Total Energy-momentum Tensor Research Articles

Assessing the dark degeneracy through gas mass fraction data

It is well-known that Einstein’s equations constrain only the total energy–momentum tensor of the cosmic substratum, without specifying the characteristics of its individual constituents. Consequently, cosmological models featuring distinct decompositions within the dark sector, while sharing identical values for the sum of dark components’ energy–momentum tensor, remain indistinguishable when assessed through observables based on distance measurements. Notably, it has been already demonstrated that cosmological models with dynamical descriptions of dark energy, characterized by a time-dependent equation of state (EoS), can always be mapped into a model featuring a decaying vacuum (w=−1) coupled with dark matter. We explore the possibility of breaking this degeneracy by using measurements of the gas mass fraction observed in massive and relaxed galaxy clusters. This data is particularly interesting for this purpose because it isolates the matter contribution, possibly allowing the degeneracy breaking. We study the particular case of the wCDM model with its interactive counterpart. We compare the results obtained from both descriptions with a non-parametric analysis obtained through Gaussian Process. Even though the degeneracy may be broken from the theoretical point of view, we find that current gas mass fraction data seems to be insufficient for a final conclusion about which approach is favored, even when combined with SNIa, BAO and CMB.

On the Wave-Particle Duality of the Photons and the Matter-Photon Particle Mixture Model

Relativistic quantum mechanics and many experimental results and observations show that electron-positron annihilation can produce photons; photon-matter and photon-photon interaction can also create electrons and positrons. The photons have no rest mass, e.g. relative to Lab frame, and always travel at the speed of light in the vacuum. In this paper, a rotational moving electric dipole model with negative and positive charges was proposed for photons. In a vacuum, the electric dipoles are moving in a twisted helical motion around their propagation axis (their center of mass). Photon particles are traveling at the speed of light along the propagation axis. This pair of negative and positive charged particles exerts both electrostatic and magnetic force on each other. Both forces are attractive and act as a centripetal force to keep the electric dipole in a continuous helical motion around the axis of rotation. With this model, the wave-particle duality of photons can be described simultaneously. The space is filled by matter (having rest mass relative to Lab frame) and photons (without rest mass); it is a multicomponent mixture fluid. In "vacuum", though there is no rest matter particle, but there are still photon gas particles, the total energy-momentum tensor should include rest matter particles and photon gas particles.

Super-horizon resonant magnetogenesis during inflation

We propose a novel mechanism for significantly enhancing the amplitude of primordial electromagnetic fields during inflation. Similar to existing proposals, our idea is based on parametric resonance effects due to conformal-symmetry-breaking coupling of a gauge field and the inflaton. Our proposed scenario, however, significantly differs from previously studied models and avoids their shortcomings. We, particularly, construct a viable system where the gauge field is exponentially amplified on super-horizon scales, therefore evading the no-go theorem formulated on the basis of widely encountered drastic backreaction of the magnetic field energy on the inflationary background. We argue that in order for the resonant scenario to work with a bounded and positive-definite coupling function, a mass term for the gauge sector is required. We compute the spectrum of the produced magnetic fields and demonstrate the compatibility with current observational constraints. We demonstrate that while the magnetic fields do not noticeably backreact on the inflationary background, the nonzero mass term can contribute significantly to the total energy-momentum tensor. We point out the parameter space where the latter issue is absent.

Conformally Schwarzschild cosmological black holes

We thoroughly investigate conformally Schwarzschild spacetimes in different coordinate systems to seek for physically reasonable models of a cosmological black hole. We assume that a conformal factor depends only on the time coordinate and that the spacetime is asymptotically flat Friedmann–Lemaître–Robertson–Walker Universe filled by a perfect fluid obeying a linear equation state p = wρ with w > −1/3. In this class of spacetimes, the McClure–Dyer spacetime, constructed in terms of the isotropic coordinates, and the Thakurta spacetime, constructed in terms of the standard Schwarzschild coordinates, are identical and do not describe a cosmological black hole. In contrast, the Sultana–Dyer and Culetu classes of spacetimes, constructed in terms of the Kerr–Schild and Painlevé–Gullstrand coordinates, respectively, describe a cosmological black hole. In the Sultana–Dyer case, the corresponding matter field in general relativity can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous null fluid, which is valid everywhere in the spacetime unlike Sultana and Dyer’s interpretation. In the Culetu case, the matter field can be interpreted as a combination of a homogeneous perfect fluid and an inhomogeneous anisotropic fluid. However, in both cases, the total energy–momentum tensor violates all the standard energy conditions at a finite value of the radial coordinate in late times. As a consequence, the Sultana–Dyer and Culetu black holes for −1/3 < w ⩽ 1 cannot describe the evolution of a primordial black hole after its horizon entry.

