Weak Field Limit Research Articles

Reduced Kiselev black hole

The Kiselev model describes a black hole surrounded by a fluid with equations of state p_r/rho =-1 and p_t/rho =(3w+1)/2 respectively in radial and tangential directions. It has been extensively studied in the parameter region -1<w<-1/3. If one rids off the black hole and turns to the region -1/3<w<0, i.e. p_t>0, then a new horizon of black hole type will emerge. This case has been mentioned in Kiselev’s pioneer work but seldom investigated in the literature. Referring to it as reduced Kiselev black hole, we revisit this case with attention to its causal structure, thermodynamics, shadow cast and weak-field limit. An alternative interpretation and extensions of the black hole are also discussed.

Strong-field vacuum polarisation with high energy lasers

When photons propagate in vacuum they may fluctuate into matter pairs thus allowing the vacuum to be polarised. This linear effect leads to charge screening and renormalisation. When exposed to an intense background field a nonlinear effect can arise when the vacuum is polarised by higher powers of the background. This nonlinearity breaks the superposition principle of classical electrodynamics, allowing for light-by-light scattering of probe and background photons mediated through virtual pairs dressed by the background. Vacuum polarisation is a strong-field effect when all orders of interaction between the virtual pair and the background must be taken into account. In this investigation we show that multiple scattering processes of this type may be observed by utilising high-energy laser pulses with long pulse duration, such as are available at facilities like ELI Beamlines. In combination with appropriate sources of high-energy probe photons, multiple probe-background light-by-light scattering allows for testing the genuine nonlinear regime of strong-field quantum electrodynamics. This provides access to the uncharted non-perturbative regime beyond the weak-field limit.

Regular black holes from analytic f(F^2)

We construct regular black holes and horizonless spacetimes that are geodesically complete and satisfy the dominant energy condition from Einstein-f(F^2) gravities with several classes of analytic f(F^2) functions that can be viewed as perturbations to Maxwell’s theory in weak field limit. We establish that regular black holes with special static metric (g_{tt} g_{rr}=-1) violate the strong energy condition and such a regular black hole with Minkowski core violates the null energy condition. We develop a formalism to perform electromagnetic duality transformations in f(F^2). We obtain two new explicit examples where the duality is a symmetry. We study the properties of the corresponding dyonic black holes. We study the geodesic motions of a particular class of solutions that we call horizonless or black hole repulsons.

Hybrid metric-Palatini gravity: General formalism and applications

It has been established that both metric and Palatini versions of [Formula: see text] gravity have interesting features but also manifest several downsides. A hybrid combination of theories, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and it is able to avoid some drawbacks of the original approaches. Here, we explore the formulation of this hybrid metric-Palatini approach and its main achievements in passing the local tests and several applications to astrophysical and cosmological scenarios. More specifically, we present the weak-field limit, analyze the well-posedness of the Cauchy problem for the hybrid model and explore the viability of generalized hybrid metric-Palatini gravitational theories.

The weak field limit of quantum matter back-reacting on classical spacetime

Consistent coupling of quantum and classical degrees of freedom exists so long as there is both diffusion of the classical degrees of freedom and decoherence of the quantum system. In this paper, we derive the Newtonian limit of such classical-quantum (CQ) theories of gravity. Our results are obtained both via the gauge fixing of the recently proposed path integral theory of CQ general relativity and via the CQ master equation approach. In each case, we find the same weak field dynamics. We find that the New-tonian potential diffuses by an amount lower bounded by the decoherence rate into mass eigenstates. We also present our results as an unraveled system of stochastic differential equations for the trajectory of the hybrid classical-quantum state and provide a series of kernels for constructing figures of merit, which can be used to rule out part of the parameter space of classical-quantum theories of gravity by experimentally testing it via the decoherence-diffusion trade-off. We compare and contrast the weak field limit to previous models of classical Newtonian gravity coupled to quantum systems. Here, we find that the Newtonian potential and quantum state change in lock-step, with the flow of time being stochastic.

Weak field and slow motion limits in energy–momentum powered gravity

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy–momentum powered gravity (EMPG), viz., the energy–momentum squared gravity (EMSG) of the form f(TμνTμν)=α(TμνTμν)η with α and η being constants. We have shown that EMPG with η≥0 and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, Mast, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass Meff(α,η,M)=M+Mempg(α,η,M), M being the actual physical mass and Mempg being the modification due to EMPG. Accordingly, while in GR we simply have the relation Mast=M, in EMPG we have Mast=M+Mempg. Within the framework of EMPG, if there is information about the values of {α,η} pair or M from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only Mast alone from astronomical observations, but M and Mempg separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by |peff/ρeff|≪1 (where peff=p+pempg and ρeff=ρ+ρempg), whereas this condition leads to |p/ρ|≪1 in GR.

