The physical acceptability conditions and the strategies to obtain anisotropic compact objects

We studied five methods to include anisotropy, or unequal stress distributions, in general relativistic matter configurations. We used nine acceptability conditions that the metric and physical variables must meet to determine if our models were astrophysically viable. Our analysis found the most effective way to introduce anisotropy while keeping a simple density profile. We also found a practical "rule of thumb" that relates the density at the boundary to the density at the centre of relativistic matter distributions. Additionally, we calculated the configuration radius and encountered that values observed by NICER for PSR J0740+6620 are consistent with several acceptable matter configurations, both isotropic and anisotropic.Comment: 20 pages, 3 figures. Typo correctio

Diseño de un curso SPOC sobre modelización matemática

Memoria ID-029. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2019-2020

Fomento del uso del programa Mathematica en las asignaturas de Ingeniería

Memoria ID-0190. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2016-2017

Elaboración de recursos didácticos para ingeniería mediante el programa Mathematica

Memoria ID-0079. Ayudas de la Universidad de Salamanca para la innovación docente, curso 2017-2018

Non-Static Fluid Spheres Admitting a Conformal Killing Vector: Exact Solutions

We carry on a general study on non-static spherically symmetric fluids admitting a conformal Killing vector (CKV). Several families of exact analytical solutions are found for different choices of the CKV in both the dissipative and the adiabatic regime. To specify the solutions, besides the fulfillment of the junction conditions on the boundary of the fluid distribution, different conditions are imposed, such as a vanishing complexity factor and quasi-homologous evolution. A detailed analysis of the obtained solutions and its prospective applications to astrophysical scenarios, as well as alternative approaches to obtain new solutions, are discussed

Hyperbolically Symmetric Versions of Lemaitre–Tolman–Bondi Spacetimes

We study fluid distributions endowed with hyperbolic symmetry, which share many common features with Lemaitre–Tolman–Bondi (LTB) solutions (e.g., they are geodesic, shearing, and nonconformally flat, and the energy density is inhomogeneous). As such, they may be considered as hyperbolic symmetric versions of LTB, with spherical symmetry replaced by hyperbolic symmetry. We start by considering pure dust models, and afterwards, we extend our analysis to dissipative models with anisotropic pressure. In the former case, the complexity factor is necessarily nonvanishing, whereas in the latter cases, models with a vanishing complexity factor are found. The remarkable fact is that all solutions satisfying the vanishing complexity factor condition are necessarily nondissipative and satisfy the stiff equation of state

Non-Static Fluid Spheres Admitting a Conformal Killing Vector: Exact Solutions

We carry on a general study on non-static spherically symmetric fluids admitting a conformal Killing vector (CKV). Several families of exact analytical solutions are found for different choices of the CKV in both the dissipative and the adiabatic regime. To specify the solutions, besides the fulfillment of the junction conditions on the boundary of the fluid distribution, different conditions are imposed, such as a vanishing complexity factor and quasi-homologous evolution. A detailed analysis of the obtained solutions and its prospective applications to astrophysical scenarios, as well as alternative approaches to obtain new solutions, are discussed

Esferas estáticas en relatividad general

Recientemente K. Lake ha presentado un algoritmo que permite obtener todas las soluciones estáticas de las ecuaciones de Einstein, para el caso de un fluido perfecto con simetría esférica, a partir de una sola función dada. Este algoritmo se extiende al caso de un fluido localmente anisótropo. Como era de esperar, este nuevo formalismo requiere del conocimiento de dos funciones en lugar de una. Para ilustrar el método se deducen de nuevo algunas  soluciones conocidas.    Recently K. Lake has presented an algorithm that allows to obtain all the static solutions of the equations of Einstein, in the case of a perfect fluid with spherical symmetry, from one given function. This algorithm is then extended to the case of locally anisotropic fluid. Predictably, this new formalism requires knowledge of two functions instead of one. To illustrate the method some known solutions are restored.

Acceptability conditions and relativistic anisotropic generalized polytropes

This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state $$P=\kappa {\rho }^{\gamma }+\alpha \rho -\beta$$ for a heuristic anisotropy. We integrated the corresponding Lane–Emden equation for several hundred models and found the parameter-space portion ensuring the physical acceptability of the configurations. Polytropes based on the total energy density are more viable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tangential pressures are greater than radial ones are also more acceptable. Finally, convective disturbances do not generate cracking instabilities. Several models emerging from our simulations could represent candidates of astrophysical compact objects

The physical acceptability conditions and the strategies to obtain anisotropic compact objects

We studied five methods to include anisotropy, or unequal stress distributions, in general relativistic matter configurations. We used nine acceptability conditions that the metric and physical variables must meet to determine if our models were astrophysically viable. Our analysis found the most effective way to introduce anisotropy while keeping a simple density profile. We also found a practical “rule of thumb” that relates the density at the boundary to the density at the centre of relativistic matter distributions. Additionally, we calculated the configuration radius and encountered that values observed by NICER for PSR J0740+6620 are consistent with several acceptable matter configurations, both isotropic and anisotropic