Nonconservative unimodular gravity: a viable cosmological scenario?

In this work we review the issue of imposing the conservation of the energy–momentum tensor as a necessary condition to recover the equivalence between the unimodular gravity and General Relativity (GR) equipped with a cosmological constant. This procedure is usually interpreted as an ad hoc imposition on the unimodular theory’s structure. Whereas the consequences of avoiding the conservation of the total energy–momentum tensor has been already introduced in the literature, it has been not widely explored so far. We study an expanding universe sourced by a single effective perfect fluid such that the null divergence of its energy–momentum tensor is not imposed. As we shall show, in this scheme, the unimodular theory has its own conservation equation obtained from the Bianchi identities. We explore the evolution of the homogeneous and isotropic expanding background and show that a viable cosmological scenario exists. Also, we consider scalar perturbations with particular attention given to the gauge issue. We show that contrary to the traditional unimodular theory where the synchronous and longitudinal (newtonian) gauge for cosmological perturbations are not permitted, if the conservation of the energy–momentum is relaxed the scalar perturbations in the synchronous condition survive and present a growing mode behavior. We study therefore a new cosmological scenario in which the dynamics of the universe transits from the radiative phase directly to a accelerated one but allowing thus for structure formation.

Nonstaticity with type II, III, or IV matter field in $$f(R_{\mu \nu \rho \sigma },g^{\mu \nu })$$ gravity

In all $n(\ge 3)$-dimensional gravitation theories whose Lagrangians are functions of the Riemann tensor and metric, we show that static solutions are absent unless the total energy-momentum tensor for matter fields is of type I in the Hawking-Ellis classification. In other words, there is no hypersurface-orthogonal timelike Killing vector in a spacetime region with an energy-momentum tensor of type II, III, or IV. This asserts that, if back-reaction is taken into account to give a self-consistent solution, ultra-dense regions with a semiclassical type-IV matter field cannot be static even with higher-curvature correction terms. As a consequence, a static Planck-mass relic is possible as a final state of an evaporating black hole only if the semiclassical total energy-momentum tensor is of type I.

Anisotropic charged Heintzmann solution using gravitational decoupling through extended geometric deformation approach

In this article, we consider a well-known charged isotropic Heintzmann solution and extend it to its anisotropic domain by using gravitational decoupling through extended geometric deformation (EGD) approach. This approach converts a complex system of field equations which corresponds to the total energy momentum tensor (EMT) into two less-complicated subsystems employing linear transformation on both radial and temporal metric coefficients. The first one is related to the standard Einstein-Maxwell field equations (EFEs), while the other one is related to additional source. We study the matching conditions at the surface of the gravitational source between inner and outer spacetime geometries and evaluate the expressions for thermodynamical quantities ρ tot , and using mimic constraint and equation of state (EoS). In order to check the viability of the anisotropic version of the solution, we consider three different realistic stars, namely SAXJ1808.4 − 3658, SMCX − 4 and PSRJ1614 − 2230, and analyze the behavior of the model against different values of intensity parameter, i.e. γ = 0, 0.2 and 0.3. We also study the situation when electric charge is not present.

