Conservation Of Energy-momentum Tensor Research Articles

First principles determination of bubble wall velocity

The terminal wall velocity of a first-order phase transition bubble can be calculated from a set of fluid equations describing the scalar fields and the plasma's state. We rederive these equations from the energy-momentum tensor conservation and the Boltzmann equation, without linearizing in the background temperature and fluid velocity. The resulting equations have a finite solution for any wall velocity. We propose a spectral method to integrate the Boltzmann equation, which is simple, efficient and accurate. As an example, we apply this new methodology to the singlet scalar extension of the standard model. We find that all solutions are naturally categorized as deflagrations ($v_w\sim c_s$) or ultrarelativistic detonations ($\gamma_w\gtrsim10$). Furthermore, the contributions from out-of-equilibrium effects are, most of the time, subdominant. Finally, we use these results to propose several approximation schemes with increasing levels of complexity and accuracy. They can be used to considerably simplify the methodology while correctly describing the qualitative behavior of the bubble wall.

Topological hydrodynamic modes and holography

We study topological modes in relativistic hydrodynamics by weakly breaking the conservation of energy momentum tensor. Several systems have been found to have topologically nontrivial crossing nodes in the spectrum of hydrodynamic modes and some of them are only topologically nontrivial with the protection of reflection symmetries in two directions. The nontrivial topology for all these systems is further confirmed from a calculation of the topological invariant. Associated transport properties and second order effects have also been studied for these systems. The nonconservation terms of the energy momentum tensor could come from an external effective symmetric tensor matter field or a gravitational field which could be generated by a specific noninertial reference frame transformation from the original inertial reference frame. Finally we introduce a possible holographic realization of one of these systems. We propose a new method to calculate the holographic Ward identities for the energy momentum tensor without calculating out all components of the Green functions and match the Ward identities of both sides.

Correspondence between energy conservation and energy-momentum tensor conservation in cosmology

The correspondence between the thermodynamic energy equation satisfied by a closed co-moving volume and the conservation equation satisfied by the energy-momentum tensor of the matter inside the co-moving volume is extended to a more general system with an arbitrary cosmological horizon and a heat source. The energy of the system consisting of a cosmological horizon and its internal matter could be conserved by defining a surface energy on the horizons. Therefore, energy conservation and energy-momentum tensor conservation can always be consistent for such a system. On the other hand, from the perspective of classical thermodynamics, one can define an effective pressure at the cosmological horizon to guarantee that the thermodynamic energy equation inside the horizon is consistent with the energy-momentum tensor conservation equation of the matter inside the horizon. These systems can satisfy the generalized second law of thermodynamics under appropriate conditions. The definitions of the surface energy and the effective pressure are extended to the gravity theory with non-minimal coupling between geometry and matter, in which geometry could be regarded as a heat source.

Dispersion relations in nonlinear electrodynamics and the kinematics of the Compton effect in a magnetic background

Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear Lagrangian built up in terms of the most general Lorentz- and gauge-invariant combinations of the electric and magnetic fields. The extended Maxwell-like equations and the energy-momentum tensor conservation are presented and discussed in their generality. We next expand the fields around a uniform and time-independent electric and magnetic backgrounds up to second order in the propagating wave, and compute dispersion relations which account for the effect of the external fields. We obtain thereby the refraction index and the group velocity for the propagating radiation in different situations. In particular, we focus on the kinematics of the Compton effect in presence of external magnetic fields. This yields constraints that relate the derivatives of the general Lagrangian with respect to the field invariants and the magnetic background under consideration. We carry out our inspection by focusing on some specific non-linear electrodynamic effective models: Hoffmann-Infeld, Euler-Heisenberg, generalized Born-Infeld and Logarithmic.

Topological modes in relativistic hydrodynamics

We show that gapless modes in relativistic hydrodynamics could become topologically nontrivial by weakly breaking the conservation of energy momentum tensor in a specific way. This system has topological semimetal-like crossing nodes in the spectrum of hydrodynamic modes that require the protection of a special combination of translational and boost symmetries in two spatial directions. We confirm the nontrivial topology from the existence of an undetermined Berry phase. These energy momentum non-conservation terms could naturally be produced by an external gravitational field that comes from a reference frame change from the original inertial frame, i.e. by fictitious forces in a non-inertial reference frame. This non-inertial frame is the rest frame of an accelerating observer moving along a trajectory of a helix. This suggests that topologically trivial modes could become nontrivial by being observed in a special non-inertial reference frame, and this fact could be verified in laboratories, in principle. Finally, we propose a holographic realization of this system.

