A Theorem Relating Solutions of a Fourth-Order Theory of Gravity to General Relativity

Within a fourth-order theory of gravity we give,for a static asymptotically flat spacetime, anexpression of the active mass (gravitational mass), infirst order in the coupling constant, , of the curvature squared term in the Lagrangiandensity, a generalization of the Tolman expression forthe energy, which establishes a relationship between theactive mass and the source structure in a static spacetime. Within this approximation, we canprove that the fourth-order theory shares with Generalrelativity (GR) the property that, for sources ofcompact support, the active mass is independent of any two-dimensional surface which encloses thesupport of the matter distribution. Finally, we provethat only for conformally invariant sources thefourth-order theory and GR share the same static andasymptotically flat solutions.     

Solutions of the Field Equations and Possible Meaning of the Hermitian Theory of Relativity

A procedure is stated, which allows to build solutions of the Hermitian theory of relativity from known solutions of the general theory of relativity. Solutions depending on three co-ordinates, built from Minkowski metric, as well as Hermitian generalizations of the Weyl-Levi Civita solution are shown. They suggest that the imaginary part of the fundamental tensor may encompass fields of different physical behaviour, like the electromagnetic field and a field responsible for forces which do not depend on the distance between charges which cannot exist as individuals. In the generalizations of the Weyl-Levi Civita solution these fields appear to be decoupled from gravitation in a peculiar way.     

Kantowski-Sachs Cosmological Model in General Theory of Relativity

The field equations for perfect fluid coupled with massless scalar field are solved with two conditions p=ρ and R=AS ⁿ for Kantowski-Sachs space time in general theory of relativity. Various physical and geometrical properties of the model have also been discussed.     

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface in an asymptotically simple space-time satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on , and are equivalent to the usual constraint equations that satisfies as a space-like hypersurface in a space-time satisfying Einstein’s vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the ‘classical’ method of Lichnerowicz and York that is used to solve the usual constraint equations.     

Charged Analogues of Henning Knutsen Type Solutions in General Relativity

In the present article, we have found charged analogues of Henning Knutsen’s interior solutions which join smoothly to the Reissner–Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra’s solutions.     

Topological Field Theory Interpretation of String Topology

The string bracket introduced by Chas and Sullivan is reinterpreted from the point of view of topological field theories in the Batalin–Vilkovisky or BRST formalisms. Namely, topological action functionals for gauge fields (generalizing Chern–Simons and BF theories) are considered together with generalized Wilson loops. The latter generate a (Poisson or Gerstenhaber) algebra of functionals with values in the S¹-equivariant cohomology of the loop space of the manifold on which the theory is defined. It is proved that, in the case of GL(n,) with standard representation, the (Poisson or BV) bracket of two generalized Wilson loops applied to two cycles is the same as the generalized Wilson loop applied to the string bracket of the cycles. Generalizations to other groups are briefly described.     

A Possible Modification of Einstein's Theory of General Relativity

This article suggests a new metric theory of gravitation, in which metric field is determined not only by matter and nongravitational field but also by vector graviton field, and in principle there is no need to introduce the Einstein's tensor. In order to satisfy automatically the geodesic postulate, an additional coordinate condition is needed.For the spherically symmetric static field, it leads us to quite different conclusions from those of Einstein's general relativity in the interior region of the surface of infinite redshift. Accurate to the first order of GM/r, it obtains the same results about the four experimental tests of general relativity.     

小谈广义相对论--"从低速到高速"之五

我们已介绍过狭义相对论；在那里爱因斯坦把牛顿的相对性原理推广到包括电磁现象，但还是指惯性系说的；各个参考系是相对做匀速运动的惯性参考系．对加速参考系又该如何呢？爱因斯坦在马赫思想的影响下提出：物理规律对所有参考系，不管是惯性系还是加速系，都应该是一样的．这个进一步推广了的相对性原理叫“广义相对性原理”．它是爱因斯坦广义相对论的一个基本原理．     

Topological Field Theory and Computing with Instantons

It is well known that dynamical systems may be employed as computing machines. However, not all dynamical systems offer particular advantages compared to the standard paradigm of computation, in regard to efficiency and scalability. Recently, it was suggested that a new type of machines, named digital –hence scalable– memcomputing machines (DMMs), that employ non‐linear dynamical systems with memory, can solve complex Boolean problems efficiently. This result was derived using functional analysis without, however, providing a clear understanding of which physical features make DMMs such an efficient computational tool. Here, we show, using recently proposed topological field theory of dynamical systems, that the solution search by DMMs is a composite instanton. This process effectively breaks the topological supersymmetry common to all dynamical systems, including DMMs. The emergent long‐range order – a collective dynamical behavior– allows logic gates of the machines to correlate arbitrarily far away from each other, despite their non‐quantum character. We exemplify these results with the solution of prime factorization, but the conclusions generalize to DMMs applied to any other Boolean problem.     

Topological Quantum Field Theory on non-Abelian gerbes

The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a generalisation of the universal bundle. We comment on the construction of observables in the arising Topological Quantum Field Theory. It is also shown how the BRST operator and the trace part of a suitably truncated set of fields on the non-Abelian gerbe reduce directly to the coboundary operator and the pertinent cochains of the underlying ?ech–de Rham complex.     

A Remark on Schwarz's Topological Field Theory

The standard evaluation of the partition function Z of Schwarz's topological field theory results in the Ray–Singer analytic torsion. Here we present an alternative evaluation which results in Z=1. Mathematically, this amounts to a novel perspective on analytic torsion: it can be formally written as a ratio of volumes of spaces of differential forms which is formally equal to 1 by Hodge duality. An analogous result for Reidemeister combinatorial torsion is also obtained.     

Field Equations due to a Constant Modification in General Relativity

In this article, by adding a constant to Einstein-Hilbert action, we derive field equations for a non-vacuum space. Also we derive a general solution for these field equations, considering a de Sitter like initial geometric constraint. It is shown that how this additional constant can affect usual gravitational field equations, which are derived from general relativity.     

On Charged Analogues of Matese and Whitman Interior Solutions in General Relativity

A set of three static fluid spheres once derived by Matese and Whitman (in Phys. Rev. D 22:1270, 1980) are charged by means of a particular electric intensity to obtain compact objects like white dwarfs, quark stars and neutron stars etc. The charged objects so obtain and their neutral counterparts are analysed on astrophysical grounds. This revealed that two of the charged spheres and one of the neutral seed solutions are well behaved. The corresponding red shift and adiabatic index together with other physical entities like pressure, density and velocity of sound through the star models are studied systematically.