Pretorius

Black Hole Collisions: 

Black Hole Collisions Frans Pretorius Princeton University Inaugural Conference of the Institute for Gravitation and the Cosmos August 9, 2007

Outline: 

Outline Motivation: why explore black hole collisions? Anatomy of a merger overview of the stages of a merger : “Newtonian”, inspiral, plunge/merger, ringdown Recent results numerical solution of the field equations look at a couple of highlights remarkable simplicity of the waveform, in particular briefness (non-existence?) of a “plunge” large kick velocities Beyond astrophysical binaries zoom-whirl like behavior at an “immediate threshold” of merger speculations about ultrarelativistic collisions, and possible applications in high energy particle experiments

Motivation: why explore black hole collisions?: 

Motivation: why explore black hole collisions? gravitational wave astronomy almost overwhelming evidence that black holes exist in our universe, and when they merge we expect them to be strong sources of gravitational waves understanding the nature of the waves emitted in the process is important for detecting such events, and moreover will be crucial in deciphering the signals extracting the parameters of the binary obtain clues about the environment of the binary how accurately does Einstein’s theory describe the event? a black hole is not “merely” a strong gravitational field, but a region in which spacetime itself is undergoing gravitational collapse, a truly remarkable concept wholly outside the realm of any present tests of general relativity understanding general relativity if general relativity is the correct theory of “gravity”, we certainly want to fully understand one of the most fundamental interactions in nature … the two body problem black hole collisions, in particular in the ultrarelativistic regime, offer an intuitive route to explore the highly dynamical, non-linear regime of the theory

Anatomy of a Merger: 

Anatomy of a Merger In the conventional scenario of a black hole merger in the universe, one can break down the evolution into 4 stages: Newtonian, inspiral, plunge/merger and ringdown Newtonian in isolation, radiation reaction will cause two black holes of mass M in a circular orbit with initial separation R to merge within a time tm relative to the Hubble time tH label the phase of the orbit Newtonian when the separation is such that the binary will take longer than the age of the universe to merge, for then to be of relevance to gravitational wave detection, other “Newtonian” processes need to operate, e.g. dynamical friction, n-body encounters, gas-drag, etc. For e.g., two solar mass black holes need to be within 1 million Schwarzschild radii ~ 3 million km two 109 solar mass black holes need to be within 6 thousand Schwarzschild radii ~ 1 parsec

Anatomy of a Merger: 

Anatomy of a Merger inspiral In the inspiral phase, energy loss through gravitational wave emission is the dominate mechanism forcing the black holes closer together to get an idea for the inspiral time scale, for equal mass, circular binaries the Keplarian orbital frequency offers a good approximation until very close to merger Post-Newtonian techniques provide an accurate description of the process until remarkably close to merger though being an expansion in v/c, that near merger the black hole velocities “only” reach v~0.3c, and that the state-of-the-art has certain aspects of the dynamics computed to (v/c)7, it is perhaps not that surprising in hind-sight

Anatomy of a Merger: 

Anatomy of a Merger plunge/merger this is the time in the merger when the two event horizons coalesce into one (viewed as an evolution with respect to some well-behaved time slice) we know the two black holes must merge into one if cosmic censorship holds (and no indications of a failure yet in any merger simulations) full numerical solution of the field equations are required to solve for the geometry of spacetime in this stage in all cases studied to date, this stage is exceedingly short, leaving its imprint in on the order of 1-2 gravitational wave cycles at roughly twice the final orbital frequency

Anatomy of a Merger: 

Anatomy of a Merger ringdown in the final phase of the merger, the remnant black hole “looses all its hair”, settling down to a Kerr black hole one possible definition for when plunge/merger ends and ringdown begins, is when the spacetime can adequately be described as a Kerr black hole perturbed by a set of quasi-normal modes (QNM) the ringdown portion of the waveform will be dominated by the fundamental harmonic of the quadrupole QNM, with characteristic frequency and decay time [Echeverria, PRD 34, 384 (1986)]: j=a/Mf , the Kerr spin parameter of the black hole

Sample evolution --- Cook-Pfeiffer Quasi-circular Initial data: 

