Quantum corpuscular corrections to the Newtonian potential Based on arxiv:1702.05918, to appear in PRD Andrea Giugno Arnold Sommerfeld Center, Ludwig Maximilians Universität, Theresienstraße 37, 80333, Munich in collaboration with R.Casadio, A.Giusti and M.Lenzi 3 rd Karl Schwarzschild Meeting, Gravity and the Gauge/Gravity duality Frankfurt am Main, July 27, 2017
Outline of the talk Motivation: Black Holes & the road to QG Matter matters! (Baryons & gravitons) Classical & Quantum corrections to the Newtonian potential Outlook
Motivation: Black Holes & the road to QG
Motivation: Black Holes & the road to QG Trapped surface g ij i r j r=0 Staticity Misner-Sharp mass Horizon r=r H =2G N M (t, r) Strong gravity scale
Motivation: Black Holes & the road to QG Trapped surface g ij i r j r=0 but nature is quantum!!! Δ x Δ p ħ Staticity Misner-Sharp mass Horizon r=r H =2G N M (t, r) λ M = ħ M Compton wavelength Strong gravity scale Q(FT) scale
Motivation: Black Holes & the road to QG Trapped surface g ij i r j r=0 but nature is quantum!!! Δ x Δ p ħ Staticity G N M ħ M Horizon r=r H =2G N M (t, r) λ M = ħ M Compton wavelength Strong gravity scale ħ=l P m P G N = l P m P QUANTUM BLACK HOLES M m P Q(FT) scale
Motivation: Black Holes & the road to QG Trapped surface g ij i r j r=0 but nature is quantum!!! Δ x Δ p ħ Staticity G N M ħ M Horizon r=r H =2G N M (t, r) λ M = ħ M Compton wavelength Strong gravity scale ħ=l P m P G N = l P m P QUANTUM BLACK HOLES N m m P Counterproposal Q(FT) scale
Matter matters! (Baryons & gravitons) R.Casadio, A.G. and A.Giusti, PLB 763 (2016) 337 BH = self-sustained BEC of gravitons Effective mass marginally bound Hawking quantum N>>1 Hawking evaporation:
Matter matters! (Baryons & gravitons) Star Black Hole
Matter matters! (Baryons & gravitons) Energy balance : Star kinetic pressure Newton Coherent state Black Hole GR correction! marginal bound recovered!
Schwarzschild GR recap Radial geodesic fall: From area to distance: ( irrelevant) Static proper time:
Schwarzschild GR recap Radial geodesic fall: From area to distance: ( irrelevant) Static proper time: Conditions: Weak field Static non-relativistic motion Standard post-newtonian from isotropic metric 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
Einstein-Hilbert action: 1) Weak field: 2) Static non-relativistic motion: 3) De Donder gauge: 4) Fierz-Pauli and some guessing Effective scalar action: A) time measure B) Newtonian C) Post-Newtonian
Newtonian potential: Field equation: Purely Newtonian potential energy Potential energy density (aka static current) : Gravitational potential self-energy
Field equation: Separate & solve: Potential energies
Classical solutions (Rough) Example: Point-like source (0 + 1) potential: (0 + 1) energies: Arbitrary!
Classical solutions (Rough) Example: Point-like source (0 + 1) potential: (0 + 1) energies: Arbitrary! Post-Newtonian too large! NO maximal packing for point source!
More realistic case: homogeneous star (0 + 1) energy:
More realistic case: homogeneous star (0 + 1) energy: Newtonian (0 + 1) potential The result holds also for other kinds of sources (e.g. Gaussian, etc.) marginally bound for
Field equation: Quantum toy model: massless scalar field Commutators: Vacuum: Newtonian ground state: Coherent! Normalisation:
Normalisation ~ occupation number UV cut-off Size of static field Typically: IR cut-off Source size Dynamics
Post-Newtonian corrections: New coherent state: Vacuum One-mode occupation: PLB 763 (2016) 337 Typically: OK for large source!
Post-Newtonian corrections: New coherent state: Vacuum One-mode occupation: PLB 763 (2016) 337 Typically: OK for large source! For black hole formation?
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!