Effective Stress-energy Tensor Research Articles

A connection between regular black holes and horizonless ultracompact stars

We illustrate that regular black holes and horizonless stars, typically considered as quite distinct families of black hole mimickers, are intimately intertwined. We show that any spherically symmetric regular black hole can be continuously deformed into a horizonless star under the mild conditions of non-negativity of gravitational energy (Misner-Sharp quasi-local mass), and an assumed linear relation between the latter and the Arnowitt-Deser-Misner (ADM) mass. We illustrate this general result by considering the family of geometries proposed by Hayward as the description of regular black holes, and we also describe the properties of the corresponding horizonless stars. The form of the associated effective stress-energy tensor shows that these horizonless stars can be identified as anisotropic gravastars with a soft surface and inner/outer light rings. We also construct dynamical geometries that could describe the evolution of regular black holes towards horizonless stars, and show that it is plausible that the effective stress-energy tensor in the first stages of evolution is generated by semiclassical effects, in agreement with independent works analyzing semiclassical backreaction.

Renormalizing one-point probability distribution function for cosmological counts in cells

We study the one-point probability distribution function (PDF) for matter density averaged over spherical cells. The leading part to the PDF is defined by spherical collapse dynamics, whereas the next-to-leading part comes from the integration over fluctuations around the saddle-point solution. The latter calculation receives sizable contributions from short modes and must be renormalized. We propose a new approach to renormalization by modeling the effective stress-energy tensor for short perturbations. The model contains three free parameters. Two of them are related to the counterterms in the one-loop matter power spectrum and bispectrum, one more parameterizes their redshift dependence. This relation can be used to impose priors in fitting the model to the PDF data. We confront the model with the results of high-resolution N-body simulations and find excellent agreement for cell radii r * ≥ 10 Mpc/h at all redshifts down to z = 0. Discrepancies at a few per cent level are detected at low redshifts for r * ≤ 10 Mpc/h and are associated with two-loop corrections to the model.

Dynamical Analysis of the Covarying Coupling Constants in Scalar–Tensor Gravity

A scalar–tensor theory of gravity was considered, wherein the gravitational coupling G and the speed of light c were admitted as space–time functions and combined to form the definition of the scalar field ϕ. The varying c participates in the definition of the variation of the matter part of the action; it is related to the effective stress–energy tensor, which is a result of the requirement of symmetry under general coordinate transformations in our gravity model. The effect of the cosmological coupling Λ is accommodated within a possible behavior of ϕ. We analyzed the dynamics of ϕ in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential V(ϕ) and no particular assumption on the Hubble function. The phase space analysis was performed both with the linear stability theory and via the more general Lyapunov method. Either method led to the conclusion that the condition G˙/G=σc˙/c, where σ=3 must hold for the rest of cosmic evolution after the system arrives at the globally asymptotically stable fixed point and the dynamics of ϕ ceases. This result realized our main motivation: to provide a physical foundation for the phenomenological model admitting G/G0=c/c03, used recently to interpret cosmological and astrophysical data. The thus covarying couplings G and c impact the cosmic evolution after the dynamical system settles to equilibrium. The secondary goal of our work was to investigate how this impact occurs. This was performed by constructing the generalized continuity equation in our scalar–tensor model and considering two possible regimes for the varying speed of light—decreasing c and increasing c—while solving our modified Friedmann equations. The solutions to the latter equations make room for radiation- and matter-dominated eras that progress to a dark-energy-type of accelerated expansion.

Traversable Wormhole Solutions Admitting Noether Symmetry in f(R,T2) Theory

This paper uses the Noether symmetry approach to examine the viable and stable traversable wormhole solutions in the framework of the f(R,T2) theory, where R is the Ricci scalar and T2=TμνTμν is the self-contraction of the stress–energy tensor. For this purpose, we consider a specific model of this modified theory to obtain the exact solutions of the Noether equations. Further, we formulate the generators of the Noether symmetry and first integrals of motion. We analyze the presence of viable and stable traversable wormhole solutions corresponding to different redshift functions. In order to determine whether this theory provides physically viable and stable wormhole geometry or not, we check the graphical behavior of the null energy constraint, causality condition and adiabatic index for an effective stress–energy tensor. It is found that viable and stable traversable wormhole solutions exist in this modified theory.

On the gravitational collapse in 4-dimensional Einstein–Gauss–Bonnet gravity

In this paper, we treat 4-dimensional Einstein–Gauss–Bonnet (EGB) gravity as general relativity with an effective stress-energy tensor. We will study the modified Oppenheimer–Snyder–Datt model of the gravitational collapse of a star in a 4-dimensional EGB black hole (BH). The inside geometry of the star is described by the spatially flat Friedmann–Robertson–Walker metric and the matter is distributed uniformly without any pre-assumption about its equation of state. The exterior EGB BH is smoothly matched to the interior geometry without the requirement of any thin shell. This gives the energy density, pressure, and the equation of state of collapsing matter. At the end, we study the time evolution of event and apparent horizons.

