Radiating black hole solutions in arbitrary dimensions

We prove a theorem that characterizes a large family of non-static solutions to Einstein equations in N-dimensional space-time, representing, in general, spherically symmetric Type II fluid. It is shown that the best known Vaidya-based (radiating) black hole solutions to Einstein equations, in both four dimensions (4D) and higher dimensions (HD), are particular cases from this family. The spherically symmetric static black hole solutions for Type I fluid can also be retrieved. A brief discussion on the energy conditions, singularities and horizons is provided.     

Radiating stars with generalised Vaidya atmospheres

We model the gravitational behaviour of a radiating star when the exterior geometry is the generalised Vaidya spacetime. The interior matter distribution is shear-free and undergoing radial heat flow. The exterior energy momentum tensor is a superposition of a null fluid and a string fluid. An analysis of the junction conditions at the stellar surface shows that the pressure at the boundary depends on the interior heat flux and the exterior string density. The results for a relativistic radiating star undergoing nonadiabatic collapse are obtained as a special case. For a particular model we demonstrate that the radiating fluid sphere collapses without the appearance of the horizon at the boundary.     

The osgood criterion and finite‐time cosmological singularities

In this paper, we apply Osgood's criterion from the theory of ordinary differential equations to detect finite‐time singularities in a spatially flat FLRW universe in the context of a perfect fluid, a perfect fluid with bulk viscosity, and a Chaplygin and anti‐Chaplygin gas. In particular, we applied Osgood's criterion to demonstrate singularity behaviour for Type 0/big crunch singularities as well as Type II/sudden singularities. We show that in each case the choice of initial conditions is important as a certain number of initial conditions leads to finite‐time, Type 0 singularities, while other precise choices of initial conditions which depend on the cosmological matter parameters and the cosmological constant can avoid such a finite‐time singularity. Osgood's criterion provides a powerful and yet simple way of deducing the existence of these singularities, and also interestingly enough, provides clues of how to eliminate singularities from certain cosmological models.     

Bianchi Type V models with a matter distribution admitting anisotropic pressure and heat flow

This paper discusses the evolution of the nontilted, diagonal, nonlocally rotationally symmetric Bianchi Type V models with a matter distribution that allows anisotropic pressure and heat flow. It is found that if the entropy of such models is assumed to be increasing, the anisotropy density necessarily decreases faster than the case with perfect fluid as the source. The factor that accelerates this decrease, in viscosity approximation, is shown to be fully characterizing the effect of viscosity. The initial value equation and the energy conservation equation for such models are derived and discussed in order to find the solution of the Einstein field equations. A new approach is devised to tackle these two equations and used in obtaining an exact solution.     

Regular black holes with improved energy conditions and their analogues in fluids

On the premise of the importance of energy conditions for regular black holes, we propose a method to remedy those models that break the dominant energy condition, e.g., the Bardeen and Hayward black holes. We modify the metrics but ensure their regularity at the same time, so that the weak, null, and dominant energy conditions are satisfied, with the exception of the strong energy condition. Likewise, we prove a no-go theorem for conformally related regular black holes, which states that the four energy conditions can never be met in this class of black holes. In order to seek evidences for distinguishing regular black holes from singular black holes, we resort to analogue gravity and regard it as a tool to mimic realistic regular black holes in a fluid. The equations of state for the fluid are solved via an asymptotic analysis associated with a numerical method, which provides a modus operandi for experimental observations, in particular, the conditions under which one can simulate realistic regular black holes in the fluid.     

Can electro-magnetic field,anisotropic source and varying Λ be sufficient to produce wormhole spacetime?

It is well known that solutions of general relativity which allow for traversable wormholes require the existence of exotic matter (matter that violates weak or null energy conditions (WEC or NEC)). In this article, we provide a class of exact solution for Einstein-Maxwell field equations describing wormholes assuming the erstwhile cosmological term Λ to be space variable, viz., Λ=Λ(r). The source considered here not only a matter entirely but a sum of matters i.e. anisotropic matter distribution, electromagnetic field and cosmological constant whose effective parts obey all energy conditions out side the wormhole throat. Here violation of energy conditions can be compensated by varying cosmological constant. The important feature of this article is that one can get wormhole structure, at least theoretically, comprising with physically acceptable matters.     

The Boulware–Deser class of spacetimes radiates

We establish the result that the standard Boulware–Deser spacetime can radiate. This allows us to model the dynamics of a spherically symmetric radiating dynamical star in five-dimensional Einstein–Gauss–Bonnet gravity with three spacetime regions. The local internal region is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the vacuum Boulware–Deser exterior. Our approach allows for all three spacetime regions to be modeled by the same class of metric functions. A large family of solutions to the field equations are presented for various realistic equations of state. A comparison of our solutions with earlier well known results is undertaken and we show that Einstein–Gauss–Bonnet analogues of these solutions, including those of Husain, are contained in our family. We also generalise our results to higher dimensions.     

Spherically symmetric radiation of charge in Einstein-Maxwell theory

We give solutions of the Einstein-Maxwell equations describing the emission of charged null fluid from a spherically symmetric body. The electromagnetic field is parallel to the direction of energy propagation, is of orderr ^–2 at infinity and is not null.This work was carried out whilst I was at Queen Elizabeth College, under a Commonwealth Universities Interchange Scheme of the British Council. I would like to thank the British Council for the travel grant and London University and Queen Elizabeth College for their hospitality.     

Bianchi cosmologies with anisotropic matter: Locally rotationally symmetric models

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following. (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence “matter matters”. Finally, we indicate that our methods can probably be extended to treat a number of open problems—in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.     