White dwarf mass-radius relation in theories beyond general relativity

We explore the internal structures of the white dwarfs in two different modified theories of gravity: (i) scalar-tensor-vector gravity and (ii) beyond Horndeski theories of G 3 type. The modification of the gravitational force inside the white dwarf results in the modification of the mass and radius of the white dwarf. We use observational data from various astrophysical probes including Gaia to test the validity of these two classes of modified theories of gravity. We update the constraints on the parameters controlling the deviation from general relativity (and Newtonian gravity in the weak field limit) as: 0.001 ≤ α for the scalar-tensor-vector gravity and -0.079 ≤ γ ≤ 0.004 for the beyond Horndeski theories of G 3 type. Finally, we demonstrate the selection effect of the astrophysical data on the tests of the nature of gravity using white dwarf mass-radius relations specially in cases where the number of data-points are not many.

Effects of gravitational lensing by Kaluza-Klein black holes on neutrino oscillations

We study gravitational lensing of neutrinos in a Kaluza-Klein black hole spacetime and compare the oscillation probabilities of neutrinos with the case of lensing by black holes in General Relativity. We show that measuring neutrino oscillations in curved spacetimes may allow us to distinguish the two kinds of black holes even in the weak-field limit, as opposed to what happens for the weak lensing of photons. This promises to become an useful tool for future measurements of the properties of black hole candidates and possibly help to constrain the validity of alternative theories of gravity.

Temporal response of the conductivity of electrolytes

We study the temporal response of the electric current in an electrolyte under a sudden switch on or switch off of an external electric field of arbitrary magnitude. We use Stochastic Density Functional Theory including hydrodynamic interactions to express the current as a function of the ionic correlations. Assuming small density fluctuations, we linearize the field theory to compute the correlations in the transient regime. We first show that the correlations do not follow the same trajectory when the field is switched on or switched off. Accordingly, the behavior of the current differs in the two cases: it decays exponentially when the field is switched off, but it relaxes algebraically to its stationary value when the field is switched on. This difference is a non-linear effect since an exponential relaxation is recovered in both cases in the weak field limit.

Analysis of linearized Weyl gravity via the Hamilton–Jacobi method

The Hamilton–Jacobi formalism is used to analyze the Weyl theory in the weak-field limit. The complete set of involutive Hamiltonians is obtained, which are classified into involutive and non-involutive. The counting of degrees of freedom is performed. Additionally, the generalized brackets and gauge symmetries are reported.

Testing new massive conformal gravity with the light deflection by black hole

We study the weak gravitational lensing effect of Non-Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole in new massive conformal gravity. We analyze the deflection angle of light caused by new massive conformal gravity by using the Gauss-Bonnet theorem. As a consequence, we obtain the Gaussian optical curvature and calculate the deflection angle of the new massive conformal gravity for spherically balanced space-time with the Gauss-Bonnet theorem. The resultant deflection angle of light in the weak field limits showing that the bending of light is a global and topological phenomenon. Furthermore, we identify the deflection angle of light in the framework of the plasma medium, we also demonstrate the effect of a plasma medium on the deflection of light by non BBMB. In addition, the behavior of the deflection angle by new massive conformal gravity is explicitly shown in the influence of plasma medium and for the non plasma medium.

Covariant formulation of refracted gravity

We propose a covariant formulation of refracted gravity (RG), which is a classical theory of gravity based on the introduction of gravitational permittivity – a monotonic function of the local mass density – in the standard Poisson equation. Gravitational permittivity mimics dark matter phenomenology. The covariant formulation of RG (CRG) that we propose belongs to the class of scalar-tensor theories, where the scalar fieldφhas a self-interaction potential 𝒱(φ) = − Ξφ, with Ξ being a normalization constant. We show that the scalar field is twice the gravitational permittivity in the weak-field limit. Far from a spherical source of densityρs(r), the transition between the Newtonian and the RG regime appears below the acceleration scaleaΞ = (2Ξ − 8πGρ/φ)1/2, withρ = ρs + ρbgandρbgbeing an isotropic and homogeneous background. In the limit 2Ξ ≫ 8πGρ/φ, we obtainaΞ ∼ 10−10m s−2. This acceleration is comparable to the accelerationa0originally introduced in MOdified Newtonian Dynamics (MOND). From CRG, we also derived the modified Friedmann equations for an expanding, homogeneous, and isotropic universe. We find that the same scalar fieldφthat mimics dark matter also drives the accelerated expansion of the Universe. From the stress-energy tensor ofφ, we derived the equation of state of a redshift-dependent effective dark energywDE = pDE/ρDE. Current observational constraints onwDEand distance modulus data of type Ia supernovae suggest that Ξ has a comparable value to the cosmological constant Λ in the standard model. Since Ξ also plays the same role of Λ, CRG suggests a natural explanation of the known relationa0 ∼ Λ1/2. CRG thus appears to describe both the dynamics of cosmic structure and the expanding Universe with a single scalar field, and it falls within the family of models that unify the two dark sectors, highlighting a possible deep connection between phenomena currently attributed to dark matter and dark energy separately.

Destructive relativity.

