TY - JOUR
T1 - Gravity from the determinant of the energy-momentum
T2 - Astrophysical implications
AU - Azri, Hemza
AU - Nasri, Salah
N1 - Publisher Copyright:
© 2022 The Author(s)
PY - 2023/1/10
Y1 - 2023/1/10
N2 - Determinants of the second rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function f(D) of the determinants of their energy-momentum, and the metric, D=|det.T|/|det.g|. We derive the gravitational field equations and examine the nonlinear terms induced by the determinant, specifically, the inverse of the energy-momentum tensor. We also show that these extensions require a nonzero stress-energy tensor for the vacuum. We propose a scale-free model, f(D)=λD1/4, and show how it induces the familiar invariant terms formed by the trace of the energy-momentum tensor by expanding the action around the stress-energy of the vacuum. We study the hydrostatic equilibrium equations for a neutron star by providing relevant values of the dimensionless constant λ. We show that the differences from the predictions of general relativity, in the mass-radius relations, which are sensitive to the equations of state, are conspicuous for λ∼−10−2. We also show that the model does not affect the predictions on the primordial nucleosynthesis when it is applied to the early radiation era. This novel and unfamiliar type of the gravity-matter coupling can lead to a rich phenomenology in gravitational physics.
AB - Determinants of the second rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function f(D) of the determinants of their energy-momentum, and the metric, D=|det.T|/|det.g|. We derive the gravitational field equations and examine the nonlinear terms induced by the determinant, specifically, the inverse of the energy-momentum tensor. We also show that these extensions require a nonzero stress-energy tensor for the vacuum. We propose a scale-free model, f(D)=λD1/4, and show how it induces the familiar invariant terms formed by the trace of the energy-momentum tensor by expanding the action around the stress-energy of the vacuum. We study the hydrostatic equilibrium equations for a neutron star by providing relevant values of the dimensionless constant λ. We show that the differences from the predictions of general relativity, in the mass-radius relations, which are sensitive to the equations of state, are conspicuous for λ∼−10−2. We also show that the model does not affect the predictions on the primordial nucleosynthesis when it is applied to the early radiation era. This novel and unfamiliar type of the gravity-matter coupling can lead to a rich phenomenology in gravitational physics.
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U2 - 10.1016/j.physletb.2022.137626
DO - 10.1016/j.physletb.2022.137626
M3 - Article
AN - SCOPUS:85144287510
SN - 0370-2693
VL - 836
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
M1 - 137626
ER -