Sample evolution --- Cook-Pfeiffer Quasi-circular Initial data This animation shows the lapse function in the orbital plane. The lapse function represents the relative time dilation between a hypothetical observer at the given location on the grid, and an observer situated very far from the system --- the redder the color, the slower local clocks are running relative to clocks at infinity If this were in “real-time” it would correspond to the merger of two ~5000 solar mass black holes Initial black holes are close to non-spinning Schwarzschild black holes; final black hole is a Kerr a black hole with spin parameter ~0.7, and ~4% of the total initial rest-mass of the system is emitted in gravitational waves A. Buonanno, G.B. Cook and F.P.; Phys.Rev.D75:124018,2007

Slide9: 

Gravitational waves from the simulation A depiction of the gravitational waves emitted in the orbital plane of the binary. Shown is the real component of the Newman Penrose scalar y4, which in the wave zone is proportional to the second time derivative of the usual plus-polarization The plus-component of the wave from the same simulation, measured on the axis normal to the orbital plane

What does the merger wave represent? : 

What does the merger wave represent? Scale the system to two 10 solar mass (~ 2x1031 kg) BHs radius of each black hole in the binary is ~ 30km radius of final black hole is ~ 60km distance from the final black hole where the wave was measured ~ 1500km frequency of the wave ~ 200Hz (early inspiral) - 800Hz (ring-down) fractional oscillatory “distortion” in space induced by the wave transverse to the direction of propagation has a maximum amplitude DL/L ~ 3x10-3 a 2m tall person will get stretched/squeezed by ~ 6 mm as the wave passes LIGO’s arm length would change by ~ 12m. Wave amplitude decays like 1/distance from source; e.g. at 10Mpc the change in arms ~ 5x10-17m (1/20 the radius of a proton, which is well within the ballpark of what LIGO is trying to measure!!) despite the seemingly small amplitude for the wave, the energy it carries is enormous — around 1030 kg c2 ~ 1047 J ~ 1054 ergs peak luminosity is about 1/100th the Planck luminosity of 1059ergs/s !! luminosity of the sun ~ 1033ergs/s, a bright supernova or milky-way type galaxy ~ 1042 ergs/s if all the energy reaching LIGO from the 10Mpc event could directly be converted to sound waves, it would have an intensity level of ~ 80dB

Numerical Relativity: 

Numerical Relativity Numerical relativity is concerned with solving the field equations of general relativity using computers. When written in terms of the spacetime metric, defined by the usual line element the field equations form a system of 10 coupled, non-linear, second order partial differential equations, each depending on the 4 spacetime coordinates it is this system of equations that we need to solve for the 10 metric elements (plus whatever matter we want to couple to gravity) for many problems this has turned out to be quite an undertaking, due in part to the mathematical complexity of the equations, and also the heavy computational resources required to solve them The field equations may be complicated, but they are the equations that we believe govern the structure of space and time (barring quantum effects and ignoring matter). That they can, in principle, be solved in many “real-universe” scenarios is a remarkable and unique situation in physics.

Minimal requirements for a formulation of the field equations that might form the basis of a successful numerical integration scheme: 

Minimal requirements for a formulation of the field equations that might form the basis of a successful numerical integration scheme Choose coordinates/system-of-variables that fix the character of the equations three common choices free evolution — system of hyperbolic equations constrained evolution — system of hyperbolic and elliptic equations characteristic or null evolution — integration along the lightcones of the spacetime For free evolution, need a system of equations that is well behaved off the ”constraint manifold” analytically, if satisfied at the initial time the constraint equations of GR will be satisfied for all time numerically the constraints can only be satisfied to within the truncation error of the numerical scheme, hence we do not want a formulation that is “unstable” when the evolution proceeds slightly off the constraint manifold Need well behaved coordinates (or gauges) that do not develop pathologies when the spacetime is evolved typically need dynamical coordinate conditions that can adapt to unfolding features of the spacetime Boundary conditions also historically a source of headaches naive BC’s don’t preserve the constraint nor are representative of the physics fancy BC’s can preserve the constraints, but again miss the physics solution … compactify to infinity Geometric singularities in black hole spacetimes need to be dealt with: excision/punctures

Computational issues in numerical solution of the field equations: 

Computational issues in numerical solution of the field equations Each equation contains tens to hundreds of individual terms, requiring on the order of several thousand floating point operations per grid point with any evolution scheme. Problems of interest often have several orders of magnitude of relevant physical length scales that need to be well resolved. In an equal mass binary black hole merger for example: radius of each black hole R~2M orbital radius ~ 20M (which is also the dominant wavelength of radiation emitted) outer boundary ~ 200M, as the waves must be measured in the weak-field regime to coincide with what detectors will see Can solve these problems with a combination of hardware technology — supercomputers — and software algorithms, in particular adaptive mesh refinement (AMR) vast majority of numerical relativity codes today use finite difference techniques (predominantly 2nd to 6th order), notable exception is the Caltech/Cornell pseudo-spectral code How to deal with the true geometric singularities that exist inside all black holes? excision, punctures

