Orbiting naked singularities in large-$$\omega $$ Brans–Dicke gravity

Brans–Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)–tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the \(\omega \longrightarrow \infty \) limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar–tensor gravity.     

Multidimensional gravitational waves. I. Purely radiative spacetimes

The concept of gravitational radiation in multidimensional Einstein gravity is studied. Due to technical difficulties the Petrov classification of the conformal tensor and the peeling off theorem cannot be generalized to spaces of dimensiond > 4. A multidimensionalpp wave is defined by analogy with that ford = 4. If the definition is supplemented by the Lichnerowicz condition for purely radiative spacetimes, the admitted solutions of the dimensionally reduced gravity theory describe a scalar (dilaton) and a gravitationalpp wave moving in the external spacetime in the same direction. The existence of the extra dimensions can be traced back by measuring the frequence of thepp wave in the external space. The condition is equally restrictive in a more general case of the internal space being a flat anisotropic manifold (i.e. an abelian group space).     

Effective Nonlocal Euclidean Gravity

A nonlocal form of the effective gravitational action could cure the unboundedness of euclidean gravity with Einstein action. On sub-horizon length scales the modified gravitational field equations seem compatible with all present tests of general relativity and post-Newtonian gravity. They induce a difference in the effective Newtonian constant between regions of space with vanishing or nonvanishing curvature scalar (or Ricci tensor). In cosmology they may lead to a value < 1 for the critical density after inflation. The simplest model considered here appears to be in conflict with nucleosynthesis, but generalizations consistent with all cosmological observations seem conceivable.     

Lower-dimensional theories of gravity and gravitational waves

We demonstrate that there are no gravitational waves in vacuum in 1+1 gravity, with or without a cosmological constant, and a wave-like field in regions of non-vanishing T_v is quite unlike a conventional gravitational wave in 3+1 gravity. This, and other dissimilarities, lend a word of caution to the extraction of information from lower-dimensional theories for the understanding of 3+1 gravity.     

The gravitational energy‐momentum pseudo‐tensor of higher‐order theories of gravity

We derive the gravitational energy momentum tensor for a general Lagrangian of any order and in particular for a Lagrangian such as . We prove that this tensor, in general, is not covariant but only affine, then it is a pseudo‐tensor. Furthermore, the pseudo‐tensor is calculated in the weak field limit up to a first non‐vanishing term of order h² where h is the metric perturbation. The average value of the pseudo‐tensor over a suitable spacetime domain is obtained. Finally we calculate the power per unit solid angle Ω carried by a gravitational wave in a direction for a fixed wave number under a suitable gauge. These results are useful in view of searching for further modes of gravitational radiation beyond the standard two modes of General Relativity and to deal with nonlocal theories of gravity where terms involving are present. The general aim of the approach is to deal with theories of any order under the same standard of Landau pseudo‐tensor.     

A formulation of linearised gravity

The formulation of linearised gravity in terms of the electric and magnetic gravitational fields is extended to take into account the presence of matter. The modes of radiation, the equations of motion and the potential in the static case are given. The relevant components of the superenergy tensor are calculated and a quantity named the superforce is introduced.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity constraints from gravitational waves

The recent LIGO observation sparked interest in the field of gravitational wave signals. Besides the gravitational wave observation the LIGO collaboration used the inspiraling black hole pair to constrain the graviton mass. Unlike general relativity, f(R) theories have a characteristic non-zero mass graviton. We apply this constraint on the graviton mass to viable f(R) models in order to find the effects on model parameters. We find it possible to constrain the parameter space with these gravity wave based observations. We consider the popular Hu–Sawicki model as a case study and find an appropriate parameter bracket. The result generalizes to other f(R) theories and can be used to constrain the parameter space.     

Free energy of a Lovelock holographic superconductor

We study thermodynamics of black hole solutions in Lanczos–Lovelock anti-de Sitter gravity in \(d+1\) dimensions coupled to nonlinear electrodynamics and a Stückelberg scalar field. This class of theories is used in the context of gauge/gravity duality to describe a high-temperature superconductor in \(d\) dimensions. A larger number of coupling constants in the gravitational side is necessary to widen the domain of validity of physical quantities in dual quantum field theory (QFT). We regularize the gravitational action and find the finite conserved quantities for a planar black hole with scalar hair. Then we derive the quantum statistical relation in the Euclidean sector of the theory, and we obtain the exact formula for the free energy of the superconductor in the holographic QFT. Our result is analytic and it includes the effects of backreaction of the gravitational field. We further discuss on how this formula could be used to analyze second order phase transitions through the discontinuities of the free energy, in order to classify holographic superconductors in terms of the parameters in the theory.     