On matching LTB and Vaidya spacetimes through a null hypersurface

In this work the matching of a LTB interior solution representing dust matter to the Vaidya exterior solution describing null fluid through a null hypersurface is studied. Different cases in which one is able to smoothly match these two solutions to Einstein equations along a null hypesurface are discussed.     

Exact relativistic models of perfect fluid disks in a magnetic field

Using the well-known “displace, cut and reflect” method we construct thin disks made of a perfect fluid in presence of a magnetic field. The models are based in a magnetic Reissner-Nordstrom metric of Einstein-Maxwell equations for a conformastatic spacetime. The influence of the magnetic field on the matter properties of the disk are analyzed. We also study the motion of charged test particles around the disks. We construct models of perfect fluid disks satisfying all the energy conditions.     

Impact localization and energy quantification based on the power flow: A low-power requirement approach

The increasing use of composite materials has led to a dramatic change in the definition of safety standards. In particular, composite structures may be subjected to internal damages caused by external impacts that may not be detected by classical inspection methods. Additional constraints related to energy requirements may also be considered in order to make the system autonomous and possibly self-powered. The purpose of this paper is to present a low-cost impact detection and quantification scheme for thin plates or shells giving the whole history of the structure solicitation. Based on the analysis of the energy that has flown over a monitored area through the use of the elastic Poynting vector (that relates the mechanical power density of travelling waves), it is shown that this global energy balance may be linked in a simple way to the voltage output of piezoelectric elements in open-circuit condition. From this estimation, it is therefore possible to detect if an impact occurred inside the monitored area (in this case, the global energy balance would be positive) as well as its associated energy. If the impact occurs out of the frame, the global energy (and thus the obtained estimator) would be negative because of energy dissipation caused by internal losses and almost null. Thanks to this energy flow approach, the system is also independent from the boundary conditions of the structure. Experimental measurements aiming at validating the theoretical predictions showed that the technique permits detecting the impact area (inside/outside the frame) as well as an accurate estimation of the impact energy if the latter occurred inside the frame, both on a steel plate (with different boundary conditions) and an anisotropic composite structure.     

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.     

Anisotropic fluid spheres in general relativity

A procedure is developed to find static solutions for anisotropic fluid spheres from known static solutions for perfect fluid spheres. The method is used to obtain four exact analytical solutions of Einstein’s equations for spherically symmetric self-gravitating distribution of anisotropic matter. The solutions are matched to the Schwarzschild exterior metric. The physical features of one of the solutions are briefly discussed. Many previously known perfect fluid solutions are derived as particular cases.     

Singularities in general relativity

The problem of singularities is examined from the stand-point of a local observer. A singularity is defined as a state with an infinite proper rest mass density. The approach consists of three steps: (i) The complete system of equations describing a non-symmetric motion of a perfect fluid under assumption of adiabatic thermodynamic processes and of no release of nuclear energy is reduced to six Einstein field equations and their four first integrals for six remaining unknown componentsgik. (ii) A differential relation for the behavior of the rest mass density is deduced. It shows that any inhomogeneity and anisotropy in the distribution and motion of a non-rotating ideal fluid accelerates collapse to a singularity which will be reached in a finite proper time. Collapse is also inevitable in a rotating fluid in the case of extremely high pressure when the relativistic limit of the equation of state must be applied. In the case of a lower or zero pressure the relation does not give an unambiguous answer if the matter is rotating. (iii) The influence of rotation on the motion of an incoherent matter is investigated. Some qualitative arguments are given for a possible existence of a narrow class of singularity-free solutions of Einstein equations. Assuming rotational symmetry the Einstein partial differential equations together with their first integrals are reduced to a system of simultaneous ordinary differential equations suitable for numerical integration. Without integrating this system the existence of the class of singularity-free solutions is confirmed and exactly delimited. These solutions, representing a new general relativistic effect, are, however, of no importance for the application in cosmology or astrophysics. It is proved that in all the other cases interesting from the point of view of application the occurrence of a point singularity in incoherent matter with a rotational symmetry is inevitable even if the rotation is present.Read on 15 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General Relativity     

Relativistic compact stars with charged anisotropic matter

In this article, we perform a detailed theoretical analysis of new exact solutions with anisotropic fluid distribution of matter for compact objects subject to hydrostatic equilibrium. We present a family solution to the Einstein-Maxwell equations describing a spherically symmetric, static distribution of a fluid with pressure anisotropy. We implement an embedding class one condition to obtain a relation between the metric functions. We generalize the properties of a spherical star with hydrostatic equilibrium using the generalised Tolman-Oppenheimer-Volkoff (TOV) equation. We match the interior solution to an exterior Reissner-Nordström one, and study the energy conditions, speed of sound, and mass-radius relation of the star. We also show that the obtained solutions are compatible with observational data for the compact object Her X-1. Regarding our results, the physical behaviour of the present model may serve for the modeling of ultra compact objects.     

An Exponential Shape Function for Wormholes in Modified Gravity

We propose a new exponential shape function in wormhole geometry within modified gravity. The energy conditions and the equation-of-state parameter are obtained. The radial and tangential null energy conditions, and also the weak energy condition are validated, which indicates the absence of exotic matter due to modified gravity allied with such a new proposal.     

Lie Groups of Conformal Motions Acting on Null Orbits

Space-times admitting a 3-dimensional Lie group of conformal motions acting on null orbits containing a 2-dimensional Abelian subgroup of isometries are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespective of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant energy conditions over the whole space-time manifold.