Myers–Perry metric

Myers–Perry metric
Name	Myers–Perry metric
First appeared	1986
Discovered by	Myers and Perry
Dimension	higher-dimensional black holes

Myers–Perry metric is a family of exact solutions describing higher-dimensional rotating black holes discovered by Roberto Emparan and Harvey Reall? (Note: original discoverers are Robert C. Myers and M. J. Perry) in 1986. The metric generalizes the four-dimensional Kerr metric to spacetimes with more than four dimensions, providing a central role in studies of string theory, M-theory, Kaluza–Klein theory, Randall–Sundrum models, and investigations of higher-dimensional gravity by researchers at institutions such as Princeton University, California Institute of Technology, University of Cambridge, University of California, Berkeley, and Imperial College London. It underpins analyses by figures like Stephen Hawking, Roger Penrose, Gary Gibbons, Juan Maldacena, Andrew Strominger, and Edward Witten.

Introduction

The Myers–Perry family extends the rotating black hole solutions of Roy Kerr and the stationary axisymmetric solutions used by Brandon Carter and Demetrios Christodoulou to higher dimensions, capturing angular momenta along multiple orthogonal planes as studied in contexts involving Paul Dirac, Albert Einstein, Isaac Newton-inspired problems in Mathematical Institute, Oxford and applications in Los Alamos National Laboratory research programs. Influential developments relate to works by James Hartle, John Preskill, Kip Thorne, Jacob Bekenstein, Stephen Adler, and the Perimeter Institute community addressing black hole thermodynamics, entropy, and holography conjectures tied to AdS/CFT correspondence pioneers like Juan Maldacena and Edward Witten.

Metric and coordinates

The solution is typically presented in Boyer–Lindquist–type coordinates introduced by the Brans-Dicke-era literature and adapted by Myers and Perry for higher dimensions; it uses radial coordinate r, time t, and a set of azimuthal angles phi_i associated with rotations in orthogonal 2-planes, reflecting symmetry groups related to SO(n), studied by mathematicians such as Élie Cartan and Hermann Weyl. The metric components involve mass parameter mu and rotation parameters a_i analogous to the spin parameter in Kerr–Newman solutions analyzed in the Harvard-Smithsonian Center for Astrophysics tradition. Coordinate choices facilitate comparison with the Schwarzschild metric and with metrics used in analyses by Roy Kerr, Subrahmanyan Chandrasekhar, and computational work at Max Planck Institute for Gravitational Physics.

Physical properties and horizons

Event horizons occur where g^{rr}=0, with horizon structure depending on dimension D and rotation parameters a_i, connecting to concepts explored by Stephen Hawking and James Bardeen in theorems paralleling the Penrose process and Area theorem. The ergoregion, frame-dragging, and superradiant scattering mirror effects investigated by Roger Penrose, W. H. Press, Saul Teukolsky, and William Unruh; these phenomena inform stability assessments akin to studies at CERN and the European Space Agency. Thermodynamic quantities—temperature, entropy, angular velocities—are computed via techniques from Jacob Bekenstein, Stephen Hawking, and methods developed in Euclidean quantum gravity communities including Gibbons and Hawking-style path integrals.

Special cases and limits

Reducing rotation parameters yields the Schwarzschild–Tangherlini solution elaborated by F. R. Tangherlini and comparisons with the Kerr and Kerr–Newman metrics yield links to the work of John Kerr and Roy Kerr. Ultra-spinning limits studied by Emparan and Reall connect to instabilities analogous to the Gregory–Laflamme instability explored by Ruth Gregory and Raymond Laflamme, and to black objects such as black rings discovered by Roberto Emparan and H. S. Reall in collaboration with groups at Yale University and University of Cambridge. The Myers–Perry metric also relates to compactification limits in Kaluza–Klein frameworks and to near-horizon geometries considered by Guica, Hartman, and Song in Kerr/CFT-type proposals.

Geodesics and particle motion

Geodesic analysis employs integrability results reminiscent of the Carter constant found by Brandon Carter and generalizations involving Killing tensors studied by Roger Penrose and V. P. Frolov. Timelike and null geodesics, photon spheres, and innermost stable circular orbits (ISCOs) are topics pursued by researchers at MIT, Caltech, Stanford University, and University of Chicago and tie into observational predictions for gravitational waveforms in studies by LIGO Scientific Collaboration, VIRGO Collaboration, and KAGRA Collaboration. Numerical relativity groups, including teams at Cornell University and University of Illinois Urbana-Champaign, simulate particle capture and accretion flows informed by the metric.

Stability and perturbations

Linear and nonlinear stability analyses draw on techniques from Teukolsky-type formalisms and perturbation theory advanced by Regge and Wheeler, Zerilli, Kodama and Ishibashi, and others. Superradiant instabilities and quasi-normal mode spectra have been computed by researchers in projects at DAMTP, ICG Portsmouth, and Max Planck Institute, with implications for cosmic censorship conjectures associated with Penrose and global analysis by Yakov Zel'dovich-inspired studies.

Applications and extensions

Applications include modeling higher-dimensional gravitational collapse relevant to scenarios at CERN-scale collisions, brane-world phenomenology from Randall and Sundrum, and holographic duals in AdS/CFT studies by Maldacena, Gubser, Klebanov, and Witten. Extensions incorporate charge (Myers–Perry–AdS analogues), inclusion in supergravity theories explored by Strominger, Vafa, and Hull, and generalizations to nontrivial asymptotics studied by groups at Perimeter Institute and KITP. The metric informs research programs connected to observational projects like Event Horizon Telescope and theoretical frameworks at Institute for Advanced Study.

Category:Exact solutions in general relativity