Aspects of quadratic gravity

We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure R² theory is indeed ghost free. Then we point out that for flat backgrounds the pure R² theory propagates only a scalar massless mode and no spin‐two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti‐de Sitter, or by changing the long‐distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string‐ or M‐theory. We demonstrate that string theory on non‐compact manifolds, like a line bundle over , may indeed lead to gravity dynamics determined by a higher curvature action.     

Massive scalar counterpart of gravitational waves in scalarized neutron star binaries

In analogy with spontaneous magnetization of ferromagnets below the Curie temperature, a neutron star (NS), with a compactness above a certain critical value, may undergo spontaneous scalarization and exhibit an interior nontrivial scalar configuration. Consequently, the exterior spacetime is changed, and an external scalar field appears, which subsequently triggers a scalarization of its companion. The dynamical interplay produces a gravitational scalar counterpart of tensor gravitational waves. In this paper, we resort to scalar–tensor theory and demonstrate that the gravitational scalar counterpart from a double neutron star (DNS) and a neutron star–white dwarf (NS-WD) system become massive. We report that (1) a gravitational scalar background field, arising from convergence of external scalar fields, plays the role of gravitational scalar counterpart in scalarized DNS binary, and the appearance of a mass-dimensional constant in a Higgs-like gravitational scalar potential is responsible for a massive gravitational scalar counterpart with a mass of the order of the Planck scale; (2) a dipolar gravitational scalar radiated field, resulting from differing binding energies of NS and WD, plays the role of a gravitational scalar counterpart in scalarized orbital shrinking NS-WDs, which oscillates around a local and scalar-energy-density-dependent minimum of the gravitational scalar potential and obtains a mass of the order of about \(10^{-21}\,{\text {eV/c}}^2\).     

Induced Gravity Theory from Noether Symmetry

We discuss the functional form of the potential and the non-minimal coupling in the scalar tensor gravity (induced gravity) theories as allowed by the Noether symmetry in the spatially homogenous and isotropic spacetime background. The solution of the field equations (for k=0) are presented by using the results obtained from the Noether symmetry. It has been observed that the potential and the coupling function obtained from the Noether symmetric approach do not satisfy the continuity equation for k=± 1. Finally we present an inflationary solution that goes over to the Einstein's gravity asymptotically as t .     

‘In’ and ‘out’ vertex operators in a class of UV-finite nonlinear σ-models

In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions.     

Kinetics of small disturbances in an isotropic universe II. Short-wave disturbances in an ultrarelativistic gas

Short-wave gravitational disturbances are considered in an isotropic, expanding universe, filled with an ultrarelativistic gas. Solutions are obtained for scalar, vector. and tensor disturbances in the limit n » 1, where n is the wave vector and n is the time coordinate x⁴.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 35–43, March, 1978.     

Gravitational collapse of charged scalar fields

In order to study the gravitational collapse of charged matter we analyze the simple model of an self-gravitating massless scalar field coupled to the electromagnetic field in spherical symmetry. The evolution equations for the Maxwell–Klein–Gordon sector are derived in the \(3+1\) formalism, and coupled to gravity by means of the stress–energy tensor of these fields. To solve consistently the full system we employ a generalized Baumgarte–Shapiro–Shibata–Nakamura formulation of General Relativity that is adapted to spherical symmetry. We consider two sets of initial data that represent a time symmetric spherical thick shell of charged scalar field, and differ by the fact that one set has zero global electrical charge while the other has non-zero global charge. For compact enough initial shells we find that the configuration doesn’t disperse and approaches a final state corresponding to a sub-extremal Reissner–Nördstrom black hole with \(|Q| . By increasing the fundamental charge of the scalar field \(q\) we find that the final black hole tends to become more and more neutral. Our results support the cosmic censorship conjecture for the case of charged matter.     