Extended gravitoelectromagnetism. II. Metric perturbation

This article makes the connection between the new gravitoelectromagnetic theory presented in the part I paper and general gravity in its weak formulation. The perturbation in the metric tensor is obtained in terms of the flat-space total energy–momentum tensor given by the sum of the consistent fully relativistic fluid and gravitoelectromagnetic field contributions. Expressions for the perturbed metric in the internal (fluid) and external (vacuum) regions are given in terms of the fluid and field variables. This formulation of gravitoelectromagnetism is compatible with the formation of gravitational waves. The geodesic equation is obtained in both the internal and external regions, including new terms neglected in the standard gravitomagnetic formulation. It is shown that the new terms reproduce the anomalous shift of planetary precession, which results from a balance between the gravitoelectric and gravitomagnetic forces.

Static spherically symmetric three-form stars

We consider interior static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field A_{alpha beta gamma }, which generates, via the field strength and a potential term, a new component in the total energy-momentum tensor of the gravitational system. We formulate the field equations in Schwarzschild coordinates and investigate their solutions numerically for different equations of state of neutron and quark matter, by assuming that the three-field potential is either a constant or possesses a Higgs-like form. Moreover, stellar models, described by the stiff-fluid, radiation-like, bag model and the Bose–Einstein condensate equations of state are explicitly obtained in both general relativity and three-form gravity, thus allowing an in-depth comparison between the astrophysical predictions of these two gravitational theories. As a general result we find that, for all the considered equations of state, three-form field stars are more massive than their general relativistic counterparts. As a possible astrophysical application, we suggest that the 2.5 M_{odot } mass compact object, associated with the GW190814 gravitational wave event, could be in fact a neutron or a quark star described by the three-form gravity theory.

TOV equations form of anisotropic pressure on two fluid models

We construct Tolman Oppenheimer Volkoff (TOV) equations for anisotropic pressure of two non-interacted perfect fluid with different four-velocities. This paper’s primary motivation is that we obtain the result that could describe the neutron stars (NS) admixed with dark matter (DM) that satisfying constraint from GW190814. Otherwise, our result also can investigate other compact objects that are admixed with two non-interacting fluids. In this work, we extend the formalism in Ref [1] by considering each fluid’s anisotropic pressure. Therefore, the total energy-momentum tensor is the sum of two non-interacting anisotropic fluids with different four-velocities. The velocity difference of both fluids denotes here by b where it comes from each of four-velocities under transformation rotation. Our result’s direct impact is that we can assess each fluid’s impact of anisotropic pressure in two fluids formalism in NS or other compact objects properties.

Multiple-scales approach to the averaging problem in cosmology

The Universe is homogeneous and isotropic on large scales, so on those scales it is usually modelled as a Friedmann-Lemaítre-Robertson-Walker (FLRW) space-time. The non-linearity of the Einstein field equations raises concern over averaging over small-scale deviations form homogeneity and isotropy, with possible implications on the applicability of the FLRW metric to the Universe, even on large scales. Here I present a technique, based on the multiple-scales method of singular perturbation theory, to handle the small-scale inhomogeneities consistently. I obtain a leading order effective Einstein equation for the large-scale space-time metric, which contains a back-reaction term. The derivation relies on a series of consistency conditions, that ensure that the growth of deviations from the large-scale space-time metric do not grow unboundedly; criteria for their satisfiability are discussed, and it is shown that they are indeed satisfied if matter is non-relativistic on small scales. The analysis is performed in harmonic gauge, and conversion to other gauges is discussed. I estimate the magnitude of the back-reaction term relative to the critical density of the Universe in the example of an NFW halo, and find it to be of the order of a few percent. In this example, the back-reaction term is interpreted as a contribution of the energy-density of gravitational potential energy, averaged over the small-scale, to the total energy-momentum tensor.

Relativistic corrections to the growth of structure in modified gravity

We present a method to introduce relativistic corrections including linear dark energy perturbations in Horndeski theory into Newtonian simulations based on the N-body gauge approach. We assume that standard matter species (cold dark matter, baryons, photons and neutrinos) are only gravitationally-coupled with the scalar field and we then use the fact that one can include modified gravity effects as an effective dark energy fluid in the total energy-momentum tensor. In order to compute the scalar field perturbations, as well as the cosmological background and metric perturbations, we use the Einstein-Boltzmann code hi_class. As an example, we study the impact of relativistic corrections on the matter power spectrum in k-essence, a subclass of Horndeski theory, including the effects of massless and massive neutrinos. For massive neutrinos with ∑ mν = 0.1 eV, the corrections due to relativistic species (photons, neutrinos and dark energy) can introduce a maximum deviation of approximately 7% to the power spectrum at k ∼ 10−3 Mpc−1 at z=0, for a scalar field with sound speed cs2∼0.013 during matter domination epoch. Our formalism makes it possible to test beyond \\lcdm models probed by upcoming large-scale structure surveys on very large scales.

