Gregory–Laflamme instability

The Gregory–Laflamme instability (after Ruth Gregory and Raymond Laflamme) is a result in theoretical physics which states that certain black strings and branes are unstable in dimensions higher than four.^[1]

In their seminal papers in 1993 and 1994, Gregory and Laflamme showed that certain branes and black string solutions in theories of gravity in higher dimensions ${\displaystyle D\geq 5}$ are found to exhibit an instability to small perturbations.^[2][3][4]

It is very interesting to know the end point of this instability, particularly whether it leads to a phase transition forming a black hole. This has been studied to higher dimensions and a critical dimension has been found to exist below which the end state of instability is a black hole phase, i.e., for ${\displaystyle 5\leq D\leq 13}$. Above the critical dimension the instability drives to a non-uniform black ring phase.^[5][6]

References

1. Ruth Gregory (2011). "The Gregory-Laflamme instability". arXiv:1107.5821 [gr-qc].
2. Ruth Gregory; Raymond Laflamme (1993). "Black Strings and p-Branes are Unstable". arXiv:hep-th/9301052 [hep-th].
3. Ruth Gregory; Raymond Laflamme (1994). "The Instability of Charged Black Strings and p-Branes". arXiv:hep-th/9404071 [hep-th].
4. Troels Harmark; Vasilis Niarchos; Niels A. Obers (2007). "Instabilities of Black Strings and Branes". arXiv:hep-th/0701022 [hep-th].
5. Barak Kol (2004). "The Phase Transition between Caged Black Holes and Black Strings - A Review". arXiv:hep-th/0411240 [hep-th].
6. Luis Lehner; Frans Pretorius (2011). "Final State of Gregory-Laflamme Instability". arXiv:1106.5184 [gr-qc].