Gravitational entropy in Szekeres class I models

Developing a self-consistent notion of gravitational entropy in the context of cosmological structure formation has been so far an elusive task. Various theoretical proposals have been presented, initially based on Penrose’s Weyl curvature hypothesis, and variations of it. A more recent proposal by Clifton, Ellis, and Tavakol (CET) considered a novel approach by defining such entropy from a Gibbs equation constructed from an effective stress–energy tensor that emerges from the ‘square root’ algebraic decomposition of the Bel–Robinson tensor, the simplest divergence-less tensor related to the Weyl tensor. Since, so far all gravitational entropy proposals have been applied to highly restrictive and symmetric spacetimes, we probe in this paper the CET proposal for a class of much less idealized spacetimes (the Szekeres class I models) capable of describing the joint evolution of arrays of arbitrary number of structures: overdensities and voids, all placed on selected spatial locations in an asymptotic ΛCDM background. By using suitable covariant variables and their fluctuations, we find the necessary and sufficient conditions for a positive CET entropy production to be a negative sign of the product of the density and Hubble expansion fluctuations. To examine the viability of this theoretical result we examine numerically the CET entropy production for two elongated over dense regions surrounding a central spheroidal void, all evolving jointly from initial linear perturbations at the last scattering era into present day Mpc-size CDM structures. We show that CET entropy production is positive for all times after last scattering at the precise spatial locations where structure growth occurs and where the exact density growing mode is dominant. The present paper provides the least idealized (and most physically robust) probe of a gravitational entropy proposal in the context of structure formation.

Tidal forces in dirty black hole spacetimes

Black holes can be inserted in very rich astrophysical environments, such as accretion disks. Although isolated black holes are simple objects in general relativity, their accretion disks may significantly enrich the field configurations of their surroundings. Alternative theories of gravity can lead to novel black hole solutions, which can be represented by small deviations in the metric due to an effective stress-energy tensor. Among the key aspects of the interaction of black holes with their surroundings, stand tidal forces phenomena. We study the tidal forces of spherically symmetric black holes in the presence of effective matter fields, dubbed as dirty black holes. These effective fields can generically represent usual or exotic matter associated to a variety of gravity theories. We show that this dirtiness leads to characteristic imprints in the tidal forces, which are absent in the case of a black hole surrounded by vacuum. We apply our results to particular cases, such as black holes coupled to linear and nonlinear electrodynamics theories and a Schwarzschild black hole surrounded by a spherical shell.

Raychaudhuri equations and gravitational collapse in Einstein-Cartan theory

The Raychaudhuri equations for the expansion, shear and vorticity are generalized in a spacetime with torsion for timelike as well as null congruences. These equations are purely geometrical like the original Raychaudhuri equations and could be reduced to them when there is no torsion. Using the Einstein-Cartan-Sciama-Kibble field equations the effective stress-energy tensor is derived. We also consider an Oppenheimer-Snyder model for the gravitational collapse of dust. It is shown that the null energy condition (NEC) is violated before the density of the collapsing dust reaches the Planck density, hinting that the spacetime singularity may be avoided if there is a non-zero torsion,i.e. if the collapsing dust particles possess intrinsic spin.

Energy conditions in the new model of loop quantum cosmology * *Supported by the National Natural Science Foundation of China (NSFC) (11775082, 12047519, 11875006, 11961131013), China Postdoctoral Science Foundation (2021M691072)

Recently, a de-Sitter epoch has been found in the new model of loop quantum cosmology, which is governed by the scalar constraint with both Euclidean and Lorentz terms. The singularity free bounce in the new LQC model and the emergent cosmology constant strongly suggest that the effective stress-energy tensor induced by quantum corrections must violate the standard energy conditions. In this study, we perform an explicit calculation to analyze the behaviors of specific representative energy conditions, i.e., average null, strong, and dominant energy conditions. We reveal that the average null energy condition is violated at all times, while the dominant energy condition is violated only at a period around the bounce point. The strong energy condition is violated not only at a period around the bounce point but also in the whole period from the bounce point to the classical phase corresponding to the de Sitter period. Our results will shed some light on the construction of a wormhole and time machine, which usually require exotic matter to violate energy conditions.

