Classical and Quantum Gravity

Classical and Quantum Gravity
Title	Classical and Quantum Gravity
Discipline	Physics
Editors	Sean Carroll, Carlo Rovelli, Abhay Ashtekar, Juan Maldacena, Roger Penrose
Publisher	Institute of Physics Publishing
First	1984
Frequency	Monthly

Classical and Quantum Gravity

Classical and Quantum Gravity surveys research on the gravitational interaction across scales from Isaac Newton and Albert Einstein to modern attempts at unifying gravity with Paul Dirac's quantum theory. The journal and field encompass topics ranging from classical solutions such as the Schwarzschild solution and Friedmann–Lemaître–Robertson–Walker metric to quantum proposals like loop quantum gravity and the AdS/CFT correspondence. Contributors include theorists associated with institutions such as Princeton University, Cambridge University, Perimeter Institute for Theoretical Physics, and Institute for Advanced Study.

Introduction

The study of gravity historically links the work of Isaac Newton, the formulation of Albert Einstein's general relativity, and experimental campaigns by teams at LIGO Scientific Collaboration, Virgo, and Event Horizon Telescope. Contemporary research sits at the intersection of classical frameworks exemplified by Karl Schwarzschild and Alexander Friedmann with quantum programs pioneered by Richard Feynman, John Wheeler, and Satyendra Nath Bose. Active communities operate in centers like CERN, Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and Kavli Institute for Theoretical Physics.

Classical Gravity: General Relativity and Alternatives

General relativity, introduced by Albert Einstein and expressed via the Einstein field equations, remains the dominant classical description of gravitation, predicting phenomena such as the perihelion precession of Mercury, gravitational lensing observed by teams at Mount Wilson Observatory, and black hole spacetimes including the Kerr metric. Analytic and numerical studies often build on work by Subrahmanyan Chandrasekhar and Roy Kerr, and numerical relativity owes much to researchers at Caltech and Cornell University who developed codes for simulating mergers detected by LIGO Scientific Collaboration. Alternatives and extensions include Brans–Dicke theory, f(R) gravity, and higher-dimensional proposals like the Kaluza–Klein theory inspired by ideas from Theodor Kaluza and Oskar Klein. Modified gravity models are tested against data from missions such as WMAP, Planck, and surveys by Sloan Digital Sky Survey teams.

Quantum Gravity Approaches

Quantum gravity approaches fragment into several research programs: canonical quantization and loop quantum gravity developed by Abhay Ashtekar and Lee Smolin; covariant path integral methods inspired by Richard Feynman and formulated in Euclidean quantum gravity by Stephen Hawking; string-theoretic frameworks including perturbative string theory and dualities exemplified by Juan Maldacena's AdS/CFT correspondence; and discrete approaches like causal dynamical triangulations by Renate Loll and J. Ambjørn. Other programs include asymptotic safety associated with Steven Weinberg, spin foam models linked to Carlo Rovelli, and noncommutative geometry approaches championed by Alain Connes. Cross-disciplinary work connects to conformal field theory studies led by groups around Alexander Polyakov and Paul Ginsparg.

Key Results and Phenomenology

Key results include the prediction and observation of gravitational waves from binary black hole and neutron star mergers by LIGO Scientific Collaboration and Virgo, the imaging of a black hole shadow by Event Horizon Telescope collaborators, and precision tests of general relativity in the solar system by teams at Jet Propulsion Laboratory and European Space Agency. Quantum-corrected phenomenology yields candidate features such as black hole entropy calculations from Stephen Hawking and Jacob Bekenstein's work, the Bekenstein–Hawking formula, and insights from string theory about microstate counting via Strominger and Vafa. Semiclassical results include Hawking radiation and the Unruh effect discussed by Paul Davies.

Experimental and Observational Tests

Experimental efforts span interferometric detectors developed at Caltech and MIT for LIGO, radio observatories coordinating through the European VLBI Network for the Event Horizon Telescope, and satellite missions like Gravity Probe B testing frame-dragging predicted by Albert Einstein. Pulsar timing arrays coordinated by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav), Parkes Pulsar Timing Array, and European Pulsar Timing Array probe nanohertz gravitational waves. Cosmological surveys by Planck and Dark Energy Survey constrain large-scale modifications, while tabletop experiments influenced by work at Stanford University seek short-range deviations from Newtonian potentials guided by theoretical proposals from Lisa Randall and Nima Arkani-Hamed.

Mathematical Methods and Formalism

Mathematical methods central to the field include differential geometry developed by Élie Cartan and Bernhard Riemann, global analysis influenced by Bernard Schutz and Robert Geroch, and functional integral techniques formalized by Richard Feynman. Hamiltonian and constraint analysis owes foundations to Paul Dirac and Bryce DeWitt, and index theorems from Atiyah–Singer appear in anomaly computations associated with Edward Witten. Topological and categorical tools appear in work by Michael Atiyah and Graeme Segal, while numerical methods derive from programs by Miguel Alcubierre and Frans Pretorius.

Open Problems and Future Directions

Open problems include the information paradox debated by Stephen Hawking, Samir Mathur, and Juan Maldacena; the microphysical origin of black hole entropy explored by Andrew Strominger; finding phenomenological signatures of loop quantum gravity and string theory in cosmology by groups at Perimeter Institute for Theoretical Physics and Institute for Advanced Study; and establishing experimentally accessible predictions from asymptotic safety advocates like Martin Reuter. Future directions emphasize multi-messenger campaigns coordinated by LIGO Scientific Collaboration and IceCube Neutrino Observatory, theoretical synthesis across programs championed at Kavli Institute for Theoretical Physics, and mathematical rigor advanced via collaborations involving Institute of Mathematics and its Applications.

Category:Gravity