Solutions In Scalar-tensor Theory Research Articles

From static to Vaidya solutions in scalar tensor theories

From static to Vaidya solutions in scalar tensor theories

Robustness of kinetic screening against matter coupling

We investigate neutron star solutions in scalar-tensor theories of gravity with first-order derivative self-interactions in the action and in the matter coupling. We assess the robustness of the kinetic screening mechanism present in these theories against general conformal couplings to matter. The latter include ones leading to the classical Damour-Esposito-Far\`ese scalarization, as well as ones depending on the kinetic term of the scalar field. We find that kinetic screening always prevails over scalarization, and that kinetic couplings with matter enhance the suppression of scalar gradients inside the star even more, without relying on the non-linear regime. Fine tuning the kinetic coupling with the derivative self-interactions in the action allows one to partially cancel the latter, resulting in a weakening of kinetic screening inside the star. This effect represents a novel way to break screening mechanisms inside matter sources, and provides new signatures that might be testable with astrophysical observations.

Linear perturbations of Einstein-Gauss-Bonnet black holes

We study linear perturbations about non rotating black hole solutions in scalar-tensor theories, more specifically Horndeski theories. We consider two particular theories that admit known hairy black hole solutions. The first one, Einstein-scalar-Gauss-Bonnet theory, contains a Gauss-Bonnet term coupled to a scalar field, and its black hole solution is given as a perturbative expansion in a small parameter that measures the deviation from general relativity. The second one, known as 4-dimensional-Einstein-Gauss-Bonnet theory, can be seen as a compactification of higher-dimensional Lovelock theories and admits an exact black hole solution. We study both axial and polar perturbations about these solutions and write their equations of motion as a first-order (radial) system of differential equations, which enables us to study the asymptotic behaviours of the perturbations at infinity and at the horizon following an algorithm we developed recently. For the axial perturbations, we also obtain effective Schrödinger-like equations with explicit expressions for the potentials and the propagation speeds. We see that while the Einstein-scalar-Gauss-Bonnet solution has well-behaved perturbations, the solution of the 4-dimensional-Einstein-Gauss-Bonnet theory exhibits unusual asymptotic behaviour of its perturbations near its horizon and at infinity, which makes the definition of ingoing and outgoing modes impossible. This indicates that the dynamics of these perturbations strongly differs from the general relativity case and seems pathological.

Black hole solutions in scalar-tensor symmetric teleparallel gravity

Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis we also derive no-hair theorems for the theory. Since the symmetric teleparallel scalar-tensor models also include f(Q) gravity, we shortly discuss this case and further prove a theorem which says that by imposing that the metric functions are the reciprocal of each other (grr = 1/gtt ), the f(Q) gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.

Neutron stars with a generalized Proca hair and spontaneous vectorization

In a class of generalized Proca theories, we study the existence of neutron star solutions with a nonvanishing temporal component of the vector field $A_\mu$ approaching 0 toward spatial infinity, as they may be the endpoints of tachyonic instabilities of neutron star solutions in general relativity with $A_{\mu}=0$. Such a phenomenon is called spontaneous vectorization, which is analogous to spontaneous scalarization in scalar-tensor theories with nonminimal couplings to the curvature or matter. For the nonminimal coupling $\beta X R$, where $\beta$ is a coupling constant and $X=-A_{\mu}A^{\mu}/2$, we show that there exist both 0-node and 1-node vector-field solutions, irrespective of the choice of the equations of state of nuclear matter. The 0-node solution, which is present only for $\beta=-{\cal O}(0.1)$, may be induced by some nonlinear effects such as the selected choice of initial conditions. The 1-node solution exists for $\beta=-{\cal O}(1)$, which suddenly emerges above a critical central density of star and approaches the general relativistic branch with the increasing central density. We compute the mass $M$ and radius $r_s$ of neutron stars for some realistic equations of state and show that the $M$-$r_s$ relations of 0-node and 1-node solutions exhibit notable difference from those of scalarized solutions in scalar-tensor theories. Finally, we discuss the possible endpoints of tachyonic instabilities.

Phantom evolving wormhole solutions in scalar-tensor theories

Wormholes are considered as one of the most interesting hypothetical objects whose existence is also predicted by Einstein’s relativity. It is generally argued that the theoretical construction of such objects demands an exotic kind of anisotropic matter (a matter which is not compatible with the energy constraints). The existence of such matter is regarded as a primary condition for the existence of such geometries. The present manuscript examines the existence of wormhole structures in f(R, ϕ) gravity by taking hyperbolic shape function with constant and logarithmic redshift functions into account. For this purpose, we check the validity of energy condition bounds in both cases graphically. It is found that the wormhole geometries can be constructed for both constant and logarithmic redshift functions when anisotropic phantom fluid characterized by the EoS ωr=pr/ρ<−1 is taken. Further, we discuss the background features of such objects.

Compactness of neutron stars and Tolman VII solutions in scalar-tensor gravity

We systematically examine the compactness of neutron stars as Tolman VII solutions in scalar-tensor theory of gravity. As a result, when the coupling constant is confined to values provided by astronomical observations we show that the maximum compactness of neutron stars in general relativity is higher than that in scalar-tensor gravity. In addition, we show that although ultra-compact stars, with radius smaller than the Regge-Wheeler potential peak, can exist in general relativity (e.g., Tolman VII solution), their scalarized counterparts cannot {be constructed} even in the limiting case of uniform density stars.

Gravitational waves from quasinormal modes of a class of Lorentzian wormholes

Quasinormal modes of a two-parameter family of Lorentzian wormhole spacetimes, which arise as solutions in a specific scalar-tensor theory associated with braneworld gravity, are obtained using standard numerical methods. Being solutions in a scalar-tensor theory, these wormholes can exist with matter satisfying the Weak Energy Condition. If one posits that the end-state of stellar-mass binary black hole mergers, of the type observed in GW150914, can be these wormholes, then we show how their properties can be measured from their distinct signatures in the gravitational waves emitted by them as they settle down in the post-merger phase from an initially perturbed state. We propose that their scalar quasinormal modes correspond to the so-called breathing modes, which normally arise in gravitational wave solutions in scalar-tensor theories. We show how the frequency and damping time of these modes depend on the wormhole parameters, including its mass. We derive the mode solutions and use them to determine how one can measure those parameters when these wormholes are the endstate of binary black hole mergers. Specifically, we find that if a breathing mode is observed in LIGO-like detectors with design sensitivity, and has a maximum amplitude equal to that of the tensor mode that was observed of GW150914, then for a range of values of the wormhole parameters, we will be able to discern it from a black hole. If in future observations we are able to confirm the existence of such wormholes, we would, at one go, have some indirect evidence of a modified theory of gravity as well as extra spatial dimensions.

Plane wave solutions in scalar tensor theories and solutions of source-free Einstein–Maxwell theory

Vacuum solutions of the field equations that satisfy the original notion of the plane wave, namely gμν=gμν(Z), Z=Σμaμxμ, aμ’s being constants and gμνZ,μZ,ν=0, are sought for both Brans–Dicke scalar–tensor theory and the more recent scalar–tensor theory due to Sen and Dunn. (Here Greek letters range from 1 to 4 and Latin letters from 1 to 3.) A complete set of solutions are obtained for both cases. Although not required at the outset, it turns out that, in both cases, the scalar field is also function of Z alone. As a by-product, one gets the complete set of solutions of the Einstein–Maxwell equations for the null electromagnetic field for the cases when gμν satisfies the above-mentioned requirement.