On the concept of time and the origin of the cosmological temperature

Time arises in the theory of gravity through the semiclassical approximation of the gravitational part of the solution of the Wheeler-De Witt equation in the manner shown by Banks (SCAG). We generalize Banks' procedure by grafting a Born-Oppenheimer type approximation onto SCAG. This allows for the feedback of matter onto gravity, wherein the latter is driven by the (quantum) mean energy-momentum tensor of matter. The wave function is nonvanishing in classically forbidden configurations of gravity. In SCAG this is described by the evolution of matter in imaginary time. This is interpreted as an inverse temperature, and the norm of the matter wave function, no longer conserved for these gravitational configurations, is a partition function. A simple cosmological model is worked out to illustrate these ideas. In this model it is shown that the temperature of the matter which emerges into the classically permitted region is the inverse bounce time of the bounce executed by the system in the forbidden region (behind the horizon).Time present and time past are both perhaps present in time future. And time future contained in time past. If all time is eternally present All time is unredeemable.—T. S. Eliot, Burnt Norton,Four Quartets, 1943.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Reconstruction of constant slow-roll inflation

Using the relations between the slow-roll parameters and the power spectra for the single field slow-roll inflation, we derive the scalar spectral tilt n_s and the tensor to scalar ratio r for the constant slow-roll inflation, and obtain the constraint on the slow-roll parameter η from the Planck 2015 results. The inflationary potential for the constant slow-roll inflation is then reconstructed in the framework of both general relativity and the scalar-tensor theory of gravity, and compared with the recently reconstructed E model potential. In the strong coupling limit, we show that the η attractor is reached.     

Can Dilaton Fields in Astrophysical Objects be Detected?

We analyze a new class of static exact solutions of Einstein-Maxwell-Dilaton gravity with arbitrary scalar coupling constant , representing a gravitational body endowed with electromagnetic dipole moment. This class possesses mass, dipole and scalar charge parameters. A discussion of the geodesic motion shows that the scalar field interaction is so weak that it cannot be measured in gravitational fields like the sun, but it could perhaps be detected in gravitational fields like pulsars. The scalar force can be attractive or repulsive. This gives rise to the hypothesis that the magnetic field of some astrophysical objects could be fundamental.     

The Investigation of the Model of Gravitational Repulsion in Einstein's General Theory of Relativity

The gravitational field of a static, sphericallysymmetric source of mass M and scalar charge q isconsidered. It is shown that the metric expression forthis source is considerably simplified in two limiting cases: a) for M2 4q²/G,that is when the mass of the source is the maincontributor in the gravitational field; b) forq² M²G/4, when theenergy-momentum tensor of the static, spherically symmetric scalar field is the main contributorin the gravitational field. In the limiting caseq² M²G/4, the geodesicsof the massive and massless particles are studied. It isshown that gravitational forces of repulsion act on a particle movingnon-radially in this field. As a result, voids should becreated in the region surrounding such sources in theUniverse. Moreover, the stars with considerable scalar charge q² M²G/4 will act not as convexgravitational lenses as in the case whenq² M²G/4, but as concavegravitational lenses for the electromagnetic rays oflarge impact parameter.     

Self-accelerated Universe Induced by Repulsive Effects as an Alternative to Dark Energy and Modified Gravities

The existence of current–time universe’s acceleration is usually modeled by means of two main strategies. The first makes use of a dark energy barotropic fluid entering by hand the energy–momentum tensor of Einstein’s theory. The second lies on extending the Hilbert–Einstein action giving rise to the class of extended theories of gravity. In this work, we propose a third approach, derived as an intrinsic geometrical effect of space–time, which provides repulsive regions under certain circumstances. We demonstrate that the effects of repulsive gravity naturally emerge in the field of a homogeneous and isotropic universe. To this end, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. Moreover, we show that repulsive gravity counterbalances the standard gravitational attraction influencing both late and early times of the universe evolution. This phenomenon leads to the present speed up and to the fast expansion due to the inflationary epoch. In so doing, we are able to unify both dark energy and inflation in a single scheme, showing that the universe changes its dynamics when \({\ddot{H}\over H}=-2 \dot{H}\), at the repulsion onset time where this condition is satisfied. Further, we argue that the spatial scalar curvature can be taken as vanishing because it does not affect at all the emergence of repulsive gravity. We check the goodness of our approach through two cosmological fits involving the most recent union 2.1 supernova compilation.