An anisotropic version of Tolman VII solution in f(R, T) gravity via gravitational decoupling MGD approach

In this work, we have adopted gravitational decoupling by Minimal Geometric Deformation (MGD) approach and have developed an anisotropic version of well-known Tolman VII isotropic solution in the framework of $f(R, T)$ gravity, where $R$ is Ricci scalar and $T$ is trace of energy momentum tensor. The set of field equations has been developed with respect to total energy momentum tensor, which combines effective energy momentum tensor in $f(R,T)$ gravity and additional source $\phi_{ij}$. Following MGD approach, the set of field equations has been separated into two sections. One section represents $f(R, T)$ field equations, while the other is related to the source $\phi_{ij}$. The matching conditions for inner and outer geometry have also been discussed and an anisotropic solution has been developed using mimic constraint for radial pressure. In order to check viability of the solution, we have considered observation data of three different compact star models, named PSR J1614-2230, PSR 1937+21 and SAX J1808.4-3658 and have discussed thermodynamical properties analytically and graphically. The energy conditions are found to be satisfied for the three compact stars. The stability analysis has been presented through causality condition and Herrera's cracking concept, which ensures physical acceptability of the solution.

Probing beyond-Horndeski gravity on ultra-large scales

The beyond-Horndeski gravity has recently been reformulated in the dark energy paradigm—which has been dubbed, Unified Dark Energy (UDE). The evolution equations for the given UDE appear to correspond to a non-conservative dark energy scenario, in which the total energy-momentum tensor is not conserved. We investigate both the background cosmology and, the large-scale imprint of the UDE by probing the angular power spectrum of galaxy number counts, on ultra-large scales; taking care to include the full relativistic corrections in the observed overdensity. The background evolution shows that only an effective mass smaller than the Planck mass is needed in the early universe in order for predictions in the given theory to match current observational constraints. We found that the effective mass-evolution-rate parameter, which drives the evolution of the UDE, acts to enhance the observed power spectrum and, hence, relativistic effects (on ultra-large scales) by enlarging the UDE sound horizon. Conversely, both the (beyond) Horndeski parameter and the kineticity act to diminish the observed power spectrum, by decreasing the UDE sound horizon. Our results show that, in a universe with UDE, a multi-tracer analysis will be needed to detect the relativistic effects in the large-scale structure. In the light of a multi-tracer analysis, the various relativistic effects hold the potential to distinguish different gravity models. Moreover, while the Doppler effect will remain significant at all epochs and, thus can not be ignored, the integrated Sachs-Wolfe, the time-delay and the potential (difference) effects, respectively, will only become significant at epochs near z = 3 and beyond, and may be neglected at late epochs. In the same vein, the Doppler effect alone can serve as an effective cosmological probe for the large-scale structure or gravity models, in the angular power spectrum—at all z.

Self-consistent description of a spherically-symmetric gravitational collapse

In spherical symmetry, the total energy-momentum tensor near the apparent horizon is identified up to a single function of time from two assumptions: a trapped region forms at a finite time of a distant observer, and values of two curvature scalars are finite at its boundary. In general relativity, this energy-momentum tensor leads to the unique limiting form of the metric. The null energy condition is violated across the apparent horizon and is satisfied in the vicinity of the inner apparent horizon. As a result, homogenous collapse models cannot describe the formation of a black hole. Properties of matter change discontinuously immediately after formation of a trapped region. Absolute values of comoving density, pressure, and flux coincide at the apparent horizon. Thus, collapse of ideal fluids cannot lead to the formation of black holes. Moreover, these three quantities diverge at the expanding apparent horizon, producing a regular (i.e., finite curvature) firewall. This firewall is incompatible with quantum energy inequalities, implying that trapped regions, once formed at some finite time of a distant observer, cannot grow.

