Narrow Results

In this study, we explore various essential aspects of a noncommutative theory that incorporates space deformation. Through the Extended Gravitational Decoupling (EGD) approach within the Strong Energy Condition (SEC), we investigate the gravitational decoupling method to obtain static black hole solutions that satisfy Einstein’s field equations with a vacuum tensor. The analysis concentrates on the thermodynamics of the static solution, examining and deriving expressions for various thermodynamic quantities. This investigation explores how temperature, free energy, and specific heat depend on the horizon radius, considering different values for both hairy and noncommutative parameters. The study suggests that thermodynamically, smaller hairy black holes exhibit greater stability compared to larger ones. It also reveals a nontrivial relationship between the horizon radius, temperature range, and specific values of the hairy parameters for static hairy black holes when considered in thermodynamic equilibrium with their Hawking radiation. The discussion extends to the implications of the first law of black hole thermodynamics in the context of the noncommutative hairy case.

The energy distribution of black holes with a dilaton and a pure monopole field is calculated by using Møller's energy–momentum complex. The four-dimensional space–times considered are static, spherically symmetric and asymptotically flat, exact solutions stemming from an action that besides gravity contains a dilaton field and a pure monopole field. The resulting "hairy" black holes have an essential singularity at the origin and two horizons. The energy obtained depends on the value of the dilaton field, the monopole charge and the ADM mass. All the momenta vanish for the space–time geometries considered.

We study the periapsis shift of a quasi-circular orbit in general static spherically symmetric spacetimes. We derive two formulae in full order with respect to the gravitational field, one in terms of the gravitational mass $m$ and the Einstein tensor and the other in terms of the orbital angular velocity and the Einstein tensor. These formulae reproduce the well-known ones for the forward shift in the Schwarzschild spacetime. In a general case, the shift deviates from that in the vacuum spacetime due to a particular combination of the components of the Einstein tensor at the radius $r$ of the orbit. The formulae give a backward shift due to the extended-mass effect in Newtonian gravity. In general relativity, in the weak-field and diffuse regime, the active gravitational mass density, ${\rho }_A=(ϵ+p_r+2p_t)/c^2$, plays an important role, where $ϵ$, $p_r$ and $p_t$ are the energy density, the radial stress and the tangential stress of the matter field, respectively. We show that the shift is backward if ${\rho }_A$ is beyond a critical value ${\rho }_c\simeq 2.8\times 10^{-15}$g/cm³${(m/M_{\odot })}^2{(r/\mathrm{\text{a.u.}})}^{-4}$, while a forward shift greater than that in the vacuum spacetime instead implies ${\rho }_A<0$, i.e. the violation of the strong energy condition, and thereby provides evidence for dark energy. We obtain new observational constraints on ${\rho }_A$ in the Solar System and the Galactic Centre.

We study the scalar sector of the quasinormal modes of charged general relativistic, static and spherically symmetric black holes coupled to nonlinear electrodynamics and embedded in a class of scalar-tensor theories. It turns out that for certain values of the parameters unstable modes are present. This implies the existence of scalar-tensor black holes with primary hair that bifurcate from the embedded general relativistic black-hole solutions at critical values of the parameters corresponding to the static zero-modes. We prove that such scalar-tensor black holes really exist by solving the full system of scalartensor field equations for the static, spherically symmetric case. The obtained branches of hairy black holes are in one to one correspondence with the bounded states of the potential governing the linear perturbations of the scalar field. The stability of the new hairy black holes is also examined.