Pressure acts as a source for the gravitational field in general relativity
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Reference and physics sources report that within general relativity, pressure serves as a source for the gravitational field alongside mass-energy density through the stress-energy tensor.
to curve. General relativity predicts that pressure acts as a gravitational source with exactly the same strength as mass–energy density. The inclusion
In physics, curved spacetime is the mathematical model in which, with Einstein's theory of general relativity, gravity naturally arises, as opposed to being described as a fundamental force in Newton's static Euclidean reference frame. Objects move along geodesics—curved paths determined by the local geometry of spacetime—rather than being influenced directly by distant bodies. This framework led
In Newton's theory of gravitation, the only source of gravitational force is mass.
In contrast, general relativity identifies several sources of spacetime curvature in addition to mass. In the Einstein field equations,
the sources of gravity are presented on the right-hand side in
T
μ
ν
,
{\displaystyle T_{\mu \nu },}
the stress–energy tensor.
Fig. 6 classifies the various sources of gravity in the stress–energy tensor:
T
i
j
{\displaystyle T^{ij}}
are the rates of flow of the i-component of momentum per unit area in the j-direction. Even if there is no bulk motion, random thermal motions of the particles will give rise to momentum flow, so the i = j terms (green) represent isotropic pressure, and the i ≠ j terms (blue) represent shear stresses.
One important conclusion to be derived from the equations is that, colloquially speaking, gravity itself creates gravity. Energy has mass. Even in Newtonian gravity, the gravitational field is associated with an energy,
E
=
m
g
h
,
{\displaystyle E=mgh,}
called the gravitational potential energy. In general relativity, the energy of the gravitational field feeds back into creation of the gravitational field. This makes the equations nonlinear and hard to solve…
Pawan Upadhyay's Pressure–Curvature Law of Gravity (PPC Law of Gravity) and Gravitational Pressure Waves Author and Researcher: Pawan Upadhyay https://orcid.org/0009-0007-9077-5924 My Research Resume: https://archive.org/details/my-research-resume Email: pawanupadhyay28@hotmail.com Date: 6 November 2025 Status: ✅ Verified on GitHub Repository: PPC Law of Gravity Discoveries by Pawan Upadhyay Official research page: 🔗 https://sites.google.com/view/discoveriesbypawanupadhyay/research-projects Full Meaning of “PPC Law of Gravity” PPC Law of Gravity stands for: P — Pawan Upadhyay P — Pressure C — Curvature So, the full form is: Pawan Upadhyay’s Pressure–Curvature Law of Gravity Mass and Energy are not separate. Main Points of PPC law :- 1. Mass Creates Pressure. 2. Pressure is the cause of Curvature Shape of Space Time 3. Mass applies Pressure. 4. Pressure of Mass bends Spacetime. 5. Force of that Pressure creates the shape of Curvature. 6. Curvature governs motion. 7. Spacetime Curvature + Dynamical Motion create the Pressure waves Mass-Energy density ➡️ Pressure ➡️ Force of Pressure ➡️ Curvature via Stress Energy Tensor ➡️ Spacetime Curvature ➡️ Motion ➡️ Pressure Waves P_g= ωE_d=ω . ρc^2, if omega=1,then P_g = ρc^2. ρ is mass density. ρ = m/V where m is mass and V is volume. E_d=E/V where E_d is Energy density. P_g is Gravitational Pressure. Mass density is mass per volume. Heavy mass bodies generate higher gravitational pressure on the spacetime fabric, while medium and small
The gravitational energy-momentum tensor and the gravitational pressure
In the framework of the teleparallel equivalent of general relativity it is possible to establish the energy-momentum tensor of the gravitational field. This tensor has the following essential features: (1) it is identified directly in Einstein's field equations; (2) it is conserved and traceless; (3) it yields expressions for the energy and momentum of the gravitational field; (4)it is free of second (and highest) derivatives of the field variables; (5) the gravitational and matter energy-momentum tensors take place in the field equations on the same footing; (6) it is unique. However, it is not symmetric. We show that the spatial components of this tensor yield a consistent definition of the gravitational pressure.
Published as: AnnalenPhys.14:723-732,2005
DOI: 10.1002/andp.200510161
arXiv categories: gr-qc
In UD theory, dark matter is the field $U_d$, the $D$ attribute in space. We derive the self-consistent density profile of $U_d$ in galactic halos from the UD field equations, and obtain its energy-momentum tensor, which contains pressure and anisotropic stress. The anisotropic stress, $\Sigma_{ij} = \partial_i U_d \partial_j U_d$, contributes to the gravitational wave source term alongside the density quadrupole, yielding a modified quadrupole formula. We estimate the stochastic gravitational wave background from dark matter halo mergers, with a peak amplitude $\Omega_{\mathrm{GW}} \sim 10^{-12}$ at LISA frequencies, subject to an uncertainty of one to three orders of magnitude. The dual role of $U_d$ in gravitational wave physics is clarified: it acts as a source through its energy-momentum tensor, while its perturbation enters the metric only at second order, leaving standard linear wave propagation unaffected. Thus, $U_d$ serves both as a source and as a nonlinear constituent of the propagation medium.
In UD theory, dark matter is the field UD, the D attribute in space. We derive the linearized Einstein equation from the UD action and show that the source term is the total energy-momentum tensor of all D attributes: Tµν = T(DD)µν + T(UD)µν. The UD field possesses pressure and anisotropic stress originating from its kinetic and potential terms. The anisotropic stress is quantified by the field gradients ∂iUD∂jUD, whose magnitude in a typical galactic halo is estimated from the selfconsistent UD density profile derived in this paper. The resulting quadrupole formula contains an additional contribution from UD. A stochastic gravitational wave background from dark matter dynamics is a necessary consequence of the theory, with an estimated peak amplitude ΩGW ∼ 10−12 at LISA frequencies, subject to an uncertainty of one to three orders of magnitude. The role of UD in gravitational wave physics is clarified: it acts as a source through its energy-momentum tensor, while its fluctuation enters the metric perturbation only at second order, ensuring that standard linear gravitational wave propagation remains unchanged in the far-field limit.
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