universal spacetime in nLab

Contents

Contents

Idea

Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the metric. Consequently, metrics of universal spacetimes solve vacuum equations of motion of all gravitational theories, i.e. extremize the Einstein-Hilbert action with given cosmological constant and arbitrary higher curvature correction. In the literature, universal metrics are also discussed as metrics with vanishing quantum corrections and as classical solutions to string theory. Widely known examples of universal metrics are certain Ricci flat pp-wave spacetimes.

References

The first examples are due to

• Daniele Amati, Ctirad Klimčík, Nonperturbative computation of the Weyl anomaly for a class of nontrivial backgrounds, Phys. Lett. B, 219:443–447, 1989 (spire:269390, 10.1016/0370-2693(89)91092-7)

• Gary Horowitz, Alan R. Steif, Spacetime singularities in string theory, Phys. Rev. Lett. 64, 260 1990 (doi:10.1103/PhysRevLett.64.260)

The terminology was introduced in

• A. A. Coley, Gary Gibbons, S. Hervik, Christopher Pope, Metrics with vanishing quantum corrections, Class. Quantum Grav., 25:145017, 2008 (arXiv:0803.2438)

Classification results are discussed in

• Sigbjørn Hervik, Vojtěch Pravda, Alena Pravdová, Type III and N universal spacetimes, Class. Quantum Grav. 31: 215005, 2014 (arXiv:1311.0234)

• Sigbjørn Hervik, Tomáš Málek, Vojtěch Pravda, Alena Pravdová, Type II universal spacetimes, Class. Quantum Grav. 32: 245012, 2015 (arXiv:1503.08448)

• Sigbjørn Hervik, Vojtěch Pravda, Alena Pravdová, Universal spacetimes in four dimensions, JHEP 1710 (2017): 28 (arXiv:1707.00264)

• Martin Kuchynka, Tomáš Málek, Vojtěch Pravda, Alena Pravdová, Almost universal spacetimes in higher-order gravity theories (arXiv:1810.02178)

Discussion for black hole spacetimes:

• Sigbjørn Hervik, Marcello Ortaggio, Universal Black Holes, J. High Energ. Phys. 2020, 47 (2020) (arXiv:1907.08788)

Discussion for Einstein-Yang-Mills theory:

• Martin Kuchynka, Einstein-Yang-Mills fields immune to quantum corrections (arXiv:2001.03768)

See also:

• Metin Gurses, Yaghoub Heydarzade, Cetin Senturk, Kerr-Schild-Kundt Metrics in Generic Gravity Theories with Modified Horndeski Couplings (arXiv:2109.01244)