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Black hole “baldness” reflected in more everyday objects: physicist

Feb. 24, 2009
Courtesy Wash­ing­ton Uni­ver­s­ity in St. Lou­is
and World Science staff

New re­search from a Wash­ing­ton Uni­ver­s­ity in St. Lou­is phys­i­cist may help sci­en­tists find spin­ning black holes or­bited by smaller black holes in space.

A black hole is an ob­ject so dense that its field of grav­i­ty per­ma­nently im­pris­ons an­y­thing that come too close, even light. Or­di­nary laws of phys­ics al­so break down in its vicin­ity.

A math­e­mat­i­cal rep­re­sen­ta­tion of a small black hole or­bit­ing a larg­er one. Phys­i­cist Clif­ford Will hopes to learn more about how these or­bits play out, where the rel­a­tiv­is­t Cart­er con­stant plays a key role. (Il­lus­tra­tion by Don Davis)


Ein­stein’s gen­er­al rel­a­ti­vity the­o­ry im­plies that ro­tat­ing black holes have only two ob­serv­a­ble prop­er­ties: mass and spin. This sim­pli­city is some­times summed up by a say­ing, “black holes have no hair.”

A small ob­ject the­o­ret­ic­ally or­bit­ing a ro­tat­ing black hole is more com­plex. It traces a twist­ing ro­sette pat­tern with no dis­cern­i­ble reg­u­lar­ity, though two quan­ti­ties as­so­ci­at­ed with the satel­lite—called en­er­gy and an­gu­lar mo­men­tum—would re­main fixed over time.

In 1968, the­o­ret­ical phys­i­cist and cos­molo­g­ist Bran­don Cart­er found that such a par­t­i­cle’s gyra­t­ions al­so hold a third var­i­a­ble fixed. The mean­ing of this quanti­ty, dubbed the “Cart­er con­stant,’’ re­mains some­what mys­te­ri­ous.

Now Clif­ford M. Will at Wash­ing­ton Uni­ver­s­ity has found that even among ob­jects that fol­low laws of gra­vity, ar­range­ments can ex­ist whose gravita­t­ional field ad­mits a Cart­er-like con­stant of mo­tion. Varia­t­ions in the gravita­t­ional field shape are de­ter­mined by equa­t­ions iden­ti­cal to those for ro­tat­ing black holes, al­so called Kerr black holes.

One or­di­nary gravita­t­ional, or “New­to­ni­an,” sys­tem fea­tur­ing this prop­er­ty is sur­pris­ingly sim­ple: two equal point mass­es rest­ing a fixed dis­tance apart, Will wrote in a pa­per in the Feb. 12 is­sue of the re­search jour­nal Phys­i­cal Re­view Let­ters.

“I was com­pletely stunned when I saw that the New­ton­ian con­di­tion for a Car­ter con­stant was iden­ti­cal to the con­di­tion im­posed by the black hole no-hair theo­r­ems,” Will said. “Do I know why this hap­pens? So far, not a clue. But what I really hope is that in­sights gained about this strange con­stant in the sim­pler New­to­nian con­text will teach us some­thing about how small black holes or­bit around ro­tat­ing mas­sive black holes in gen­er­al rel­a­ti­vity, where the rel­a­tivistic Cart­er con­stant plays a key role.”

This has im­plica­t­ions for as­tron­o­my, he said, be­cause sig­nals from such events may be de­tect­a­ble via ex­ot­ic emis­sions pre­dicted by Ein­stein known as grav­i­ta­t­ional waves, rip­ples in the fab­ric of space and time. Human-built de­tec­tors such as the La­ser In­ter­fer­om­eter Gravita­t­ional Wave Ob­serv­a­to­ry (LIGO) in the Un­ited States and the pro­posed La­ser In­ter­fer­om­eter Space An­ten­na (LI­SA) may be able to pick up these fluctua­t­ions, he added.


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New research from a Washington University in St. Louis physicist may help scientists find spinning black holes orbited by smaller black holes in space. A black hole is an object so dense that its gravitatational field permanently imprisons anything that come too close, even light. Ordinary laws of physics also break down in its vicinity. Einstein’s general relativity theory implies that rotating black holes have only two observable properties: mass and spin, a simplicity sometimes summed up by the saying “black holes have no hair.” A small object theoretically orbiting a rotating black hole is more complex. It traces a twisting rosette pattern with no discernible regularity, though two quantities associated with the satellite—called energy and angular momentum—would remain fixed over time. In 1968, theoretical physicist and cosmologist Brandon Carter found that such a particle’s gyrations also hold a third variable fixed. The meaning of this quantity, dubbed the “Carter constant,’’ remains somewhat mysterious. Now Clifford M. Will at Washington University has found that even among objects that follow laws of gravity, arrangements can exist whose gravitational field admits a Carter-like constant of motion. Variations in the gravitational field shape are determined by equations identical to those for rotating black holes, also called Kerr black holes. One ordinary gravitational, or “Newtonian,” system featuring this property is surprisingly simple: two equal point masses resting a fixed distance apart, Will wrote in a paper in the Feb. 12 issue of the research journal Physical Review Letters. “I was completely stunned” by the equations’ similarity, Will said. “Do I know why this happens? So far, not a clue. But what I really hope is that insights gained about this strange constant in the simpler Newtonian context will teach us something about how small black holes orbit around rotating massive black holes in general relativity, where the relativistic Carter constant plays a key role.” This has implications for astronomy, he said, because signals from such events may be detectable via exotic emissions predicted by Einstein known as gravitional waves, ripples in the fabric of space and time. Human-built detectors such as the Laser Interferometer Gravitational Wave Observatory (LIGO) in the United States and the proposed Laser Interferometer Space Antenna (LISA) may be able to pick up these fluctuations, he added.