Black hole thermodynamics and spacetime symmetry breaking David - PowerPoint PPT Presentation

Black hole thermodynamics and spacetime symmetry breaking David Mattingly University of New Hampshire Experimental Search for Quantum Gravity, SISSA, September 2014

What do we search for? What does the experimental quantum gravity community look for? Non-locality Extra QG induced dimensions decoherence Dimensional B-mode reduction polarization Symmetry Extra violation dimensions

What do we search for? What does the experimental quantum gravity community look for? Non-locality Extra QG induced dimensions decoherence Dimensional B-mode reduction polarization Symmetry Extra violation dimensions

Locality An easy multiple choice question is should be Fundamentally, a local quantum field theory. may be quantum gravity should not be is not

Many approaches give up quantum gravity as local QFT Why is this a popular choice? In many ways it’s the most radical! should be Fundamentally, a local quantum field theory. may be quantum gravity should not be is not

Why are we so comfortable with giving up local QFT? 𝑇 ∼ 1 2 ∫ 𝑒 4 𝑦[ 𝜖ℎ 2 + 𝜆 𝜖ℎ 2 ℎ] GR is perturbatively non- renormalizable Divergent Finite IR irrelevant operators in operators far UV Formation of black holes/unitarity issues with ultrahigh energy scattering 𝑆 ≈ 𝑀 𝑄𝑚𝑏𝑜𝑑𝑙 (c.f. Giddings et. al. 1005.5408) Others – c.f. Oriti 1302.2849

Why are we so comfortable with giving up local QFT? Black hole thermodynamics itself Finiteness of entropy Density of states from UV scale Firewalls invariance • As horizon microstates • Unitarity 𝐹 3 implies discreteness? Sorkin, • Equivalence principle • 𝑇 𝑅𝐺𝑈 ∝ hep-th/0504037 3+𝑨 • Local QFT near horizon • 𝑇 𝐶𝐼 ∝ 𝐹 2 • As entanglement entropy Please needs cutoff pick c.f. Solodukhin 1104.3712 your favorite two 𝛾 functions AMPS, 1207.3123 vanish in UV Giddings, 1211.7070 c.f. Shomer, 0709.3555

So what if gravity IS a local QFT? What happens in putative quantum gravity theories where gravity remains a local, renormalizable QFT? Can black hole physics inform how we think about those theories as well?

So what if gravity IS a local QFT? N=8 General black hole thermodynamics in N=8 SUGRA only recently computed (Chow, Compere 1404.2602) Supergravity Approaches to Asymptotic Work still needs to be done in understanding black hole renormalizable QG solutions in ASG. c.f. Koch, Saueressig, 1401.4452 Safety Horava- Black hole solutions understood in some cases. Lifshitz Thermodynamics yields interesting interplay with how to implement H-L theory in matter sector. gravity

So what if gravity IS a local QFT? N=8 General black hole thermodynamics in N=8 SUGRA only recently computed (Chow, Compere 1404.2602) Supergravity Approaches to Asymptotic Work still needs to be done in understanding black hole renormalizable QG solutions in ASG. c.f. Koch, Saueressig, 1401.4452 Safety Horava- Black hole solutions understood in some cases. Lifshitz Thermodynamics yields interesting interplay with how to implement H-L theory in matter sector. gravity

The fundamental questions Can there even be black hole thermodynamics? Does requiring black hole thermodynamics lead to interesting restrictions on parameter space of Horava-Lifshitz gravity? I’m not asking or worrying about experimental limits on Horava-Lifshitz gravity

Horava-Lifshitz theory Horava-Lifshitz theory timelike infinity Horava: 0901.3775 There exists a time function U spacelike infinity generating a preferred foliation in spacetime.

Horava-Lifshitz theory timelike infinity Horava-Lifshitz theory There exists a time function U generating a preferred foliation spacelike infinity in spacetime. UV theory has Lifshitz symmetry 𝑢 → 𝑐 𝑨 𝑢, 𝑦 → 𝑐𝑦

Horava-Lifshitz theory Dynamical Horava-Lifshitz theory Blas, Pujolas,Sibiryakov 0909.3525 𝐸𝑧𝑜𝑏𝑛𝑗𝑑𝑏𝑚 foliation given by time function U. 𝛼 𝑏 𝑉 𝑣 𝑏 : = −𝛼 𝑐 𝑉𝛼 𝑐 𝑉 3+1 split, due to reduced symmetry more terms in gravitational action...

Horava-Lifshitz theory Dynamical Horava-Lifshitz theory – gravitational piece 𝑂 = 𝑚𝑏𝑞𝑡𝑓 𝑕 𝑏𝑐 = 𝑡𝑞𝑏𝑢𝑗𝑏𝑚 𝑛𝑓𝑢𝑠𝑗𝑑 𝐿 𝑗𝑘 = 𝑓𝑦𝑢𝑠𝑗𝑜𝑡𝑗𝑑 𝑑𝑣𝑠𝑤𝑏𝑢𝑣𝑠𝑓 𝑝𝑔 𝑉 ℎ𝑧𝑞𝑓𝑠𝑡𝑣𝑠𝑔𝑏𝑑𝑓 𝑆 = 3𝑒 𝑆𝑗𝑑𝑑𝑗 𝑡𝑑𝑏𝑚𝑏𝑠 𝑏 𝑗 = 𝑏𝑑𝑑𝑓𝑚𝑓𝑠𝑏𝑢𝑗𝑝𝑜 𝑝𝑔 𝑣 𝑏 Changes UV divergence structure without introducing ghosts by permitting higher spatial derivatives in propagators without higher time derivatives.

