### Abstract

Torsion gravity is a natural extension to Einstein gravity in the presence of fermion matter sources. In this paper we adopt Wald's covariant method of calculating the Noether charge to construct the quasilocal energy of the Einstein-Cartan-fermion system, and find that its explicit expression is formally independent of the coupling constant between the torsion and axial current. This seemingly topological nature is unexpected and is reminiscent of the quantum Hall effect and topological insulators. However, a coupling dependence does arise when evaluating it on shell, and thus the situation is pseudotopological. Based on the expression for the quasilocal energy, we evaluate it for a particular solution on the entanglement wedge and find agreement with the holographic relative entropy obtained before. This shows the equivalence of these two quantities in the Einstein-Cartan-fermion system. Moreover, the quasilocal energy in this case is not always positive definite, and thus it provides an example of a swampland in torsion gravity. Based on the covariant Noether charge, we also derive the nonzero fermion effect on the Komar angular momentum. The implications of our results for future tests of torsion gravity in gravitational-wave astronomy are also discussed.

Original language | English |
---|---|

Article number | 049905 |

Journal | Physical Review D |

Volume | 96 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2017 Aug 15 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*96*(4), [049905]. https://doi.org/10.1103/PhysRevD.96.044044

**Pseudotopological quasilocal energy of torsion gravity.** / Ko, Sheng Lan; Lin, Feng Li; Ning, Bo.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 96, no. 4, 049905. https://doi.org/10.1103/PhysRevD.96.044044

}

TY - JOUR

T1 - Pseudotopological quasilocal energy of torsion gravity

AU - Ko, Sheng Lan

AU - Lin, Feng Li

AU - Ning, Bo

PY - 2017/8/15

Y1 - 2017/8/15

N2 - Torsion gravity is a natural extension to Einstein gravity in the presence of fermion matter sources. In this paper we adopt Wald's covariant method of calculating the Noether charge to construct the quasilocal energy of the Einstein-Cartan-fermion system, and find that its explicit expression is formally independent of the coupling constant between the torsion and axial current. This seemingly topological nature is unexpected and is reminiscent of the quantum Hall effect and topological insulators. However, a coupling dependence does arise when evaluating it on shell, and thus the situation is pseudotopological. Based on the expression for the quasilocal energy, we evaluate it for a particular solution on the entanglement wedge and find agreement with the holographic relative entropy obtained before. This shows the equivalence of these two quantities in the Einstein-Cartan-fermion system. Moreover, the quasilocal energy in this case is not always positive definite, and thus it provides an example of a swampland in torsion gravity. Based on the covariant Noether charge, we also derive the nonzero fermion effect on the Komar angular momentum. The implications of our results for future tests of torsion gravity in gravitational-wave astronomy are also discussed.

AB - Torsion gravity is a natural extension to Einstein gravity in the presence of fermion matter sources. In this paper we adopt Wald's covariant method of calculating the Noether charge to construct the quasilocal energy of the Einstein-Cartan-fermion system, and find that its explicit expression is formally independent of the coupling constant between the torsion and axial current. This seemingly topological nature is unexpected and is reminiscent of the quantum Hall effect and topological insulators. However, a coupling dependence does arise when evaluating it on shell, and thus the situation is pseudotopological. Based on the expression for the quasilocal energy, we evaluate it for a particular solution on the entanglement wedge and find agreement with the holographic relative entropy obtained before. This shows the equivalence of these two quantities in the Einstein-Cartan-fermion system. Moreover, the quasilocal energy in this case is not always positive definite, and thus it provides an example of a swampland in torsion gravity. Based on the covariant Noether charge, we also derive the nonzero fermion effect on the Komar angular momentum. The implications of our results for future tests of torsion gravity in gravitational-wave astronomy are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=85029048293&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029048293&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.96.044044

DO - 10.1103/PhysRevD.96.044044

M3 - Article

AN - SCOPUS:85029048293

VL - 96

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 4

M1 - 049905

ER -