Quantum corpuscular corrections to the Newtonian potential

Transcription

1 Quantum corpuscular corrections to the Newtonian potential Based on arxiv: , 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

2 Outline of the talk Motivation: Black Holes & the road to QG Matter matters! (Baryons & gravitons) Classical & Quantum corrections to the Newtonian potential Outlook

3 Motivation: Black Holes & the road to QG

4 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

5 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

6 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

7 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

8 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:

9 Matter matters! (Baryons & gravitons) Star Black Hole

10 Matter matters! (Baryons & gravitons) Energy balance : Star kinetic pressure Newton Coherent state Black Hole GR correction! marginal bound recovered!

11 Schwarzschild GR recap Radial geodesic fall: From area to distance: ( irrelevant) Static proper time:

12 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

13 Einstein-Hilbert action: 1) Weak field: 2) Static non-relativistic motion: 3) De Donder gauge: 4) Fierz-Pauli and some guessing

14 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

15 Newtonian potential: Field equation: Purely Newtonian potential energy Potential energy density (aka static current) : Gravitational potential self-energy

16 Field equation: Separate & solve: Potential energies

17 Classical solutions (Rough) Example: Point-like source (0 + 1) potential: (0 + 1) energies: Arbitrary!

18 Classical solutions (Rough) Example: Point-like source (0 + 1) potential: (0 + 1) energies: Arbitrary! Post-Newtonian too large! NO maximal packing for point source!

19 More realistic case: homogeneous star (0 + 1) energy:

20 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

21 Field equation: Quantum toy model: massless scalar field Commutators: Vacuum: Newtonian ground state: Coherent! Normalisation:

22 Normalisation ~ occupation number UV cut-off Size of static field Typically: IR cut-off Source size Dynamics

23 Post-Newtonian corrections: New coherent state: Vacuum One-mode occupation: PLB 763 (2016) 337 Typically: OK for large source!

24 Post-Newtonian corrections: New coherent state: Vacuum One-mode occupation: PLB 763 (2016) 337 Typically: OK for large source! For black hole formation?

25 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

26 Thank you!