Energy momentum tensor and the D term in the bag model

The energy-momentum tensor (EMT) form factors pave new ways for exploring hadron structure. Especially the D-term related to the EMT form factor D(t) has received a lot of attention due to its attractive physical interpretation in terms of mechanical properties. We study the nucleon EMT form factors and the associated densities in the bag model which we formulate for an arbitrary number of colors Nc and show that the EMT form factors are consistently described in this model in the large-Nc limit. The simplicity of the model allows us to test in a lucid way many theoretical concepts related to EMT form factors and densities including recently introduced concepts like normal and tangential forces, or monopole and quadrupole contributions to the angular momentum distribution. We also study the D-terms of rho-meson, Roper resonance, other N* states and Delta-resonances. Among the most interesting outcomes is the lucid demonstration of the deeper connection of EMT conservation, stability, the virial theorem and the negative sign of the D-term.

Consequences of energy conservation violation: late time solutions of Lambda (mathsf{T}) mathsf{CDM} subclass of f(mathsf{R},mathsf{T}) gravity using dynamical system approach

Very recently, Josset and Perez (Phys. Rev. Lett. 118:021102, 2017) have shown that a violation of the energy-momentum tensor (EMT) could result in an accelerated expansion state via the appearance of an effective cosmological constant, in the context of unimodular gravity. Inspired by this outcome, in this paper we investigate cosmological consequences of a violation of the EMT conservation in a particular class of f(mathsf{R},mathsf{T}) gravity when only the pressure-less fluid is present. In this respect, we focus on the late time solutions of models of the type f(mathsf{R},mathsf{T})=mathsf{R}+beta Lambda (-mathsf{T}). As the first task, we study the solutions when the conservation of EMT is respected, and then we proceed with those in which violation occurs. We have found, provided that the EMT conservation is violated, that there generally exist two accelerated expansion solutions of which the stability properties depend on the underlying model. More exactly, we obtain a dark energy solution for which the effective equation of state depends on the model parameters and a de Sitter solution. We present a method to parametrize the Lambda (-mathsf{T}) function, which is useful in a dynamical system approach and has been employed in the model. Also, we discuss the cosmological solutions for models with Lambda (-mathsf{T})=8pi G(-mathsf{T})^{alpha } in the presence of ultra-relativistic matter.

Hamiltonian formulation of mimetic gravity

The Hamiltonian formulation of Mimetic Gravity is formulated. Although there are two more equations than those of general relativity, these are proved to be the constraint equation and the conservation of energy-momentum tensor. The Poisson brackets are then computed and closure is proved. At the end, Wheeler-DeWitt equation was solved for a homogeneous and isotropic universe. This was done first for a vanishing potential where agreement with the dust case was shown, and then for a constant potential.

Bianchi -V Space -Time with Anisotropic Dark Energy in General Relativity

In a spatially homogeneous and anisotropic Bianchi type-V space-time the consequences of the presence of dynamically anisotropic dark energy and perfect fluid with heat-conduction are studied. We assume that dark energy is minimally interacting with matter and has an equation of state which is modified in a consistent way with the conservation of energy momentum tensor. Exact solutions of Einstein field equations are obtained by taking constant value of deceleration parameter. We find that this assumption is reasonable for the observation of the present day universe. The physical and geometrical properties of the models, the behavior of the anisotropy of dark energy and the thermodynamical relations that govern such solutions are discussed in detail.

Hydrodynamics with conserved current from the gravity dual

We determine the structure of the hydrodynamics with conserved current, using the gauge/gravity duality of charged black-hole background. It turns out that even in the presence of the external electromagnetic field at the boundary, bulk Einstein equation is equivalent to the boundary conservation of energy momentum tensor and that of current. As a consequence, the thermal conductivity and electric conductivity are calculated in terms of the parameters of the fundamental theory. We find that Wiedemann-Franz law hold with Lorentz number 1/e2.

New QCD sum rule for the structure functions of a photon target

Basing on gauge invariance, renormalizability, asymptotic freedom and conservation of energy-momentum tensor in QCD we deduce QCD sum rule for the leading twist parton structure functions of a real and virtual photon target which accounts for any order QCD radiative corrections.