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Experimental tests of the no- hair theorems of black holes


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Experimental tests of the no- hair theorems of black holes

Thu, Mar 25, 2010 Nordita

M.J.Valtonen, S.Mikkola, H.Lehto, A.Gopakumar

HIP & Tuorla Observatory, U.Turku

& Tata Inst. Fund. Res., Mumbai



Isaac Newton



Albert Einstein


Proving GR correct

Proving existence of BH

No hair theorem


Testing no-hair theorem I

• Observe stars orbiting the Galactic Center

from orbits of stars (period ~ few 10 yr), BH mass ~ 3.6 10


solar mass

needed : star orbits with period 0.1 yr, measurement accuracy 10



periastron advance: M

classical spin-orbit coupling: Q GR spin-orbit coupling: S

Do such stars exist?

Can we find them?


Testing no-hair theorem II

• Millisecond pulsars

Find a pulsar in ~ 1 hour eccentric orbit around > 10 solar mass BH

Periastron advance: M and S Q difficult to measure

Needed : 10


second accuracy in pulse timing (SKA)

Do such systems exist? Can we find them?


Square Kilometer Array

Most importantly, SKA observations will finally address the fundamental question of whether GR

can describe nature in the ultra-strong field limit.

One can not only study stellar black holes but also apply the same timing techniques to pulsars

around the super-massive black hole in the Galactic Centre. This allows a direct comparison

of the properties of these objects: one can determine mass, spin and quadrupole moment of

black holes to test their description in Einstein's theory (the "no-hair"-theorem) for the first time

obviously a major achievement in the history of physics!


Testing no-hair theorem III

• Gravitational wave antenna LISA

Needed : Observe merger of two black holes

Do we ever see a merger? Do we understand

the physics?




Observing the violent mergers of massive black hole is not the only way to probe their mysteries. Black holes at the center of galaxies are surrounded by swarms of orbiting stars, caught in the gravitational

grip of the black hole. In our own Milky Way galaxy, we observed the stars close to the Sgr A* black hole for more than a decade, long enough to see the stars

trace out entire orbits.

The gravitational waves emitted during the slow inspiral encode a map of the black hole spacetime, precisely

revealing the shape and structure of the gravitational field around the black hole. This spacetime map will for the

first time allow astronomers to compare the shape,

structure and nature of true astrophysical black holes to the mathematical predictions of gravitational theory.


• .




OJ287 light variations


OJ287 light variations


Solution of the timing problem.

Level I

• Six well timed outbursts

• Iterative code

• Astrophysical effects: disk bending, delay

of radiation burst


Black hole – Accretion disk collision

• Ivanov et al. 1998


Collision 2


Collision 3





Prediction: 2nd outburst at Sept 13,



September 13 2007, unpolarized


Testing no-hair theorem IV

• Timing OJ287 outbursts Periastron precession: M

Disk impacts far from periastron: S

Disk impacts close to periastron: Q


Solution of the timing problem.

Level II


1913 outburst


1957 outburst


Outburst times normalized to 1982.964 0.0005

• 1912.98 0.02

• 1947.282 0.003

• 1957.08 0.03

• 1972.94 0.015

• 1984.13 0.005

• 1995.842 0.0015

• 2005.745 0.01

• 2007.692 0.0015


Post Newtonian terms

• .


1. order Post Newtonian term


2. Order Post Newtonian term


Radiation term


Spin – orbit term


Quadrupole term



• 39.066

• 1.83

• 1.32

• 0.33

• 55.87

• 0.6594

• 1.0

• 0.78




ergs/s corresponds to 10






Al/m-dot =14

If m-dot =0.01



Correct for H


=72, S



gives m


=1.4 10





Better value in 2015


...or in 1945


New tests of no-hair theorem

• Historical data

• Do more data exist?



• The no-hair theorem is confirmed at 30%


• Black holes are (probably) real

• General Relativity is (probably) the correct theory of gravitation

• We know more in 2019, accuracy level

down to 10% ?


Tidal outbursts




Rossi X-ray Timing Experiment:

detections by quarter year


No outburst in hard X-rays; outburst .

in soft X-rays


Radio position angle



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