Brief (and incomplete) history of the binary black hole problem in numerical relativity: 

Brief (and incomplete) history of the binary black hole problem in numerical relativity Hahn and Lindquist, Ann. Phys. 19, 304 (1964) First simulation of “wormhole” initial data L. Smarr, PhD Thesis (1977) : First head-on collision simulation P. Anninos, D. Hobill, E.Seidel, L. Smarr, W. Suen PRL 71, 2851 (1993) : Improved simulation of head-on collision B. Bruegmann Int. J. Mod. Phys. D8, 85 (1999) : First grazing collision of two black holes mid 90’s-early 2000: Binary Black Hole Grand Challenge Alliance Cornell,PSU,Syracuse,UT Austin,U Pitt, UIUC,UNC, Wash. U, NWU … head-on collisions, grazing collisions, cauchy-characteristic matching, singularity excision B. Bruegmann, W. Tichy, N. Jansen PRL 92, 211101 (2004) : First full orbit of a quasi-circular binary FP, PRL 95, 121101 (2005) : First “complete” simulation of a non head-on merger event: orbit, coalescence, ringdown and gravitational wave extraction M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower PRL 96, 111101, (2006); J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter PRL 96, 111102, (2006) … several other groups have now repeated these results: PSU, Jena, AEI, LSU, Caltech/Cornell note that to go from “a to b” here has required a tremendous amount of research in understanding the mathematical structure of the field equations, stable discretization schemes, dealing with geometric singularities inside black holes, computational algorithms, initial data, extracting useful physical information from simulations, etc.

Current state of the field : 

Current state of the field Two quite different, stable methods of integrating the Einstein field equations for this problem generalized harmonic coordinates with constraint damping, F.Pretorius, PRL 95, 121101 (2005) Caltech/Cornell, L. Lindblom et al., Class.Quant.Grav. 23 (2006) S447-S462 PITT/AEI/LSU, B. Szilagyi et al., gr-qc/0612150 BSSN with “moving punctures”, M. Campanelli, C. O. Lousto, P. Marronetti, Y. Zlochower PRL 96, 111101, (2006); J. G. Baker, J. Centrella, D. Choi, M. Koppitz, J. van Meter PRL 96, 111102, (2006) Pennstate, F. Herrmann et al., gr-gc/0601026 Jena/FAU, J. A. Gonzalez et al., gr-gc/06010154 LSU/AEI/UNAM, J. Thornburg et al., gr-gc/0701038 U.Tokyo/UWM, M. Shibata et al, astro-ph/0611522 U. Sperhake, gr-qc/0606079

Slide16: 

Many studies to date suggest the structure of the waveform is remarkably “simple” most detailed examination of waveforms from non-spinning initial conditions, though qualitatively results seem to hold for more generic cases “quadrupole” physics seems to dominates GW emission; I.e. no strong signs of non-linear mode-coupling, intricacies in the inspiral portion of the wave structure come from orbital evolution merger/plunge phase short; in fact difficult to even identify a distinctive plunge Simplicity of the merger waveform Most useful consequence of the simple waveform structure is that it seems like it will be possible to construct fully analytical perturbative models of the waveforms, with numerical simulations supplying key matching parameters Best example to date is from A. Buonanno, Y.Pan, J. G. Baker, J. Centrella, B. J. Kelly, S.T. McWilliams and J. R. van Meter, arXiv:0706.3732 (figure to right showns 4:1 mass ratio example) effective-one-body (EOB) PN inspiral connected to the 3 dominant QNMs, at peak of resummed EOB frequency added “pseudo” 4PN term to EOB model, with coefficient determined by a best-fit match to a set of numerical results used simulation results for final spin and black hole mass to fix the QNM frequencies and decay constants

Results: Large recoil velocities in binary mergers: 

