arXiv subjects

Ludovic Ducobu

Publications and source records attributed to Ludovic Ducobu.

7 recordsLinked to original sources

arXiv2024

Metric-affine cosmological models and the inverse problem of the calculus of variations. Part II: Variational bootstrapping of the $\Lambda$CDM model

The method of variational bootstrapping, based on canonical variational completion, allows one to construct a Lagrangian for a physical theory depending on two sets of field variables, starting from a guess of the field equations for only one such set. This setup is particularly appealing for the construction of modified theories of gravity, since one can take lessons from GR for an "educated guess" of the metric field equations; the field equations for the other fields are then fixed by the obtained Lagrangian (up to terms that are completely independent from the metric tensor). In the present paper, we apply variational bootstrapping to determine metric-affine models which are, in a variational sense, closest to the $\Lambda$CDM model of cosmology. Starting from an "educated guess" that formally resembles the Einstein field equations with a cosmological "constant" (actually, a scalar function built from the metric and the connection) and a dark matter term, the method then allows to find "corrected" metric equations and to "bootstrap" the connection field equations. Lagrangians obtained via this method, though imposing some restricting criteria, still encompass a wide variety of metric-affine models. In particular, they allow for a subclass of quadratic metric-affine theories restricted to linear terms in the curvature tensor.

gr-qc↗

arXiv2024

Metric-affine cosmological models and the inverse problem of the calculus of variations. Part 1: variational bootstrapping -- the method

The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations -- based on an intuitive ``educated guess'' -- into the Euler-Lagrange one attached to a Lagrangian, by adding a canonical correction term. Here, we extend this technique to theories that involve at least two sets of dynamical variables : we show that an educated guess of the field equations with respect to one of these sets of variables only is sufficient to variationally complete these equations and recover a Lagrangian for the full theory, up to terms that do not involve the respective variables. Applying this idea to natural metric-affine theories of gravity, we prove that, starting from an educated guess of the metric equations only, one can find the full metric equations, together with a generally covariant Lagrangian for the theory, up to metric-independent terms; the latter terms (which can only involve the distortion of the connection) are then completely classified over 4-dimensional spacetimes, by techniques pertaining to differential invariants.

math-ph↗

arXiv2023

Distinctive Features of Hairy Black Holes in Teleparallel Gauss-Bonnet Gravity

We examine the teleparallel formulation of non-minimally coupled scalar Einstein-Gauss-Bonnet gravity. In the teleparallel formulation, gravity is described by torsion instead of curvature, causing the usual Gauss-Bonnet invariant expressed through curvature to decay into two separate invariants built from torsion. Consequently, the teleparallel formulation permits broader possibilities for non-minimal couplings between spacetime geometry and the scalar field. In our teleparallel theory, there are two different branches of equations in spherical symmetry depending on how one solves the antisymmetric part of the field equations, leading to a real and a complex tetrad. We first show that the real tetrad seems to be incompatible with the regularity of the equations at the event horizon, which is a symptom that scalarized black hole solutions beyond the Riemannian Einstein-Gauss-Bonnet theory might not exist. Therefore, we concentrate our study on the complex tetrad. This leads to the emergence of scalarized black hole solutions, where the torsion acts as the scalar field source. Extending our previous work, we study monomial non-minimal couplings of degrees one and two, which are intensively studied in conventional, curvature-based, scalar Einstein-Gauss-Bonnet gravity. We discover that the inclusion of torsion can potentially alter the stability of the resulting scalarized black holes. Specifically, our findings indicate that for a quadratic coupling, which is entirely unstable in the pure curvature formulation, the solutions induced by torsion may exhibit stability within certain regions of the parameter space. In a limiting case, we were also able to find black holes with a strong scalar field close to the horizon but with a vanishing scalar charge.

gr-qc↗

arXiv2023

Spontaneous Scalarization of Black Holes in Gauss-Bonnet Teleparallel Gravity

In this paper, we find new scalarized black holes by coupling a scalar field with the Gauss-Bonnet invariant in Teleparallel gravity. The Teleparallel formulation of this theory uses torsion instead of curvature to describe the gravitational interaction and it turns out that, in this language, the usual Gauss-Bonnet term in four dimensions, decays in two distinct boundary terms, the Teleparallel Gauss-Bonnet invariants. Both can be coupled individually, or in any combination to a scalar field, to obtain a Teleparallel Gauss-Bonnet extension of the Teleparallel equivalent of general relativity. The theory we study contains the familiar Riemannian Einstein-Gauss-Bonnet gravity theory as a particular limit and offers a natural extension, in which scalarization is triggered by torsion and with new interesting phenomenology. We demonstrate numerically the existence of asymptotically flat scalarized black hole solutions and show that, depending on the choice of coupling of the boundary terms, they can have a distinct behaviour compared to the ones known from the usual Einstein-Gauss-Bonnet case. More specifically, non-monotonicity of the metric functions and the scalar field can be present, a feature that was not observed until now for static scalarized black hole solutions.

gr-qc↗

arXiv2022

Scalarized Black Holes in Teleparallel Gravity

Black holes play a crucial role in the understanding of the gravitational interaction. Through the direct observation of the shadow of a black hole by the event horizon telescope and the detection of gravitational waves of merging black holes we now start to have direct access to their properties and behaviour, which means the properties and behaviour of gravity. This further raised the demand for models to compare with those observations. In this respect, an important question regarding black holes properties is to know if they can support "hairs". While this is famously forbidden in general relativity, in particular for scalar fields, by the so-called no-hair theorems, hairy black holes have been shown to exist in several class of scalar-tensor theories of gravity. In this article we investigate the existence of scalarized black holes in scalar-torsion theories of gravity. On one hand, we find exact solutions for certain choices of couplings between a scalar field and the torsion tensor of a teleparallel connection and certain scalar field potentials, and thus proof the existence of scalarized black holes in these theories. On the other hand, we show that it is possible to establish no-scalar-hair theorems similar to what is known in general relativity for other choices of these functions.

gr-qc↗

arXiv2016

Slowly rotating neutron stars in the nonminimal derivative coupling sector of Horndeski gravity

This work is devoted to the construction of slowly rotating neutron stars in the framework of the nonminimal derivative coupling sector of Horndeski theory. We match the large radius expansion of spherically symmetric solutions with cosmological solutions and we find that the most viable model has only one free parameter. Then, by using several tabulated and realistic equations of state, we establish numerically the upper bound for this parameter in order to construct neutron stars in the slow rotation approximation with the maximal mass observed today. We finally study the surface redshift and the inertia of these objects and compare them with known data.

gr-qc↗

arXiv2015

Quantum and classical probability distributions for arbitrary Hamiltonian

In the limit of large quantum excitations, the classical and quantum probability distributions for a Schrödinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is extended for one-dimensional Hamiltonians with a non-usual kinetic part. The validity of the approach is tested with a Hamiltonian containing a relativistic kinetic energy operator.

quant-ph↗