Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
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1 Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
2 Outline Outline Description of the Loop Black Holes: Shape and Metric Thermodynamic properties Cosmological Implications: Creation Process Constraints on Inflation Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
3 Description of the Loop Black Holes Loop Quantum Cosmology Applied to Black Holes The space time inside a black hole is homogeneous: apply LQC techniques and extend analytically outside. [Abhay Ashtekar, Martin Bojowald, Leonardo Modesto, Parampreet Singh,etc.] Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
4 Description of the Loop Black Holes Shape of Ultra Light Loop Black Holes Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
5 The Metric Description of the Loop Black Holes ds 2 = (r r +)(r r )(r + r ) 2 r 4 + a 2 dt 2 0 dr 2 ( a r 2 + r2) dω 2, + (r r + )(r r )r 4 (r+r ) d 2 (r 4 +a 2 0 ) r + = 2m, r = 2mP, r = 2mP 2 ; 0 < P < 1. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
6 Description of the Loop Black Holes Loop Black Hole Temperature T(m) = (2m) 3 4π[(2m) 4 + a 2 0 ]. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
7 Creation Cosmological Implications ρ(m) 1 π 3 exp( F/T) where F = F BH F R. Validity of thermodynamics: local equilibrium: t reaction < t exp H 1 T < GeV. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
8 Inflation Cosmological Implications 0 (a(t i )) 3 m 0 (m i )ρ i (m i ) (a(t 0 )) 3 dm i = 0.22ρ crit = ρ DM a(t 0) a(t i ) = e85 60 e-folds ago, was the end of inflation which lasted for at least 60 e-folds. T inflation GeV a(t 0) a(t i ) = e85 Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
9 Conclusion Conclusion Light Loop Black Holes: small cross-section, stable, heavy. Possible Dark matter. Would be created during Inflation. Constrains at least 2-stage inflation. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
10 Conclusion Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
11 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = (1 2m r )dt2 + dr2 1 2m r + r 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
12 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dr2 1 2m r (1 2m r )dt2 + r 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
13 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
14 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
15 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
16 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
17 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
18 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
19 Deriving the Loop Quantum Black Hole Restrict consideration to Kantowski-Sachs space-time inside BH. ds 2 = dt2 1 + (2m t 2m t 1)dr 2 + t 2 dω 2 Introduce polymerisation and Ashtekar variables. Use holonomies and density triads as fundamental variables. Semiclassical evolution: using Poisson brackets. Resulting metric exhibits a minimum in area. Fix minimum area, simplest way: minimum area of full LQG. Extend metric analytically outside (the two) Horizons. Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
20 Ultra High Energy Cosmic Rays The GZK Cutoff Figure: Modification of a figure by Angela V. Olinto (U. Chicago). distance > 50Mpc E cosmic ray < ev we observe E cosmic ray > distance < 50Mpc, no observed sources Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
21 Ultra High Energy Cosmic Rays The GZK Cutoff Figure: Modification of a figure by Angela V. Olinto (U. Chicago). distance > 50Mpc E cosmic ray < ev we observe E cosmic ray > distance < 50Mpc, no observed sources Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
22 Ultra High Energy Cosmic Rays The GZK Cutoff Figure: Modification of a figure by Angela V. Olinto (U. Chicago). distance > 50Mpc E cosmic ray < ev we observe E cosmic ray > distance < 50Mpc, no observed sources Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
23 Ultra High Energy Cosmic Rays Radiation Emitted by Ultra Light LQBH In the Universe at Large: a 0 /2 R BH (ν) = ρ 0 (m 0 ) 2A min m 0 =0 π In the vicinity of the Solar System: a 0 /2 R SSBH (ν) = ρ L (m 0 ) 2A min m 0 =0 π ν 2 ν T e BH (m 0) 1 ν 2 ν dm 0 T e BH (m 0) 1 dm 0 ; ρ L (m 0 ) = ρ DM ρ i (m 0 ) m=0 ρ i(m)mdm Isabeau Prémont-Schwarz (AEI) Cosmological Implications of LBH DM Naxos Sept / 13
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