Equivalence Between Self-energy and Self-mass in Classical Electron Model

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, $$E=mc^2$$ , but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called 4/3-problem without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincare, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field.

Inflation driven by massive vector fields with derivative self-interactions

Inspired by the Generalized Proca Theory, we study a vector–tensor model of inflation with massive vector fields and derivative self-interactions. The action under consideration contains a usual Maxwell-like kinetic term, a general potential term and a term with nonminimal derivative coupling between the vector field and gravity, via the dual Riemann tensor. In this theory, the last term contains a free parameter, [Formula: see text], which quantifies the nonminimal derivative coupling. In this scenario, taking into account a spatially flat Friedmann–Robertson–Walker (FRW) universe and a general vector field, we obtain the general expressions for the equation of motion and the total energy–momentum tensor. Choosing a Proca-type potential, a suitable inflationary regimen driven by massive vector fields is studied. In this model, the isotropy of expansion is guaranteed by considering a triplet of orthogonal vector fields. In order to obtain an inflationary solution with this model, the quasi de Sitter expansion was considered. In this case, the vector field behaves as a constant. Finally, slow-roll analysis is performed and slow-roll conditions are defined for this model, which, for suitable constraints of the model parameters, can give the required number of e-folds for sufficient inflation.

Energy–Momentum Tensor in the Relativistic Theory of Gravity

It has been shown that the following modification of the symmetric (Gilbert) total energy–momentum tensor (EMT) density $${t^{\mu v}} \to {t^{\mu v}} - \frac{{{m^2}}}{{16\pi G}}{\tilde \varphi ^{\mu v}}$$ leads to incorrect results in basic energetic calculations. It is pointed out that some attempts to prove the positive definiteness of the gravitational radiation flux in the RTG are based on the nonconservative energy–momentum tensor.

Secondary isocurvature perturbations from acoustic reheating

The superhorizon (iso)curvature perturbations are conserved if the following conditions are satisfied: (i) (each) non adiabatic pressure perturbation is zero, (ii) the gradient terms are ignored, that is, at the leading order of the gradient expansion (iii) (each) total energy momentum tensor is conserved. We consider the case with the violation of the last two requirements and discuss the generation of secondary isocurvature perturbations during the late time universe. Second order gradient terms are not necessarily ignored even if we are interested in the long wavelength modes because of the convolutions which may pick products of short wavelength perturbations up. We then introduce second order conserved quantities on superhorizon scales under the conditions (i) and (iii) even in the presence of the gradient terms by employing the full second order cosmological perturbation theory. We also discuss the violation of the condition (iii), that is, the energy momentum tensor is conserved for the total system but not for each component fluid. As an example, we explicitly evaluate second order heat conduction between baryons and photons due to the weak Compton scattering, which dominates during the period just before recombination. We show that such secondary effects can be recast into the isocurvature perturbations on superhorizon scales if the local type primordial non Gaussianity exists a priori.

Gravitational Energy and No Big Bang Starts the Universe

Gravitation in flat space-time is described as field and studied in several articles. In addition to the flat space-time metric a quadratic form formally similar to that of general relativity defines the proper-time. The field equations for the gravitational field are non-linear differential equations of second order in divergence form and have as source the total energy-momentum tensor (inclusive that of gravitation). The total energy-momentum is conserved. It implies the equations of motion for matter in this field. The application of the theory gives for weak fields to measurable accuracy the same results as general relativity. The results of cosmological models are quite different from those of general relativity. The beginning of the universe starts from uniformly distributed gravitational energy without matter and radiation which is generated in the course of time. The solution is given in the pseudo-Euclidean metric, i.e. space is flat and non-expanding. There are non-singular solutions, i.e. no big bang. The redshift is a gravitational effect and not a Doppler effect. Gravitation is explained as field with attractive property and the condensed gravitational field converts to matter, radiation, etc. in the universe whereas the total energy is conserved. There is no contraction and no expansion of the universe.