Gravitational radiation from dynamical black holes

An effective energy tensor for gravitational radiation is identified for uniformly expanding flows of the Hawking mass-energy. It appears in an energy conservation law expressing the change in mass due to the energy densities of matter and gravitational radiation, with respect to a Killing-like vector encoding a preferred flow of time outside a black hole. In a spin-coefficient formulation, the components of the effective energy tensor can be understood as the energy densities of ingoing and outgoing, transverse and longitudinal gravitational radiation. By anchoring the flow to the trapping horizon of a black hole in a given sequence of spatial hypersurfaces, there is a locally unique flow and a measure of gravitational radiation in the strong-field regime.Comment: 5 revtex4 pages. Additional comment

M{\o}ller Energy for the Kerr-Newman metric

The energy distribution in the Kerr-Newman space-time is computed using the M{\o}ller energy-momentum complex. This agrees with the Komar mass for this space-time obtained by Cohen and de Felice. These results support the Cooperstock hypothesis.Comment: 8 pages, 1 eps figure, RevTex, accepted for publication in Mod. Phys. Lett.

A Cosmological Constant Limits the Size of Black Holes

In a space-time with cosmological constant $\Lambda>0$ and matter satisfying the dominant energy condition, the area of a black or white hole cannot exceed $4\pi/\Lambda$. This applies to event horizons where defined, i.e. in an asymptotically deSitter space-time, and to outer trapping horizons (cf. apparent horizons) in any space-time. The bound is attained if and only if the horizon is identical to that of the degenerate `Schwarzschild-deSitter' solution. This yields a topological restriction on the event horizon, namely that components whose total area exceeds $4\pi/\Lambda$ cannot merge. We discuss the conjectured isoperimetric inequality and implications for the cosmic censorship conjecture.Comment: 10 page

Energy Associated with Schwarzschild Black Hole in a Magnetic Universe

In this paper we obtain the energy distribution associated with the Ernst space-time (geometry describing Schwarzschild black hole in Melvin's magnetic universe) in Einstein's prescription. The first term is the rest-mass energy of the Schwarzschild black hole, the second term is the classical value for the energy of the uniform magnetic field and the remaining terms in the expression are due to the general relativistic effect. The presence of the magnetic field is found to increase the energy of the system.Comment: RevTex, 8 pages, no figures, a few points are clarified, to appear in Int. J. Mod. Phys. A. This paper is dedicated to Professor G. F. R. Ellis on the occasion of his 60th birthda

Construction and enlargement of traversable wormholes from Schwarzschild black holes

Analytic solutions are presented which describe the construction of a traversable wormhole from a Schwarzschild black hole, and the enlargement of such a wormhole, in Einstein gravity. The matter model is pure radiation which may have negative energy density (phantom or ghost radiation) and the idealization of impulsive radiation (infinitesimally thin null shells) is employed.Comment: 22 pages, 7 figure

An algorithm to identify rheumatoid arthritis in primary care: a Clinical Practice Research Datalink study

Objective: Rheumatoid arthritis (RA) is a multisystem, inflammatory disorder associated with increased levels of morbidity and mortality. While much research into the condition is conducted in the secondary care setting, routinely collected primary care databases provide an important source of research data. This study aimed to update an algorithm to define RA that was previously developed and validated in the General Practice Research Database (GPRD). Methods: The original algorithm consisted of two criteria. Individuals meeting at least one were considered to have RA. Criterion 1:≥1 RA Read code and a disease modifying antirheumatic drug (DMARD) without an alternative indication. Criterion 2:≥2RA Read codes, with at least one 'strong' code and no alternative diagnoses. Lists of codes for consultations and prescriptions were obtained from the authors of the original algorithm where these were available, or compiled based on the original description and clinical knowledge. 4161 people with a first Read code for RA between 1 January 2010 and 31 December 2012 were selected from the Clinical Practice Research Datalink (CPRD, successor to the GPRD), and the criteria applied. Results: Code lists were updated for the introduction of new Read codes and biological DMARDs. 3577/ 4161 (86%) of people met the updated algorithm for RA, compared to 61% in the original development study. 62.8% of people fulfilled both Criterion 1 and Criterion 2. Conclusions: Those wishing to define RA in the CPRD, should consider using this updated algorithm, rather than a single RA code, if they wish to identify only those who are most likely to have RA

Energy distribution in a BTZ black hole spacetime

We evaluate the energy distribution associated with the (2+1)-dimensional rotating BTZ black hole. The energy-momentum complexes of Landau-Lifshitz and Weinberg are employed for this computation. Both prescriptions give exactly the same form of energy distribution. Therefore, these results provide evidence in support of the claim that, for a given gravitational background, different energy-momentum complexes can give identical results in three dimensions, as it is the case in four dimensions.Comment: 16 pages, LaTeX; v2: comments, clarifications and references added, version to appear in Int.J.Mod.Phys.

Energy Distribution in Melvin's Magnetic Universe

We use the energy-momentum complexes of Landau and Lifshitz and Papapetrou to obtain the energy distribution in Melvin's magnetic universe. For this space-time we find that these definitions of energy give the same and convincing results. The energy distribution obtained here is the same as we obtained earlier for the same space-time using the energy-momentum complex of Einstein. These results uphold the usefulness of the energy-momentum complexes.Comment: 8 pages, RevTex, no figure

Gravitational waves, black holes and cosmic strings in cylindrical symmetry

Gravitational waves in cylindrically symmetric Einstein gravity are described by an effective energy tensor with the same form as that of a massless Klein- Gordon field, in terms of a gravitational potential generalizing the Newtonian potential. Energy-momentum vectors for the gravitational waves and matter are defined with respect to a canonical flow of time. The combined energy-momentum is covariantly conserved, the corresponding charge being the modified Thorne energy. Energy conservation is formulated as the first law expressing the gradient of the energy as work and energy-supply terms, including the energy flux of the gravitational waves. Projecting this equation along a trapping horizon yields a first law of black-hole dynamics containing the expected term involving area and surface gravity, where the dynamic surface gravity is defined with respect to the canonical flow of time. A first law for dynamic cosmic strings also follows. The Einstein equation is written as three wave equations plus the first law, each with sources determined by the combined energy tensor of the matter and gravitational waves.Comment: 10 pages, revtex. Published version with further detail

Complex lapse, complex action and path integrals

Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.Comment: 12 pages, Te