Horava-Lifshitz and Einstein-Aether Einstein aether theory: Jacobson, DM gr-qc/0007031 Assume aether is hypersurface orthogonal. 𝛼 𝑏 𝑉 𝑣 𝑏 : = −𝛼 𝑐 𝑉𝛼 𝑐 𝑉 Dynamical, non-projectable HL theory in IR: 𝑑 13 = 𝑑 1 + 𝑑 3 …

Simplest regular massive vacuum solutions What is H- L “Schwarzschild” black hole? Schwarzschild aether/Killing Four Infrared solution Vacuum vectors aligned dimensional at infinity spherically asymptotically Trivial 𝑁 → 0 Static symmetric flat limit Note: Other solutions (rotating, dS/AdS asymptotics, 2+1) exist

Simplest regular massive vacuum solutions AS AN EXAMPLE we’ll use the analytic solutions that exist when 𝑑 14 = 0 or 𝑑 123 = 0 . 𝑑 123 = 0 One parameter family of solutions, controlled by 𝑠 0 𝑒𝑡 2 = −𝑓 𝑠 𝑒𝑤 2 + 2 𝑔 𝑠 𝑒𝑤𝑒𝑠 + 𝑠 2 𝑒Ω 2 𝑣 ⋅ 𝜓 = −1 + 𝑠 𝑉𝐼 𝑠 2 2 − 𝑑 14 𝑠 𝑉𝐼 𝑡 ⋅ 𝜓 = 𝑣 𝑏 𝑡 𝑏 2 1 − 𝑑 13 𝑠 2 𝑔 𝑠 = 1 2 𝑓 𝑠 = 1 − 𝑠 0 𝑠 + 𝑑 14 − 2𝑑 13 𝑠 𝑉𝐼 𝑠 2 2 1 − 𝑑 13 𝑠 𝑉𝐼 = 𝑠 0 2 Killing horizon 𝜓 2 = 0 Universal horizon 𝑣 ⋅ 𝜓 = 0

Is there a black hole? Is there any surface of constant r that acts as a trapped surface for propagating excitations above the vacuum, matter or otherwise? Need to specify a matter Lagrangian e.g. 2 2 𝛼 𝑐 𝜚 ± (𝛼 2 ) 𝑜 𝜚 𝑡 𝜚 𝑏𝑐 𝛼 𝑀 𝜚 = − 2 𝑕 𝜚 𝑏 𝜚 4𝑜−2 2𝑙 0 Flat space dispersion relation: 𝑏𝑐 = 𝑕 𝑏𝑐 − 𝑡 𝜚 −2 − 1 𝑣 𝑏 𝑣 𝑐 𝑕 𝜚 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 ± 4𝑜−2 𝑙 0 𝑡 𝜚 is speed of low energy mode, n is an integer, related to UV Lifshitz scaling

Is there a black hole? Flat space dispersion relation: 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 ± 4𝑜−2 𝑙 0 We phenomenologically test such modified dispersion with +, - sign. Is there a difference between these two cases from the perspective of BH thermo?

Is there a black hole? Natural to start with a minus sign as then all propagating modes have a finite speed, the naïve guess as to what you need for a horizon. Flat space dispersion relation: 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 − 4𝑜−2 𝑙 0 t x

Is there a black hole? 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 − 4𝑜−2 𝑙 0 A rainbow causal horizon

Deviations from thermal spectrum 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 − 4𝑜−2 𝑙 0 Calculate spectrum via mode conversion Corley/Jacobson hep-th/9601073 Thermal spectrum only reproduced to a high degree for very low frequency with respect to 𝑙 0 outgoing radiation. Different fields with different 𝑡 𝜚 have different T More importantly…

First law 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 − 4𝑜−2 𝑙 0 There are first law problems! Via Noether at infinity and Killing horizon (Foster, gr-qc/0509121) 𝜀𝑁 Standard TdS form Non-standard contribution proportional to c’s Generically, Noether approach on fixed r hypersurfaces does not yield a thermodynamics where 𝑇 ∝ 𝐵

First law Demanding a first law that has 𝑇 ∝ 𝐵 kills the rainbow horizon situation and hence 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 − 4𝑜−2 𝑙 0 does not yield full black hole thermodynamics

First law again However, first law on the universal horizon is a “standard” first law (Bhattacharyya, DM 1408.6479, 1202.4497) 𝑑 123 = 0: 𝜀𝑁 = 1 − 𝑑 13 𝜆 𝑉𝐼 𝜀𝐵 8𝜌𝐻 − 1 𝑏 𝜓 𝑐 𝛼 𝑏 𝜓 𝑐 𝜆 𝑉𝐼 = 2 𝛼 If you want a standard/holographic first law for black hole thermodynamics, you have to use the universal horizon!

Is there a black hole part deux? Universal horizon IS also the causal horizon for 𝑙 4𝑜 𝜕 2 = 𝑡 𝜚 2 𝑙 2 + 4𝑜−2 𝑙 0

Is there a black hole part deux? Wang et. al. 1408.5976

Radiation from universal horizon Tunneling approach Requirements Vacuum: assume the infalling vacuum No matter/aether Cerenkov radiation so 𝑑 123 = 0 𝑝𝑠 𝑑 14 = 0 Lifshitz coefficient yields chemical (Technically convenient but likely not necessary) potential – preserves thermality − 𝜕−𝜈 2 𝑙 0 𝜈 = − 𝑑 𝑏𝑓 2𝑂 , 𝑈 𝑉𝐼 = 𝜆 𝑉𝐼 I ∝ 𝑓 𝑈𝑉𝐼 4𝜌𝑑 𝑏𝑓 𝑇 = 1 − 𝑑 13 𝑑 𝑏𝑓 𝐵 𝑉𝐼 Berglund, Bhattacharyya, DM:1210.4940 2𝐻 𝑏𝑓