Equivalence between Horndeski and beyond Horndeski theories and imperfect fluids

In this paper we show that an equivalence between Horndeski and beyond Horndeski theories and general relativity with an effective imperfect fluid can be formally established. The formal equivalence is discussed for several particular cases of interest. Working in the cosmological framework, it is shown that, while the effective stress-energy tensor of viable Horndeski theories is formally equivalent to that of an imperfect fluid with anisotropic stresses and vanishing heat flux vector, the effective stress-energy tensor of beyond Horndeski theories is equivalent to the one of a perfect fluid instead.

Matter Accretion Versus Semiclassical Bounce in Schwarzschild Interior

We discuss the properties of the previously constructed model of a Schwarzschild black hole interior where the singularity is replaced by a regular bounce, ultimately leading to a white hole. We assume that the black hole is young enough so that the Hawking radiation may be neglected. The model is semiclassical in nature and uses as a source of gravity the effective stress-energy tensor (SET) corresponding to vacuum polarization of quantum fields, and the minimum spherical radius is a few orders of magnitude larger than the Planck length, so that the effects of quantum gravity should still be negligible. We estimate the other quantum contributions to the effective SET, caused by a nontrivial topology of spatial sections and particle production from vacuum due to a nonstationary gravitational field and show that these contributions are negligibly small as compared to the SET due to vacuum polarization. The same is shown for such classical phenomena as accretion of different kinds of matter to the black hole and its further motion to the would-be singularity. Thus, in a clear sense, our model of a semiclassical bounce instead of a Schwarzschild singularity is stable under both quantum and classical perturbations.

Towards rotating noncircular black holes in string-inspired gravity

We study stationary slowly rotating black holes, up to quadratic order in the spin angular momentum, in dynamical Chern-Simons gravity and shift symmetric Einstein scalar Gauss-Bonnet gravity, as models of string-inspired gravities. These gravity theories modify general relativity by introducing dynamical scalar fields coupled with curvature invariants. We show that the linear time dependence of the scalar fields is allowed from the stationarity of the effective stress energy tensors. However, these time dependent scalar fields yield singular behavior of the metric functions at the black hole horizons, or they are incompatible with the stationarity of the spacetimes. Thus, these gravity theories admit only known solutions as regular stationary solutions. Our results suggest the non-existence of rotating non-circular black holes in these gravity theories.

Properties of ultracompact particlelike solutions in Einstein-scalar-Gauss-Bonnet theories

Besides scalarized black holes and wormholes, Einstein-scalar-Gauss-Bonnet theories allow also for particle-like solutions. The scalar field of these particle-like solutions diverges at the origin, akin to the divergence of the Coulomb potential at the location of a charged particle. However, these particle-like solutions possess a globally regular metric, and their effective stress energy tensor is free from pathologies, as well. We determine the domain of existence for particle-like solutions in a number of Einstein-scalar-Gauss-Bonnet theories, considering dilatonic and power-law coupling functions, and we analyze the physical properties of the solutions. Interestingly, the solutions may possess pairs of lightrings, and thus represent ultra-compact objects. We determine the location of these lightrings, and study the effective potential for the occurrence of echoes in the gravitational-wave spectrum. We also address the relation of these particle-like solutions to the respective wormhole and black-hole solutions, and clarify the limiting procedure to recover the Fisher solution (also known as Janis-Newman-Winicourt-Wyman solution).

Gravitational decoupling minimal geometric deformation model in modified f(R,T) gravity theory

The present paper is devoted to investigating the possibility of getting stellar interiors for ultra-dense compact spherical systems portraying an anisotropic matter distribution, employing the gravitational decoupling by means of Minimal Geometric Deformation (MGD) procedure within the modified theory of gravity: f ( R , T ) . In this regard, we have considered the algebraic function as f ( R , T ) = R + 2 χ T . The corresponding effective stress–energy tensor is conserved as well as the exact solutions are derived, where χ indicates a coupling constant which incorporates a new gravity aspect in the system. However, the MGD was introduced through a coupling constant α which makes the fluid go beyond to the perfect fluid–structure (i.e. introduce anisotropy). In this connection, we also discussed how both parameters α and χ affect the system. Moreover, the physical quantities associated with the new solutions are well-behaved from the physical and mathematical point of view which are affirmed by performing several physical tests of the main salient features, such pressure, density, dynamical equilibrium, energy conditions, and dynamical stability. We also performed the junction conditions for this chosen linear f ( R , T ) function. On the other hand, we have generated the M − R curves from our solutions in different scenarios, including GR, GR+MGD, f ( R , T ) and f ( R , T ) + MGD, and we found a perfect fit for many compact spherical objects in these scenarios by varying α and χ . The present study reveals that the modified f ( R , T ) gravity through gravitational decoupling by means of MGD method is a suitable theory to explain compact stellar structures.

