RB, Sherf, Black Hole Love Story In progress RB, Medved, Ram Brustein Many papers ' 15 - Now ןב תטיסרבינוא-ןוירוג • Love # • Love # vanishes for GR BHs – BSM! • The case for horizon-scale corrections : implications for Love # • Can Love # be measured ?
Introduction • What is a BH ? • Schwarzchild/Kerr geometry correct ? • Probe the near horizon region • Probe quantum structure of BHs
Deviations from GR • Q: Why expect anything besides GR during a BH merger ? • A: Fundamental physics principles & established facts Internal “ quantum ” structure • Q: What type of deviations from GR ? • A: Internal structure Additional ringdown modes, nonzero Love # • Q: What type of deviations from GR do not expect ? • A: Different talk
Meaning of “ Interior / quantum structure ” 2 2 1 2 2 2 2 GM ds dt dr r d 1 2 r GM 2 1 r Interior ~ r < 2 GM State of interior Quantum state of collapsed object Classically Causally separated from exterior
Excited BH relaxes to equilibrium Quantum mechanically Classically: horizon tidal deformation -ive null energy +ive null energy horizon grows Causality ( Hartle ’ 73, Poisson + ) horizon shrinks Causality (Mathur ’ 17, Maldacena+ ’ 17) Ringdown/Merger – “ large ” deformation, short time – “ small ” deformation, Inspiral long time
Excited BH relaxes to equilibrium Amount of information that can Can we use be “ read ” determined by the Ringdown degree of excitation D E/E ? Inspiral, Love # to probe quantum structure ? Ringdown/Merger – “ large ” deformation, short time – “ small ” deformation, Inspiral long time
Blanchet LRR ' 06 Love number(s) n i x i Hinderer 0711.2420 r Thorn 9706057 Porto 1606.08895 Q 2 i j ij i j 2 M ij 1 1 g n n r n n 1 3 r 3 3 2 tt ij r 2 3 Newtonian ( ) 1 Q d x x x x ext ij i j 3 ij ij x x 2 Star Q i j ~ ~ M Q 5 Excitation of l = 2 mode of star @ w = 0 R Linear response 2 ~ M 3 Q k ij ij 2 2 R 5 2 ~ R ~ 2 3 MR ~ Q R
Hinderer 0711.2420 Love number(s) for NS Thorn 9706057 Boundary conditions 1. Regularity @ r = 0 2. Continuity @ r = R
Hinderer 0711.2420 Love number(s) for NS NS: C~ ¼, BH C = 1/2 2 1 2 A C k ~ 2 2 1 2 1 2 ln 1 2 B C D C C
Love number(s) = 0 for 4D GR BHs • 0906.1366 Binnington, Poisson • 0906.0096 Damour, Nagar – No Hair • Tidal deformation of BHs but Love #s = 0 Boundary conditions 1411.4711 Poisson 1. Regularity @ r = 0 horizon • No-Hair theorem Love #s = 0 2. Continuity @ r = R infinity 1503.03240 Gurlebeck /. external sources G: “ The change in the geometry of the • 1606.08895 Porto horizon is, however, not reflected in the asymptotic multipole moments ” • Love #s in higher dimensions don ’ t vanish Kol, Smolkin 1110.3764
Love number(s) scaling for hypothetical compact objects 1701.01116v4, Cardoso et al. Original uses x instead of 5 | ln( /10 ) |~100 l M P Hypothetical compact objects 2 1 2 A C k ~ with radius larger than R S 2 2 1 2 1 2 ln 1 2 B C D C C
The case for horizon-scale corrections : implications for Love # / Love # = 0 scaling for compact objects Requires new internal “ fluid modes ” (or a horizonless object) Otherwise same issue as for GR BHs: “ The change in the geometry of the horizon is, however, not reflected in the asymptotic multipole moments ”
The case for horizon-scale corrections : implications for Love # Introducing ln : Assume a surface @ D r from the object ’ s Schwarzschild radius D r ln r R * R S S redshift D R R 1 1 r g S S r tt D R r S 1 R S RS
BH as a bound state of strings @ Hagedorn temperature “ collapsed polymer ” , maximal entropy state • From the outside, in equilibrium, looks exactly like a BH • Mass and entropy scale correctly • Does not collapse – entropy dominated/uncertainty principle • Extremely sharp horizon RB, Medved • Correct rate of Hawking radiation 1805.11667 2 ~ hbar Two parameters: T-T Hag , g s 1607.03721 1602.07706 1505.07131
New internal “ fluid modes ” of quantum BHs g 2 " " Hagedorn phase strings, “ collapsed polymer ” s v c sound • Paremetrically smaller frequencies • Parematerically longer damping times RB, Medved, Yagi 1704.05789 Intrinsic dissipation 1701.07444 Only matter that saturates KSS-like bound can support waves! 1811.12283 RB, Sherf 1902.08449
Spectrum of additional fluid modes: Frequency (without rotation) Two perspectives same estimate 1 D R R 1 1 r g S S Exterior r tt D R r | ln | S 1 R S RS Velocity = c redshift z f ~ c/ R S (-g tt ) 1/2 << c/ R S redshift ~ v/c Interior c 2 , 2 2 / " " g v s Non-Relativistic wave & frequency v/c << 1 f ~ v/R S << c/ R S RB, Medved 1902.07990 No additional relativistic 1805.11667 modes that interfere with 1709. 03566 the GR spacetime modes
The case for horizon-scale corrections : implications for Love # Sound velocities in the “ collapsed polymer ” Not a calculation yet, a reliable estimate - force per unit area 2 2 2 2 ~ / " " k v c g s D L/L – fractional deformation K I - Elastic modulus for mode of type I All dimensionful parameters included in – energy density definition of k 2 2 v sound K p I I 2 c
Can Love be measured ? LISA 1703.10612, Masseli + 5/2 5/2 w TD 2 ~ ~ GM R k k 2 2 3 r c 2 2 ~10 k LISA sensitivity 5 4 1 10 , :10 10 M M f H z 2 TD ~10 k 2 LIGO +, 3 rd generation 4 ~ 10 N cycles only sensitive to large 2 2 2 2 ~ / 1/10 k v c g values of k 2 s
RB, Sherf, Black Hole Love Story In progress RB, Medved, Ram Brustein Many papers ' 15 - Now ןב תטיסרבינוא-ןוירוג • Love # • Love # vanishes for GR BHs – BSM! • The case for horizon-scale corrections : implications for Love # • Can Love # be measured ?
Maximal entropy Causal Entropy Bound (RB+Veneziano ' 99) S(V)=S BH EV “ Maximally quantum ” S s G G
Maximal entropy Maximal positive pressure p sT p
• Introduction – Love, what is it good for ? In 1911 (some authors have 1906)[1] Augustus Edward Hough Love introduced the values h and k which characterize the overall elastic response of the Earth to the tides. For elastic Earth the Love numbers lie in the range 0.304< k 2 < 0.312
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