Results: Large recoil velocities in binary mergers much excitement about the large kick velocities of upwards of 4000km/s seen in simulations [F. Herrmann et al., gr-qc/0701143; M. Koppitz et al., gr-qc/0701163; M. Campanelli et al. gr-qc/0701164 & gr-qc/0702133, J.A. Gonzalez et al, arXiv:gr-qc/0702052, W. Tichy and P. Marronetti, arXiv:gr-qc/0703075v1] initial concern that this is an apparent contradiction with the observation that supermassive black holes are observed in the centers of most galaxies together with the standard hierarchical structure formation scenario, however uniform sampling over spin vector orientations and mass ratios for two a=.9 black holes with m1/m2 between 1 and 10 suggested only around 2% of parameter space has kicks larger than 1000km/s, and 10% larger than 500km/s [J. Schnittman & A. Buonanno, astro-ph/0702641] astrophysical population is most likely highly non-uniform, e.g. torques from accreting gas in supermassive merger scenarios tend to align the spin and orbital angular momenta, which will result in more modest kick velocities <~200km/s [T.Bogdanovic et al, astro-ph/0703054] a couple of studies so far looking at 1) growth of supermassive black holes from intermediate mass seeds [M.Micic, T. Abel and S. Sigurdsson, astro-ph/0512123] and 2) following the growth of black holes through a simplified merger tree model [J. Schnittman, arXiv:0706.1548] found that the presence of supermassive black holes in most galactic centers is rather robust even if large kick velocities are assumed recent in-depth explanations of this [B. Bruegmann et al., arXiv:0707.0135v1, J. Schnittman et al., arXiv:0707.0301v1]

Large recoil velocities in binary mergers: 

Large recoil velocities in binary mergers scenario giving rise to very large kick velocities is, at a first glance, quite bizarre: equal masses with equal but opposite spin vectors in the orbital plane kick direction is normal to the orbital plane, but magnitude depends sinusoidally on the initial phase is linearly dependent on the magnitude of the spin still “small” from a dimensional analysis point of view, but enormous in an astrophysical setting

Frame dragging induced kicks: 

Frame dragging induced kicks Can intuitively understand this phenomena as a frame dragging effect think of BH 1 (2) moving in the background space time of BH 2 (1) relative to BH 1 (2)’s spin vector, BH 2 (1) has zero orbital angular momentum … such a “particle” in a BH background is dragged by the rotation of the BH with a velocity v ~ 2 m a sin(q) / r2

Frame dragging induced kicks: 

Frame dragging induced kicks The result of this in the equal mass problem with the particular configuration for maximum kicks is that the entire orbital plane will oscillate sinusoidally in the direction normal to the orbital plane with the orbital frequency, and maximum velocity of 2 m a / r2 The binary is emitting gravitational radiation, with the largest flux normal to the orbital plane … the frame dragging induced oscillations will cause a periodic doppler shift of the radiation along the axis, alternating between red and blue shift in one direction with the opposite in the other Averaged over an orbit, and without inspiral, the net momentum radiated is zero. However, the merger event stops this process, and depending on where it’s stopped there will be linear momentum radiated normal to the orbital plane … to conserve momentum the final black hole is given a kick in the opposite direction

Frame dragging induced kicks: 

Frame dragging induced kicks To estimate the maximum kick: assume radiation stops once the black hole separation is within r~2M (M=2m) energy of a gravitational wave ~ frequency-squared … doppler shift by maximum frame dragging velocity at r let the net energy radiated over the last ½ orbit be eM, then: vrecoil ~ e(a/m)/2 with typical e ~ 1-2%, get vrecoil ~ (a/m) 1500-3000 km/s

Frame-dragging induced kicks: 

Frame-dragging induced kicks this seems to be consistent with what’s happening in simulations however, none of this is gauge invariant, so take this in the same spirit as the order-of-magnitude calculation equal mass merger, “scattering” initial conditions with impact parameter ~14m, initial velocities ~0.12 in +- y direction, initial spins a/m=0.5 anti-aligned in +- x direction

The threshold of immediate merger: 

The threshold of immediate merger Consider the black hole scattering problem in general two, distinct end-states possible one black hole, after a collision two isolated black holes, after a deflection because there are two distinct end-states, there must be some kind of threshold behavior approaching a critical impact parameter b* b m1,v1 m2,v2

The threshold of immediate merger: 

The threshold of immediate merger The following illustrates what could happen as one tunes to threshold, assuming smooth dependence of the trajectories as a function of b non-spinning case (so we have evolution in a plane) only showing one of the BH trajectories for clarity solid blue (black) – merger (escape) dashed blue (black) – merger (escape) for values of b closer to threshold

The immediate threshold in the geodesic limit for equatorial orbits : 

