[Paper Review] Higgs Mechanism and the Structure of the Energy-Momentum Tensor in Einstein Gravity and Conformal Gravity

Philip D. Mannheim, Demosthenes Kazanas|ArXiv.org|Sep 23, 1994

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates how the Higgs mechanism affects the energy-momentum tensor in both Einstein and conformal gravity, showing that despite the Higgs mechanism altering the mass structure of fundamental particles, the standard geodesic motion and Euler hydrodynamics remain valid in the one-particle sector. The key result is that the energy-momentum tensor differs significantly from the conventional perfect fluid form, even though dynamics remain unchanged under the standard prescription.

ABSTRACT

In the standard treatment of the Einstein gravitational theory the energy-momentum tensor has always been taken to be composed of perfect fluid aggregates of kinematic Newtonian point test particles with fundamental mechanical masses. Moreover, this standard prescription was not revised after the discovery of the mass-generating Higgs mechanism which is known to be present in the elementary particle physics of these self-same sources and which is also required in the conformal invariant gravitational alternative being considered by Mannheim and Kazanas. In this short contribution we show that despite the presence of the Higgs mechanism, the standard geodesic motion and Euler hydrodynamics still obtain in the one-particle sector of the theory even while the overall energy-momentum tensor differs substantially from the conventional kinematic one.

Motivation & Objective

• To examine the implications of the Higgs mechanism on the energy-momentum tensor in gravitational theories.
• To address the inconsistency in standard general relativity where the Higgs mechanism—known to generate mass in elementary particles—was not incorporated into the energy-momentum tensor formulation.
• To investigate whether the standard geodesic and hydrodynamic equations remain valid in the presence of Higgs-generated masses.
• To compare the structure of the energy-momentum tensor in Einstein gravity versus conformal gravity under the influence of the Higgs mechanism.
• To reconcile the Higgs mechanism with gravitational dynamics in both standard and conformal invariant formulations of gravity.

Proposed method

• Formal analysis of the energy-momentum tensor in the context of Einstein gravity and conformal gravity.
• Incorporation of the Higgs mechanism into the mass generation of fundamental particles within the gravitational framework.
• Use of the standard one-particle sector to analyze geodesic motion and hydrodynamic equations.
• Comparison of the resulting energy-momentum tensor with the conventional perfect fluid form.
• Application of conformal invariance principles to assess consistency in the alternative gravitational model.
• Derivation of the modified energy-momentum tensor structure while preserving standard equations of motion.

Experimental results

Research questions

• RQ1 How does the Higgs mechanism alter the structure of the energy-momentum tensor in Einstein gravity?
• RQ2 Does the inclusion of Higgs-generated masses affect the validity of geodesic motion and Euler hydrodynamics in the one-particle sector?
• RQ3 What is the difference between the standard perfect fluid energy-momentum tensor and the Higgs-modified version in both Einstein and conformal gravity?
• RQ4 Can conformal invariance be preserved in the presence of Higgs-generated masses in the energy-momentum tensor?
• RQ5 Why was the Higgs mechanism not previously incorporated into the standard formulation of the energy-momentum tensor in general relativity?

Key findings

• The energy-momentum tensor in the presence of the Higgs mechanism differs substantially from the conventional perfect fluid form.
• Despite the modified tensor structure, the standard geodesic equation and Euler hydrodynamics remain valid in the one-particle sector.
• The Higgs mechanism does not alter the dynamical equations of motion for single particles in the theory.
• The modified energy-momentum tensor arises from Higgs-generated masses rather than kinematic masses, indicating a fundamental change in tensor composition.
• The results are consistent in both Einstein gravity and the conformal gravity framework proposed by Mannheim and Kazanas.
• The paper resolves a long-standing inconsistency by showing that the Higgs mechanism can be incorporated without disrupting standard gravitational dynamics.