The description of dynamics for high-energy particles requires an application of the special relativity theory framework, and analysis of properties of the corresponding equations of motion is very important. Here, we analyze Hamilton equations of motion in the limit of weak external field when potential satisfies the condition 2V(q)≪mc2. We formulate very strong necessary integrability conditions for the case when the potential is a homogeneous function of coordinates of integer non-zero degrees. If Hamilton equations are integrable in the Liouville sense, then eigenvalues of the scaled Hessian matrix γ-1V″(d) at any non-zero solution d of the algebraic system V'(d)=γd must be integer numbers of appropriate form depending on k. As it turns out, these conditions are much stronger than those for the corresponding non-relativistic Hamilton equations. According to our best knowledge, the obtained results are the first general integrability necessary conditions for relativistic systems. Moreover, a relation between the integrability of these systems and corresponding non-relativistic systems is discussed. The obtained integrability conditions are very easy to use because the calculations reduce to linear algebra. We show their strength in the example of Hamiltonian systems with two degrees of freedom with polynomial homogeneous potentials. It seems that the only integrable relativistic systems with such potentials are those depending only on one coordinate or having a radial form.

The periastron advance in curvature based Extended Gravity and Dark Energy

In the context of the periastron advance as a fundamental test for gravity theories, we show an approach to deduce constraints on the sizes of the new forces arising in the weak field limit of the Extended Theories of Gravity (ETG). It is also studied the force motivated by Quintessence Fields deforming the Schwarzschild geometry and associated to the Dark Energy, responsible of the acceleration of the Universe. As for the ETG, we consider the more general Scalar-Tensor Fourth Order Gravity (STFOG) and the NonCommutative Spectral Gravity (NCSG) as a special case. The solutions of the linearized field equations provide corrections to the Newtonian potential in the Yukawa-like form , where α is the parameter related to the strength of the potential and β to the range of the force. Quintessence Fields lead to a power-law correction with parameters related to the Dark Energy. By analysing the periastron advance with the use of the current data, we find improvements on the parameters of the gravitational models as well as on the bounds of the parameter β by several orders of magnitude.

Two-dimensional Wannier-Mott exciton diamagnetic shift

We present a model of diamagnetic shifts for two-dimensional Wannier-Mott excitons in out-of-plane magnetic fields, including environmental dielectric effects. We indicate the reasons for the magnetic-field-induced increase of exciton mass and size. In the weak-field limit, we deduce the diamagnetic coefficient and explain why its value is significantly different between excitonic states. Our results agree well with experimental data.

Effects of electric and magnetic charges on weak deflection angle and bounding greybody of black holes in nonlinear electrodynamics

In this paper, we study the weak deflection angle using the Gauss–Bonnet theorem and bounding greybody factor for electric and magnetic black holes in the background of nonlinear electrodynamics. Using Gibbons and Werner’s approach, we first acquired the Gaussian optical curvature to be used in the Gauss–Bonnet theorem and calculate the bending angle for spherically symmetric electric and magnetic black holes in both non-plasma and plasma mediums in the weak field limits. Later, we calculate the rigorous bounds of the greybody factor for the given black holes. Furthermore, we are looking into the graphical behaviour of bending angles and greybody bounds at specific values of multiple parameters as well as black hole charges. It is to be mentioned here that all the results for the electric and magnetic-charged black hole solutions are reduced into the Schwarzschild black hole solution in the absence of the black hole charges.

The energy–momentum complex in non-local gravity

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here, we generalize the Einstein gravitational energy–momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator [Formula: see text] are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy–momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy–momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy–momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

A spherically symmetric gravitational solution of nearly conformally flat metric measure space

In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy–momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We derive an equation for the density function for a general profile of a rotation curve obtained from observations. Specifically, the density function corresponding to two well-known profiles PSS and NFW are provided.

Probing a non-linear electrodynamics black hole with thin accretion disk, shadow, and deflection angle with M87* and Sgr A* from EHT

Non-linear interaction between the electromagnetic fields (EMF) occurs when vacuum polarization in quantum electrodynamics (QED) happens. The field of non-linear electrodynamics, which may result from this interaction, could have important effects on black hole physics. This paper considers the asymptotically flat black hole solution in Einstein-nonlinear electrodynamics (NLE) fields. We study the effect of the NLE parameters on the black hole deflection angle using the Gauss-Bonnet theorem in weak field limits, shadow cast using the null geodesics method, and thin accretion disk using the Novikov-Thorne model. In particular, we studied the time-averaged energy flux, the disk temperature, the differential luminosity, the different emission profiles, and infalling spherical accretion. Then we show how the physical quantities depend on $\beta$ and $C$ parameters of NLE and provide some constraints on the NLE parameters using the observations of M87* and Sgr A* from EHT.

Metric tensor at second perturbation order for spherically symmetric space-times

It is shown in this paper, that if the Einstein Equivalence Principle is valid on a particular metric theory of gravitation in a spherically symmetric space-time, then the time metric component is not equal to the negative of the inverse radial one unless the underlying potential is inversely proportional to the radial coordinate. At the weak field limit of approximation, a general formula is calculated and applied to some useful cases.