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     

Regular black holes in quadratic gravity

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayón-Beato and Garcí a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.     

Nonsingular black holes in quadratic Palatini gravity

We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius $r_{\mathrm{core}}\approx N_{q}^{1/2}l_{\mathrm{P}}/3$ , where l _P is the Planck length and N _q is the number of electric charges. The singularity is avoided if the mass of the object satisfies the condition $M_{0}^{2}\approx m_{\mathrm{P}}^{2} \alpha_{\mathrm{em}}^{3/2} N_{q}^{3}/2$ , where m _P is the Planck mass and α _em is the fine-structure constant. For astrophysical black holes this amount of charge is so small that their external horizon almost coincides with their Schwarzschild radius. We work within a first-order (Palatini) approach.     

Field equations for gravity quadratic in the curvature

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian—namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type—is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differ from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built.     

Cosmological solutions of a quadratic theory of gravity with torsion

Following the general approach of Hehl, and Hayashi and Shirafuji, we give the gravity equations for the lagrangian $\text{L}\text{=(}\text{e}\text{/2L}{}^2\text{)(F+}\text{1}\text{2}\text{×F}{}^2\text{) +}\text{L}{}_{\mathrm{M}}$. We have found the explicit Einstein-de Sitter solutions for a spinless dust. We have discussed in this case the singularity problem for the metric and for the torsion.     

Vacuum decay and quadratic gravity: the massive case

General Relativity and Gravitation - In this article we discuss some aspects of double field theory cosmology with an emphasis on the role played by the dilaton. The cosmological solutions of...     

Einstein gravity emerging from quantum Weyl gravity

We advocate a conformal invariant world described by the sum of the Weyl, Dirac, and Yang-Mills action. Quantum fluctuations bring back Einstein gravity so that the long-distance phenomenology is as observed. Formulas for the induced Newton's constant and Eddington's constant are derived in quantized Weyl gravity. We show that the analogue of the trace anomaly for the Weyl action is structurally similar to that for the Yang-Mills action.     

Einstein gravity as spontaneously broken Weyl gravity

We study the locally conformal invariant Weyl theory of gravitation and introduce a conformally coupled scalar field. Einstein gravity is induced by spontaneous breaking of the local conformal symmetry in an effective long range approximation. The effective potential for the scalar field is calculated at the one-loop level up to curvature squared in order in an arbitrary curved background. The non-zero vacuum expectation value of the scalar field induces the dimensional Einstein's gravitational coupling constant stably in case ofR > 0. ForR < 0, the phase transition occurs from the symmetric phase to the broken phase as the curvature decreases. This theory may be an attractive candidate for the primordial inflationary universe scenario.     

Echoes of gravity

The study of anisotropies in the Cosmic Microwave Background radiation is progressing at a phenomenal rate, both experimentally and theoretically. These anisotropies can teach us an enormous amount about the way that fluctuations were generated and the way they subsequently evolved into the clustered galaxies which are observed today. In particular, on sub-degree scales the rich structure in the anisotropy spectrum is the consequence of gravity-driven acoustic oscillations occurring before the matter in the universe became neutral. The frozen-in phases of these sound waves imprint a dependence on many cosmological parameters, that we may be on the verge of extracting.This essay received the third award from the Gravity Research Foundation, 1995-Ed.     

Topological gravity

A version of conformal gravity is formulated with a local fermionic symmetry that is reminiscent of BRST invariance. It may have mathematical applications (gravitational counterpart of Donaldson theory) or physical ones (unbroken phase of general relativity).     

Cohomological gravity

We construct a theory of cohomological gravity in arbitrary dimensions based upon a local vector supersyrnmetry algebra. The observables in this theory are polynomial, but generally non-local operators, and have a natural interpretation in terms of a universal bundle for gravity. As such, their correlation functions correspond to cohomology classes on moduli spaces of Riemannian connections. In this uniformization approach different moduli spaces are obtained by introducing curvature singularities on codimension two submanifolds via a puncture operator. This puncture operator is constructed from a naturally occurring differential form of co-degree two in the theory, and we are led to speculate on connections between this continuum quantum field theory, and the discrete Regge calculus.This essay received an honorable mention from the Gravity Research Foundation, 1992-Ed.     

Higgs-field gravity

It is shown that any excited Higgs field mediates an attractive scalar gravitational interaction of Yukawa type between the elementary particles, which become massive by the ground state of the Higgs field.