Cosmic censorship and spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.Comment: 16 pages, Latex file, two figures, uses epsf.st

Interior Weyl-type Solutions of the Einstein-Maxwell Field Equations

Static solutions of the electro-gravitational field equations exhibiting a functional relationship between the electric and gravitational potentials are studied. General results for these metrics are presented which extend previous work of Majumdar. In particular, it is shown that for any solution of the field equations exhibiting such a Weyl-type relationship, there exists a relationship between the matter density, the electric field density and the charge density. It is also found that the Majumdar condition can hold for a bounded perfect fluid only if the matter pressure vanishes (that is, charged dust). By restricting to spherically symmetric distributions of charged matter, a number of exact solutions are presented in closed form which generalise the Schwarzschild interior solution. Some of these solutions exhibit functional relations between the electric and gravitational potentials different to the quadratic one of Weyl. All the non-dust solutions are well-behaved and, by matching them to the Reissner-Nordstr\"{o}m solution, all of the constants of integration are identified in terms of the total mass, total charge and radius of the source. This is done in detail for a number of specific examples. These are also shown to satisfy the weak and strong energy conditions and many other regularity and energy conditions that may be required of any physically reasonable matter distribution.Comment: 21 pages, RevTex, to appear in General Relativity and Gravitatio

Adoption of Waste Heat Recovery Technologies: Reviewing the Relevant Barriers and Recommendations on How to Overcome Them

Data Availability: All data generated or analyzed during this study are included in this published article.Copyright © The Author(s) 2022. The wide adoption of heat recovery technologies in industry is hampered by specific “barriers” related to both technical and non-technical issues. This paper attempts to determine these barriers and make recommendations on how to address them. First, a literature review of related material is presented. Among numerous barriers, the main ones identified are (i) lack of information, (ii) lack of technology knowledge, (iii) technology risks, (iv) high initial and running and maintenance costs, (v) lack of financial support and lack of governmental incentives, (vi) size and available space limitations, (vii) lack of available infrastructure, (viii) production constraints and risk of production disruptions, (x) risk of the system negative impact on the company operations, and (xi) policy and regulations restrictions. Then, based on the above, a structured questionnaire on barriers to the adoption of waste heat recovery (WHR) technologies was prepared and issued to a number of industries throughout the European Union. Upon analyzing the questionnaire, an assessment of the importance and negative impact of each of the above-mentioned barriers is made. Subsequently, strategies and recommendations on how to overcome the barriers is reported. These recommendations are hoped to be adopted as far as possible in the packaging, installation, commissioning, and demonstration of new and old WHR technologies.European Union’s Horizon 2020 research and innovation program under Grant agreement No. 680599

Black holes vs. naked singularities formation in collapsing Einstein's clusters

Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial density, velocity and angular momentum profiles. The final state of collapse, black hole or naked singularity, turns out to depend on the order of the first non-vanishing derivatives of such functions at the centre. The work extends recent results by Harada, Iguchi and Nakao.Comment: 13 pages, LaTeX format. To appear in Physical Review

Spherical Universes with Anisotropic Pressure

Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, tau, experienced by the dust particles. The general solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed.Comment: 24 pages, 11 figures, accepted for publication in Classical and Quantum Gravit

Methodology for estimating the ground heat absorption rate of Ground Heat Exchangers

In Ground Source Heat Pump systems, the heat exchange rate is an important factor with regard to the initial cost of the system. When the Ground Heat Exchanger (GHE) is installed in a lithology with high thermal properties in the presence of groundwater, the heat exchange rates are larger than in the cases with poor thermal response of the ground and no groundwater. This research, hence, focuses on a methodology of measuring and analyzing the thermal properties of the lithologies encountered in an area, which can be used for the prediction of heat injection rates of a GHE, depending on its characteristics, the installation area ground properties and groundwater flow. A tool was created with the use of FlexPDE software, and a study case was chosen in order to validate the results. Twenty-two, 100 m in depth, boreholes located in Lefkosia (Cyprus) were tested through simulation for their geothermal performance over time. Subsequently the estimated heat load for the boreholes, after 24 h of operation in cooling mode, was used with the help of Geographic Information System software for the compilation of a heat load per meter depth map that can be transferred to the ground by a GHE. A review of similar studies and Geographical Information System applications referring to other countries is also presented and their results are compared to the results of this study. The step by step procedure presented in this paper can be used by engineers handling geothermal projects as a useful guide for sizing GHEs and calculating the heat injection rates of any area

Gravastar Solutions with Continuous Pressures and Equation of State

We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.Comment: 19 pages, 9 figures. Latest version contains new and updated references along with some clarifying remarks in the stability analysi

How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.Comment: 30 pages, 1 figure. v3: Added references and minor clarification

Static charged perfect fluid spheres in general relativity

Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. General formulas are found in many cases. Explicit new global solutions are given as illustrations. Known solutions are briefly reviewed.Comment: 23 pages, Revtex (galley), journal version, to appear in Phys.Rev.