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 -