A proposal for the gravitational energy–momentum tensor, known in the

literature as the square root of Bel–Robinson tensor (SQBR), is analyzed

in detail. Being constructed exclusively from the Weyl part of the Riemann

tensor, such tensor encapsulates the geometric properties of free gravitational

felds in terms of optical scalars of null congruences: making use of the

general decomposition of any energy–momentum tensor, we explore the

thermodynamic interpretation of such geometric quantities. While the matter

energy–momentum is identically conserved due to Einstein’s feld equations,

the SQBR is not necessarily conserved and dissipative terms could arise in its

vacuum continuity equation. We discuss the possible physical interpretations

of such mathematical properties.

literature as the square root of Bel–Robinson tensor (SQBR), is analyzed

in detail. Being constructed exclusively from the Weyl part of the Riemann

tensor, such tensor encapsulates the geometric properties of free gravitational

felds in terms of optical scalars of null congruences: making use of the

general decomposition of any energy–momentum tensor, we explore the

thermodynamic interpretation of such geometric quantities. While the matter

energy–momentum is identically conserved due to Einstein’s feld equations,

the SQBR is not necessarily conserved and dissipative terms could arise in its

vacuum continuity equation. We discuss the possible physical interpretations

of such mathematical properties.

typ: | article |
---|---|

journal: | Class. Quantum Grav. |

volume: | 35 |

pages: | 095001 |

year: | 2018 |

pacs: | https://doi.org/10.1088/1361-6382/aab1c7 |