Cosmological solutions in macroscopic gravity

In the macroscopic gravity approach to the averaging problem in cosmology, the Einstein field equations on cosmological scales are modified by appropriate gravitational correlation terms. We present exact cosmological solutions to the equations of macroscopic gravity for a spatially homogeneous and isotropic macroscopic space-time and find that the correlation tensor is of the form of a spatial curvature term. We briefly discuss the physical consequences of these results.     

Helical solutions in scalar gravity

We construct solutions, for small values of G and angular frequency Ω, of special relativistic scalar gravity coupled to ideally elastic matter which have helical but no stationary or axial symmetry. They correspond to a body without any symmetries in steady rotation around one of its axes of inertia, or two bodies moving on a circle around their center of gravity. Our construction is rigorous, but modulo an unproved conjecture on the differentiability of a certain functional.     

Multipole-like solutions in metric-affine gravity

We consider a non-Riemannian metric-affine theory of gravity containing as a sector the axion-dilaton theory coming from the low energy string theory, and map the Einstein-Maxwell sector of this dilaton-gravity to it, finding a complete class of soliton and multipole-like solutions.     

Swampland dS conjecture in mimetic f(R,T) gravity

In this paper, we study a theory of gravity called mimetic f(R, T) in the presence of swampland dS conjecture. For this purpose, we introduce several inflation solutions of the Hubble parameter H(N) from f(R, T) = R + δT gravity model, in which R is Ricci scalar, and T denotes the trace of the energy–momentum tensor. Also, δ and N are the free parameter and a number of e-fold, respectively. Then we calculate quantities such as potential, Lagrange multiplier, slow-roll, and some cosmological parameters such as n_s and r. Then we challenge the mentioned inflationary model from the swampland dS conjecture. We discuss the stability of the model and investigate the compatibility or incompatibility of this inflationary scenario with the latest Planck observable data.     

On bouncing solutions in non-local gravity

A non-local modified gravity model with an analytical function of the d’Alembert operator, is considered. This model has been recently proposed as a possible way of resolving the singularities problem in cosmology. We present exact bouncing solution, which is simpler compared to the already known one in this model, in the sense it does not require an additional matter to satisfy all gravitational equations.     

Exact string-like solutions in conformal gravity

The cylindrically-symmetric static vacuum equations of Conformal Gravity are solved for the case of additional boost symmetry along the axis. We present the complete family of solutions which describe the exterior gravitational field of line sources in Conformal Gravity. We also analyze the null geodesics in these spaces.     

Analytic solutions in nonlinear massive gravity

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r(g)m(2))(1/3), where m is the graviton mass and r(g) is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.     

Static vacuum solutions in non-Riemannian gravity

In the framework of non-Riemannian geometry, we derive exact static vacuum solutions of the field equations obtained from the full equivalent version of the Einstein–Hilbert action when torsion degrees of freedom are taken into account. By imposing spherical symmetry and a suitable choice for the contorsion degrees of freedom, the static geometry provides deviations on the predictions of the observational tests predicted by General Relativity—namely on the advance of planetary perihelia and the bending of light rays—which we infer. The analytical extension is built in two particular domains of the parameter space. In the first domain we obtain a solution exhibiting an event horizon analogous to that of the Schwarzschild geometry. For the second domain, we show that the metric furnishes an exterior event horizon, and two interior horizons which enclose the singularity. For both branches we examine the effects of torsion corrections on the Hawking radiation. In this scenario the model extends Bekenstein’s black hole geometrical thermodynamics, with an extra work term connected to a torsion parameter.     

Static cosmological solutions in quadratic gravity

General Relativity and Gravitation - A correction to this paper has been published: https://doi.org/10.1007/s10714-021-02825-z     

Particle-like platonic solutions in scalar gravity

We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang–Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein–Yang–Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map of degree N=4$N=4$. We present the first two solutions of the cubic N=4$N=4$ sequence, and expect this sequence to converge to an extremal Reissner–Nordström solution with magnetic charge P=4$P=4$.     

Self-dual solutions to euclidean gravity

Recent work on Euclidean self-dual gravitational fields is reviewed. We discuss various solutions to the Einstein equations and treat asymptotically locally Euclidean self-dual metrics in detail. These latter solutions have vanishing classical action and nontrivial topological invariants, and so may play a role in quantum gravity resembling that of the Yang-Mills instantons.     

De Sitter solutions in higher order gravity

We consider de Sitter solutions, relevant for instance in studies of inflation, in cosmologies where the gravitational Lagrangian is a functionf(R),R being the scalar curvature. Previous investigations have mostly concentrated onf(R) = R+R² which always has a solution matching the conventional de Sitter one. We show that this circumstance is rather exceptional, and that one must go to higher terms to see signs of the generic behaviour, In general the de Sitter solutions are different from those of Einstein gravity. We present complete solutions for the general cubic Lagrangian. We also address the question of when the solutions to equations from truncated actions can be expected to well represent solutions of some full (and possibly unknown) theory. Such theories provide the possibility of weakening the bounds on the energy density of the inflaton, allowing an easier reconciliation of the inflationary universe with structure-forming topological defects.     

Helically symmetric N-particle solutions in scalar gravity

Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded plus half-advanced solution of the scalar wave equation, we consider an N-body problem: We investigate configurations of N particles which form an equilateral N angle and are in helical motion about their common center. We prove that there exists a unique equilibrium configuration and compute the equilibrium radius explicitly in a post-Newtonian expansion.     

Plausible black hole solutions in higher-derivative gravity

Here we obtain explicit black hole solutions in Extension Gravity models with high-order derivative terms, while the Lichnerowicz-type theorem simplifies our analysis by vanishing Ricci's scalar curvature. We find out two explicit static, spherical solutions that satisfy the presented action: the first one is the same usual Schwarzschild solution and the other one is the new non-Schwarzschild solution. It means that Schwarzschild's solution following the no-hair theorem can describe any black hole object on each gravity theory. Without considering the first law of thermodynamics for it, we show that the non-Schwarzschild solution is depending on its set of constants, and then we consider its entropy and other thermodynamic parameters for specific values of the constants.     

Cylindrical wave solutions of a scalar-tensor theory

A class of exact solutions of the cylindrically symmetric space-time with two degrees of freedom corresponding to the vacuum field equations of a scalar-tensor theory proposed by Dunn is obtained. The solutions possess wavelike character.