Particle-like ultracompact objects in Einstein-scalar-Gauss-Bonnet theories

We present a new type of ultracompact objects, featuring lightrings and echoes in the gravitational-wave spectrum. These particle-like solutions arise in Einstein-scalar-Gauss-Bonnet theories in four spacetime dimensions, representing globally regular spacetime manifolds. The scalar field diverges at the center, but the effective stress-energy tensor is free from pathologies. We determine their domain of existence and compare with wormhole solutions, black holes and the Fisher solution.

Noncommutative-geometry wormholes without exotic matter

A fundamental property of Morris-Thorne wormholes is the so-called flare-out condition that automatically results in a violation of the null energy condition (NEC) in classical general relativity. By contrast, in $f(R)$ modified gravity, the material threading the wormhole may actually satisfy the NEC, while, at the same time, the effective stress-energy tensor arising from the modified theory violates the NEC, thereby sustaining the wormhole. It is shown in this paper that noncommutative geometry, an offshoot of string theory, can be viewed as a special case of $f(R)$ gravity and can therefore sustain a wormhole without the use of exotic matter. It also provides a motivation for the choice of $f(R)$ in the modified gravitational theory.

Ghost-free modification of the Polyakov action and Hawking radiation

In this paper we discuss possible effects of non-locality in black hole spacetimes. We consider a two-dimensional theory in which the action describing matter is a ghost-free modification of the Polyakov action. For this purpose we write the Polyakov action in a local form by using an auxiliary scalar field and modify its kinetic term by including into it a non-local ghost-free form factor. We demonstrate that the effective stress-energy tensor is modified and we study its properties in a background of a two-dimensional black hole. We obtain the expression for the contribution of the ghost-free auxiliary field to the entropy of the black hole. We also demonstrate that if the back-reaction effects are not taken into account, such a ghost-free modification of the theory does not change the energy flux of the Hawking radiation measured at infinity. We illustrate the discussed properties for black hole solution of a 2D dilaton gravity model which admits a rather complete analytical study.

Scattering of spinning black holes from exponentiated soft factors

We provide evidence that the classical scattering of two spinning black holes is controlled by the soft expansion of exchanged gravitons. We show how an exponentiation of Cachazo-Strominger soft factors, acting on massive higher-spin amplitudes, can be used to find spin contributions to the aligned-spin scattering angle, conjecturally extending previously known results to higher orders in spin at one-loop order. The extraction of the classical limit is accomplished via the on-shell leading-singularity method and using massive spinor-helicity variables. The three-point amplitude for arbitrary-spin massive particles minimally coupled to gravity is expressed in an exponential form, and in the infinite-spin limit it matches the effective stress-energy tensor of the linearized Kerr solution. A four-point gravitational Compton amplitude is obtained from an extrapolated soft theorem, equivalent to gluing two exponential three-point amplitudes, and becomes itself an exponential operator. The construction uses these amplitudes to: 1) recover the known tree-level scattering angle at all orders in spin, 2) recover the known one-loop linear-in-spin interaction, 3) match a previous conjectural expression for the one-loop scattering angle at quadratic order in spin, 4) propose new one-loop results through quartic order in spin. These connections link the computation of higher-multipole interactions to the study of deeper orders in the soft expansion.

Constraints on Horndeski theory using the observations of Nordtvedt effect, Shapiro time delay and binary pulsars

Alternative theories of gravity not only modify the polarization contents of the gravitational wave, but also affect the motions of the stars and the energy radiated away via the gravitational radiation. These aspects leave imprints in the observational data, which enables the test of general relativity and its alternatives. In this work, the Nordtvedt effect and the Shapiro time delay are calculated in order to constrain Horndeski theory using the observations of lunar laser ranging experiments and Cassini time-delay data. The effective stress-energy tensor is also obtained using the method of Isaacson. Gravitational wave radiation of a binary system is calculated, and the change of the period of a binary system is deduced for the elliptical orbit. These results can be used to set constraints on Horndeski theory with the observations of binary systems, such as PSR J1738 + 0333. Constraints have been obtained for some subclasses of Horndeski theory, in particular, those satisfying the gravitational wave speed limits from GW170817 and GRB 170817A.

Quantum corrections to the gravitational backreaction

Effective field theory techniques are used to study the leading order quantum corrections to the gravitational wave backreaction. The effective stress-energy tensor is calculated and it is shown that it has a non-vanishing trace that contributes to the cosmological constant. By comparing the result obtained with LIGO’s data, the first bound on the amplitude of the massive mode is found: epsilon < 1.4times 10^{-33}.