Second Order In Curvature Research Articles

Singularity Theorems in the Effective Field Theory for Quantum Gravity at Second Order in Curvature

In this paper, we discuss singularity theorems in quantum gravity using effective field theory methods. To second order in curvature, the effective field theory contains two new degrees of freedom which have important implications for the derivation of these theorems: a massive spin-2 field and a massive spin-0 field. Using an explicit mapping of this theory from the Jordan frame to the Einstein frame, we show that the massive spin-2 field violates the null energy condition, while the massive spin-0 field satisfies the null energy condition, but may violate the strong energy condition. Due to this violation, classical singularity theorems are no longer applicable, indicating that singularities can be avoided, if the leading quantum corrections are taken into account.

New class of ghost- and tachyon-free metric affine gravities

We construct the spin-projection operators for a theory containing a symmetric two-index tensor and a general three-index tensor. We then use them to analyse, at linearized level, the most general action for a metric-affine theory of gravity with terms up to second order in curvature, which depends on 28 parameters. In the metric case we recover known results. In the torsion-free case, we are able to determine the most general six-parameter class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons.

The Spectrum of Quantum Gravity

In this paper we consider the degrees of freedom beyond the graviton present in the effective field theory for quantum gravity. We point out that the position of the poles due to $${{R}^{2}}$$ and $${{R}_{{\mu \nu }}}{{R}^{{\mu \nu }}}$$ cannot be affected by operators that are higher order in curvature. On the other hand, operators of the type $$R\square R$$ will lead to new poles while shifting the positions of the poles found at second order in curvature. New degrees of freedom can be identified either, as just described, by looking at the poles of the graviton propagator corrected by quantum gravity or by mapping the Jordan frame theory to the Einstein frame theory. While this procedure is very well defined for second order curvature terms in the effective action, we point out that higher order terms in curvature lead to a nonlinear and non-local relation between the propagating scalar degree of freedom and the Ricci scalar. We show how to resolve these ambiguities and how to obtain the correct action in the Einstein frame. We illustrate our results by looking at $$f(R)$$ gravity.

Quantum gravitational corrections to a star metric and the black hole limit

In this paper we consider the full set of quantum gravitational corrections to a star metric to second order in curvature. As we use an effective field theoretical approach, these corrections apply to any model of quantum gravity that is based on general coordinate invariance. We then discuss the black hole limit and identify an interesting phenomenon which could shed some light on the nature of astrophysical black holes: while star metrics receive corrections at second order in curvature, vacuum solutions such as black hole metrics do not. What happens to these corrections when a star collapses?

Hawking radiation of non-Schwarzschild black holes in higher derivative gravity: A crucial role of grey-body factors

The higher derivative gravity includes corrections of the second order in curvature and allows for both Schwarzschild and non-Schwarzschild asymptotically flat black-hole solutions. Here we find the grey-body factors and energy emission rates for Hawking radiation of test Dirac and electromagnetic fields in the vicinity of such a non-Schwarzschild black hole. The temperature and mass of the black hole monotonically decrease from its Schwarzschild value to zero when the coupling constant is increased up to its extremal value. Nevertheless, for small and moderate values of the coupling constant the Hawking radiation is enhanced, and only in the regime of large coupling it is suppressed, as one could expect. The reason for such counter-intuitive behavior is the important role of the grey-body factors: for small and moderate couplings the temperature falls relatively slowly, while the effective potentials for black holes of the same mass become considerably lower, allowing for much higher transmission rates. We have also estimated the lifetime of such black holes and shown that the range of black-hole masses at which ultra-relativistic emission of massive electrons and positrons starts is shifted towards smaller black-hole masses when the coupling constant is large.

Vanishing of quantum gravitational corrections to vacuum solutions of general relativity at second order in curvature

In this note we prove that quantum gravitational corrections to vacuum solutions of Einstein's equations vanish at second order in curvature.

Gravitational effective action at second order in curvature and gravitational waves

We consider the full effective theory for quantum gravity at second order in curvature including non-local terms. We show that the theory contains two new degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost and a massive scalar field. Furthermore, we show that it is impossible to fine-tune the parameters of the effective action to eliminate completely the classical spin-2 ghost because of the non-local terms in the effective action. Being a classical field, it is not clear anyway that this ghost is problematic. It simply implies a repulsive contribution to Newton’s potential. We then consider how to extract the parameters of the effective action and show that it is possible to measure, at least in principle, the parameters of the local terms independently of each other using a combination of observations of gravitational waves and measurements performed by pendulum type experiments searching for deviations of Newton’s potential.

Perturbed black holes in Einstein-dilaton-Gauss-Bonnet gravity: Stability, ringdown, and gravitational-wave emission

Gravitational waves emitted by distorted black holes---such as those arising from the coalescence of two neutron stars or black holes---carry not only information about the corresponding spacetime but also about the underlying theory of gravity. Although general relativity remains the simplest, most elegant and viable theory of gravitation, there are generic and robust arguments indicating that it is not the ultimate description of the gravitational universe. Here we focus on a particularly appealing extension of general relativity, which corrects Einstein's theory through the addition of terms which are second order in curvature: the topological Gauss-Bonnet invariant coupled to a dilaton. We study gravitational-wave emission from black holes in this theory, and {\bf(i)} find strong evidence that black holes are linearly (mode) stable against both axial and polar perturbations; {\bf(ii)} discuss how the quasinormal modes of black holes can be excited during collisions involving black holes, and finally {\bf(iii)} show that future ringdown detections with large signal-to-noise ratio would improve current constraints on the coupling parameter of the theory.

Accelerated expansion of the Universe in a higher dimensional modified gravity with Euler-Poincaré terms

A higher dimensional modified gravity theory with an action that includes dimensionally continued Euler-Poincaré forms up to second order in curvatures is considered. The variational field equations are derived. Matter in the Universe at large scales is modeled by a fluid satisfying an equation of state with dimensional dichotomy. We study solutions that describe higher dimensional steady state cosmologies with constant volume for which the three dimensional external space is expanding at an accelerated rate while the (compact) internal space is contracting. We showed that the second order Euler-Poincaré term in the constructions of higher dimensional steady state cosmologies could be crucial.

Particle production from nonlocal gravitational effective action

In this paper we show how the nonlocal effective action for gravity, obtained after integrating out the matter fields, can be used to compute particle production and spectra for different space-time metrics. Applying this technique to several examples, we find that the perturbative calculation of the effective action up to second order in curvatures yields exactly the same results for the total number of particles as the Bogolyubov transformations method, in the case of massless scalar fields propagating in a Robertson-Walker space-time. Using an adiabatic approximation we also obtain the corresponding spectra and compare the results with the traditional WKB approximation.

Vesicles in solutions of hard rods

The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shapes. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is nonanalytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the nonanalytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rodlike (colloidal) particles. The presence of the particles induces a change in the equilibrium shape and a shift of the prolate-oblate transition in the vesicle phase diagram, which are calculated within the framework of the spontaneous curvature model. As a consequence of the special form of the energy contribution due to the rods, these changes cannot be accounted for by a simple rescaling of the elastic constants of the vesicle as for solutions of spherical colloids or polymers.

Dynamics of massless higher spins in the second order in curvatures

The consistent equations of motion of interacting massless fields of all spins s = 0, 1 2 , 1, …, ∞ are constructed explicitly to the second order of the expansion in powers of the higher spin strengths.