# Nico Yunes, Astrophysical Observational Signatures for Dynamical Chern-Simons Gravity :::{.remark} Question: what observable signatures are produced by gravitational waves, black holes, neutron stars? Why are there more baryons than anti-baryons in the universe? General relativity predicts singularities -- problematic due to infinities. Unclear if Chern-Simons a. Has nothing to do with these phenomena, or b. Explains them entirely. ::: :::{.remark} New data: gravitational wages at LIGO in 2015, wavelike perturbations of the metric tensor that decay like $1/r$. After traveling $\sim 10^3$ megaparsecs, yields a very weak observable. Around 50 similar events in the years after, high level of confidence in measurements ($>5\sigma$). Signatures help us figure out what to sift for in experimental data. ::: :::{.remark} Pontryagin invariant: $R^*R$? Lagrangian density: perturbed Einstein equations for GR where tensor and scalar field are coupled? Recovers classical GR in a limit: \[ L\sim R - {1\over 2} (\nabla_a \nu) (\nabla^a \nu) + \alpha_{\mathrm{dCS}} \nu R^*R ,\] for $R$ the Ricci tensor. Now vary with respect to degrees of freedom. Currents: something whose divergence is the original thing? Third derivatives: not good in physics, causes ghosts, unbounded Hamiltonians. Metric is GR metric plus order $\alpha^2$ terms. Need to reduce order to get rid of third derivatives, unphysical unstable modes, due to insistence on treating this as an exact theory. ::: :::{.remark} Chern-Simons form here: \[ \Tr(dA \wedge A + c A\wedge A \wedge A), && c=2/3 .\] ::: :::{.remark} Spherically symmetric black holes: assuming static and vacuum, the unique solution is the Schwarzschild metric. See box operator, d'Alembertian? \[ \Box \proportional \dd{^2}{t^2} - \Laplacian &= \diag(1,-1,-1,-1) \nabla^2(t,x,y,z) \\ &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} \Laplacian(t,x,y,z) \\ &= \dd{^2}{t^2} -\dd{^2}{x^2} -\dd{^2}{y^2} -\dd{^2}{z^2} .\] Effective field theory treatment for axially symmetric black holes, yields 2nd order PDE, no exact solution. Can take first order solution, not bad to do by hand. Second and fifth order, much more complicated but easily handled by a computer, no clear obstructions to higher order expansions. Yields "hairy" black hole solutions: a $1/r^2$ scalar field, a perturbed horizon and ergosphere, no naked singularities, polar "caps": regions where geodesics need not focus. No killing tensor, so no 4th constant of motion. Are there observational signatures for the caps? Could there be chaos in geodesic motion for test particles in orbit around dynamical Chern-Simons black holes? Chaos in this dynamical system, say around supermassive black holes, should imprint on gravitational waves. Recent results: quasinormal modes carry such a dynamical signature. ::: :::{.remark} Summary: - Spinning black holes are not Kerr, bc they excite a scalar field - Binary black hole space time has two scalar fields anchored with each black hole. - Dynamical CS induces a $2PN$ correction to the orbital evolution. $\mathrm{dCS}$ is a $v/4$ correction to GR. Plot frequencies of orbit, play as sound -- collision causes a chirp as amplitude and frequency spike, correction causes a different chirp. Now add the sinusoids to obtain beats/nodes in the waves, LIGO looks for these! ![](figures/2021-11-18_09-56-35.png) ::: :::{.remark} Problem with wave detection on Earth: seismic noise, creates a frequency wall. Future projects: labs in space in 2035-2045! Things that haven't been worked out in dCS yet: - AdS black holes? - Exact rotating solutions - Gravitational collapse - Singularity theorems - Area theorems :::