The immediate threshold in the geodesic limit for equatorial orbits work with D. Khurana, gr-qc/0702084 Here, regardless of the initial conditions (as long as we have an interpolating family), near threshold the geodesic enters a phase where it orbits arbitrarily close to one of the unstable circular geodesics of the spacetime about a Schwarzschild BH circular orbits become unstable in the range r=1.5Rs (the “light ring”) to r=3Rs (the ISCO - innermost stable circular orbit) the number of orbits spent in the near-circular configuration scales as where g = w/2pl, with w the orbital frequency and l the Lyapunov exponent of the unstable orbit un-bound orbit example bound orbit example; the threshold solution is a homoclinic orbit

The threshold of immediate merger for equal mass black holes: 

The threshold of immediate merger for equal mass black holes work with D. Khurana, gr-qc/0702084 In the equal mass problem the immediate threshold also exists, and remarkable exhibits quantitatively similar properties to the geodesic case the primary difference is that in the circular phase the binary is emitting copious amounts of gravitational radiation (on the order of 1-1.5% per orbit) that the system is losing energy implies that the process cannot continue for ever, and will (probably) stop after all the excess kinetic energy of the orbit has been radiated away, which in the high-speed limit can be an arbitrary large fraction of the net energy of the spacetime two cases tuned close to threshold (only 1 BH trajectory shown) dominant component of emitted gravitational waves

Animations …: 

Animations … Lapse function a, orbital plane Real component of the Newman-Penrose scalar Y4( times rM), orbital plane

How quantitatively similar is the geodeosic and equal mass behavior? : 

How quantitatively similar is the geodeosic and equal mass behavior? In the equal mass case there is no sensible notion of an unstable circular orbit, though we can still probe this regime by setting up a similar scattering experiment and seeing whether the relationship between the impact parameter and number of whirl-orbits hold Indeed it does, and the scaling exponent is even close to an “analogous” geodesic problem, considering a geodesic corotating about a black hole with spin equal to the final spin of the merged object in the equal mass case (~0.7) Equal mass merger approach to immediate threshold Scaling exponents for Kerr equatorial geodesics (thin dashed black lines from analytic perturbative calculation, colored lines from numerical integration of geodiscs; red ellipse is single “dot” from the equal mass case)

How far can this go in the non-linear case?: 

How far can this go in the non-linear case? System is losing energy, and quite rapidly, so there must be a limit to the number of orbits we can get Hawking’s area theorem: assume cosmic censorship and “reasonable” forms of matter, then net area of all black holes in the universe can not decrease with time the area of a single, isolated black hole is: initially, we have two non-rotating (J=0) black holes, each with mass M/2: maximum energy that can be extracted from the system is if the final black hole is also non-rotating: in otherwords, the maximum energy that can be lost is a factor 1-1/√2 ~ 29% If the trend in the simulations continues, and the final J~0.7M2, we still get close to 24% energy that could be radiated the simulations show around 1-1.5% energy is lost per whirl, so we may get close to 15-30 orbits at the threshold of this fine-tuning process!

Can we go even further?: 

Can we go even further? What about the black hole scattering problem? give the black holes sizeable boosts, such that the net energy of the system is dominated by the kinetic energy of the black holes set up initial conditions to have a one-parameter family of solutions that smoothly interpolate between coalescence and scatter “natural” choice is the impact parameter it is plausible that at threshold, all of the kinetic energy is converted to gravitational radiation this can be an arbitrarily large fraction of the total energy of the system (scale the rest mass to zero as the boost goes to 1) In the infinite g limit, taken so that the energy remains finite, each initial “black hole” is described by the Aichelburg-Sexl solution, which does not contain an event horizon. Thus, in this case the threshold of immediate merger will also correspond to the threshold of black hole formation If Choptuik’s hypothesis of universality at threshold holds, the threshold ultrarelativistic black hole collision solution will (for a time) be given by the Abrahams & Evans Brill wave critical collapse spacetime

An application to the LHC?: 

