Critical Phenomena in Gravitational Collapse Thomas Baumgarte - PowerPoint PPT Presentation

Critical Phenomena in Gravitational Collapse Thomas Baumgarte Bowdoin College ICERM, Brown University, Oct. 27, 2020

Critical Phenomena Critical Phenomena in gravitational collapse Critical Phenomena in gravitational collapse Thomas Baumgarte, Bowdoin College 2

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Consider scalar wave 1 . 2 � φ ≡ g ab ∇ a ∇ b φ = 0 η = 0.1 1 . 0 coupled to Einstein’s equations 0 . 8 • Initial data 0 . 6 α φ = η exp( − R 2 /R 2 0 ) 0 . 4 0 . 2 0 . 0 • try out different η ... η = 0.6 − 0 . 2 0 1 2 3 4 5 6 7 8 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 3 < η ∗ < 0 . 4 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave � φ ≡ g ab ∇ a ∇ b φ = 0 1 . 0 coupled to Einstein’s equations η = 0.31 0 . 8 • Initial data 0 . 6 α φ = η exp( − R 2 /R 2 0 ) 0 . 4 0 . 2 0 . 0 • try out different η ... η = 0.39 − 0 . 2 0 1 2 3 4 5 6 7 8 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 3 < η ∗ < 0 . 31 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave � φ ≡ g ab ∇ a ∇ b φ = 0 1 . 0 coupled to Einstein’s equations η = 0.301 0 . 8 • Initial data 0 . 6 α φ = η exp( − R 2 /R 2 0 ) 0 . 4 0 . 2 0 . 0 • try out different η ... η = 0.309 − 0 . 2 0 1 2 3 4 5 6 7 8 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303 < η ∗ < 0 . 304 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave 1 . 2 � φ ≡ g ab ∇ a ∇ b φ = 0 1 . 0 η =0.3031 coupled to Einstein’s equations 0 . 8 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.3039 − 0 . 2 • try out different η ... 0 2 4 6 8 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 3033 < η ∗ < 0 . 3034 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave 1 . 2 � φ ≡ g ab ∇ a ∇ b φ = 0 1 . 0 η =0.30331 coupled to Einstein’s equations 0 . 8 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.30339 − 0 . 2 • try out different η ... 0 2 4 6 8 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 30337 < η ∗ < 0 . 30338 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave 1 . 2 � φ ≡ g ab ∇ a ∇ b φ = 0 1 . 0 η =0.303371 coupled to Einstein’s equations 0 . 8 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.303379 − 0 . 2 • try out different η ... 0 2 4 6 8 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303375 < η ∗ < 0 . 303376 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.303371 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 8 coupled to Einstein’s equations 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.303379 • try out different η ... 5 . 8 6 . 0 6 . 2 6 . 4 6 . 6 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303375 < η ∗ < 0 . 303376 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.3033751 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 8 coupled to Einstein’s equations 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.3033759 • try out different η ... 5 . 8 6 . 0 6 . 2 6 . 4 6 . 6 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 3033759 < η ∗ < 0 . 3033760 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.30337591 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 8 coupled to Einstein’s equations 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.30337599 • try out different η ... 5 . 8 6 . 0 6 . 2 6 . 4 6 . 6 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 30337599 < η ∗ < 0 . 30337600 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.303375991 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 8 coupled to Einstein’s equations 0 . 6 • Initial data α 0 . 4 φ = η exp( − R 2 /R 2 0 ) 0 . 2 0 . 0 η =0.303375999 • try out different η ... 5 . 8 6 . 0 6 . 2 6 . 4 6 . 6 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303375994 < η ∗ < 0 . 303375995 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.303375991 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 6 coupled to Einstein’s equations 0 . 4 • Initial data α 0 . 2 φ = η exp( − R 2 /R 2 0 ) 0 . 0 η =0.303375999 • try out different η ... 6 . 45 6 . 50 6 . 55 6 . 60 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303375994 < η ∗ < 0 . 303375995 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.3033759941 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 6 coupled to Einstein’s equations 0 . 4 • Initial data α 0 . 2 φ = η exp( − R 2 /R 2 0 ) 0 . 0 η =0.3033759949 • try out different η ... 6 . 45 6 . 50 6 . 55 6 . 60 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 3033759947 < η ∗ < 0 . 3033759948 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.30337599471 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 6 coupled to Einstein’s equations 0 . 4 • Initial data α 0 . 2 φ = η exp( − R 2 /R 2 0 ) 0 . 0 η =0.30337599479 • try out different η ... 6 . 45 6 . 50 6 . 55 6 . 60 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 30337599472 < η ∗ < 0 . 30337599473 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.303375994721 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 6 coupled to Einstein’s equations 0 . 4 • Initial data α 0 . 2 φ = η exp( − R 2 /R 2 0 ) 0 . 0 η =0.303375994729 • try out different η ... 6 . 45 6 . 50 6 . 55 6 . 60 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303375994729 < η ∗ < 0 . 303375994730 Thomas Baumgarte, Bowdoin College 3

Critical Phenomena Critical Phenomena in gravitational collapse A numerical experiment... • Let’s say scalar wave η =0.303375994721 0 . 4 � φ ≡ g ab ∇ a ∇ b φ = 0 0 . 3 coupled to Einstein’s equations 0 . 2 • Initial data α φ = η exp( − R 2 /R 2 0 . 1 0 ) 0 . 0 η =0.303375994729 • try out different η ... − 0 . 1 6 . 5825 6 . 5850 6 . 5875 6 . 5900 6 . 5925 t Have critical value η ∗ so that η < η ∗ α → 1 end up with flat space η > η ∗ α → 0 end up with black hole Black-hole threshold 0 . 303375994729 < η ∗ < 0 . 303375994730 Thomas Baumgarte, Bowdoin College 3