℏ
Compton wavelength
Strong gravity scale
λM=ℏ
M
Q(FT) scale
Motivation: Black Holes & the road to QG
Horizon
Staticity
Trapped surface
gij ∇ ir ∇ j r=0
r=RH=2GN M (t , r)
… but nature is quantum!!!
Δ x Δ p≥ℏ
Compton wavelength
Strong gravity scale
λM=ℏ
M
Q(FT) scale
GN M≥ℏ
M
QUANTUM BLACK HOLES
M≥mPℏ=lPmP
GN=lPmP
Motivation: Black Holes & the road to QG
Horizon
Staticity
Trapped surface
gij ∇ ir ∇ j r=0
r=RH=2GN M (t , r)
… but nature is quantum!!!
Δ x Δ p≥ℏ
Compton wavelength
Strong gravity scale
λM=ℏ
M
Q(FT) scale
GN M≥ℏ
M
QUANTUM BLACK HOLES
N m≥mPℏ=lPmP
GN=lPmP
Counterproposal
N>>1
Hawking quantum
BH = self-sustained BEC of gravitons
Hawking evaporation:
“marginally bound”
Matter matters! (Baryons & gravitons)R.Casadio, A.G. and A.Giusti, PLB 763 (2016) 337
Effective mass
Star
Black Hole
Matter matters! (Baryons & gravitons)
kinetic pressure
Star
Black Hole
GR correction!
Coherent state
Newton
“Energy balance’’:
“marginal bound” recovered!
Matter matters! (Baryons & gravitons)
From area to distance:
Radial geodesic fall:
Static proper time:
( … irrelevant)
Post-Newtonian effective theoryGR recap
Schwarzschild
Conditions:Weak field Static non-relativistic motion
From area to distance:
Radial geodesic fall:
Static proper time:
Standard post-Newtonian from isotropic metric
( … irrelevant)
Post-Newtonian effective theoryGR recap
Schwarzschild
Watch out!Different parametrisations of t...but same functional form
Einstein-Hilbert action:
1) Weak field:
2) Static non-relativistic motion:
3) De Donder gauge:
4) Fierz-Pauli and some guessing …
Post-Newtonian effective theory
Einstein-Hilbert action:
1) Weak field:
2) Static non-relativistic motion:
3) De Donder gauge:
Effective scalar action:
A) time measure
B) Newtonian
C) Post-Newtonian
4) Fierz-Pauli and some guessing …
Post-Newtonian effective theory
Newtonian potential:
Field equation:
Purely Newtonian potential energyPotential energy density
(aka static current) :
Gravitational potential self-energy
Post-Newtonian effective theory
Field equation:
Potential energies
Post-Newtonian effective theory
Separate & solve:
Classical solutions
(Rough) Example: Point-like source
(0 + 1) potential:
Arbitrary!(0 + 1) energies:
Post-Newtonian effective theory
Classical solutions
(Rough) Example: Point-like source
(0 + 1) potential:
Arbitrary!(0 + 1) energies:
Post-Newtonian too large!
NO maximal packing for point source!
Post-Newtonian effective theory
Post-Newtonian effective theory
More realistic case: homogeneous star
(0 + 1) energy:
Post-Newtonian effective theory
More realistic case: homogeneous star
(0 + 1) potential(0 + 1) energy:
“marginally bound” for
Newtonian
The result holds also for other kindsof sources (e.g. Gaussian, etc.)
Quantum toy model: massless scalar field
Newtonian ground state:
Field equation:
Commutators:
Vacuum:
Normalisation:
Post-Newtonian effective theory
Coherent!
Post-Newtonian effective theoryNormalisation ~ occupation number
Typically:
UV cut-off
IR cut-off
Size of static field
Source size
Dynamics…
Post-Newtonian corrections:
Vacuum
New coherent state:
One-mode occupation:
Typically:
PLB 763 (2016) 337
OK for large source!
Post-Newtonian effective theory
Post-Newtonian corrections:
Vacuum
New coherent state:
One-mode occupation:
Typically:
PLB 763 (2016) 337
OK for large source!
For black hole formation?
Post-Newtonian effective theory
Outlook
Quantum post-Newtonian corrections: Phenomenological consequences for (neutron) stars Phenomenological consequences for BH formation
Thermal fluctuations: Quantum matter effects Hawking radiation
Quantum resolution of inner BH structure
Thank you!