An application to the LHC? The Large Hadron Collider (LHC) is a particle accelerator currently under construction near Lake Geneva, Switzerland it will be able to collide beams of protons with center of mass energies up to 14 TeV In recent years the idea of large extra dimensions have become popular [N. Arkani-Hamed , S. Dimopoulos & G.R. Dvali, Phys.Lett.B429:263-272; L. Randall & R. Sundrum [Phys.Rev.Lett.83:3370-3373] we (ordinary particles) live on a 4-dimensional brane of a higher dimensional spacetime “large” extra dimensions are sub-mm in size, but large compared to the 4D Planck length of 10-33 cm gravity propagates in all dimensions The 4D Planck Energy, where we expect quantum gravity effects to become important, is 1019 GeV; however the presence of extra dimensions can change the “true” Planck energy A Planck scale in the TeV range is preferred as this solves the hierarchy problem current experiments rule out Planck energies <~ 1TeV Collisions of particles with super-Planck energies in these scenarios would cause black holes to be produced at the LHC! can “detect” black holes via Hawking radiation or missing energy

The parton scattering problem : 

The parton scattering problem Consider the high speed collision of two partons with impact parameter b if the energy is beyond the Planck regime, to a good approximation this may look like a black hole collision for sufficiently high velocities charge and spin of the parton will be irrelevant (though both will probably be important at LHC energies) if similar scaling behavior is seen as with geodesics and full simulations of the equal mass/low velocity regime in general, can use the geodesic analogue to obtain an approximate idea of the cross section and energy loss to radiation vs. impact parameter … Ingredients: map geodesic motion on a Kerr back ground with (M,a) to the scattering problem with total initial energy E=M and angular momentum a of the black hole that’s formed near threshold find g and b* using geodesic motion assume a constant fraction e of the remaining energy of the system is radiated per orbit near threshold (estimate using quadrupole formula) Integrate near-threshold scaling relation to find E(b) with the above parameters and the following “boundary” conditions: E(0), E(b*) and E(infinity) E(b*) must be ~ 1 in kinetic energy dominated regime E(infinity)=0 E(0) … need some other input, either perturbative calculations, or full numerical simulations.

The parton scattering problem : 

The parton scattering problem What value of the Kerr spin parameter to use? in the ultra-relativistic limit the geodesic asymptotes to the light-ring at threshold it also seems “natural” that in this limit the final spin of the black hole at threshold is a=1. This is consistent with simple estimates of energy/angular momentum radiated quadrupole physics gives the following for the relative rates at which energy vs. angular momentum is radiated in a circular orbit with orbital frequency w: for the scattering problem with the same impact parameter as a threshold geodesic on an extremal Kerr background, the initial J/E2=1. The Boyer-Lindquist value of Ew is ½ for a geodesic on the light ring of an extremal Kerr BH, in that regime d(J/ E2)=0 But now we have a bit of a dilemma, as the extremal Kerr background has no unstable circular geodesics, and hence g tends to infinity in this limit will use a close to but not exactly 1 to find out what E(b) might look like

Sample energy radiated vs. impact parameter curves (normalized) : 

Sample energy radiated vs. impact parameter curves (normalized) An estimate of E(0) from Cardoso et al., Class.Quant.Grav. 22 (2005) L61-R84 Cross section for black hole formation (b<~1) would thus be 2pE2 In higher dimensions for equatorial geodesics of Myers-Perry black holes g becomes quite small regardless of the spin (C. Merrick) probably related to the fact that there are no stable circular geodesics for d>4 implies E(b) is well approximated by the function, modulo the “spike” at b=b* dE/dn ~ p/40 in this limit, so expect all the energy to be radiated away in around a dozen orbits.

Conclusions: 

Conclusions the next few of decades are going to be a very exciting time for gravitational physics numerical simulations are finally allowing us to fully reveal the fascinating landscape of binary coalescence within Einstein’s theory of general relativity gravitational wave detectors should allow us to see the universe in gravitational radiation for the first time if extra dimensions exists, the next generation of high energy particle experiments might discover them black holes could therefore revolutionize our understanding of the universe from the smallest to largest scales!

Conclusions: 

Conclusions Why are the results in the “full, non-linear” regime so simple? they’re not really … what the results are saying is that all the mathematical machinery developed over the years to study aspects of the two body problem has, despite not having full solutions, uncovered much of the interesting phenomonology: rich orbital motion (perihelion precession and zoom-whirl orbits, unstable orbits, chaotic orbits, spin-spin and spin-obit precession, …) the “instability” of a binary to gravitational wave emission the end-state of the two body problem is a perturbed Kerr black hole, quickly ringing down to the Kerr solution any surprises yet to come? probably not it in generic scenarios place to look would be in extreme settings : a 1, g though if the last two years of results are any indication, the interesting gems will be contained in the work of Penrose, D’eath, Szekeres, … from the 60’s and 70’s!