H. J. Schmidt

Bio: H. J. Schmidt is an academic researcher. The author has contributed to research in topics: Gravitation & Metric (mathematics). The author has an hindex of 2, co-authored 2 publications receiving 23 citations.

On the history of fourth order metric theories of gravitation 1

Abstract: We present the history of fourth order metric theories of gravitation from its beginning in 1918 until 1988.

On the history of fourth order metric theories of gravitation

Abstract: We present the history of fourth order metric theories of gravitation from its beginning in 1918 until 1988

Introduction to the Theory of Relativity

Abstract: THE number of systematic treatises on relativity is not unduly large. This is partly because, since the first few years after Einstein's announcement of the 'general' theory in 1917, it has undergone no fundamental development, and partly because the early expositions were so good. One cannot forbear mentioning those of Eddington, von Laue, Pauli, and Weyl. But these were addressed mainly to professionals, and, in spite of subsequent accounts from various points of view, there is still room for a plain text-book suitable for undergraduates reading relativity as a special subject, or for research students needing a working knowledge of it. Prof. Bergmann's book is designed to meet such requirements. Introduction to the Theory of Relativity By Prof. Peter Gabriel Bergmann. (Prentice-Hall Physics Series.) Pp. xvi + 287. (New York: Prentice-Hall, Inc., 1942.) 4.50 dollars.

Regular black holes in quadratic gravity

Abstract: The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ayon-Beato and Garci a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.

Gravitational lensing with $ f(χ)=χ^{3/2} $ gravity in accordance with astrophysical observations

Abstract: In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity f(χ) = χ 3/2 developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemann’s tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.

Why the Big Bang Singularity Does Not Help the Kalām Cosmological Argument for Theism

Abstract: The Big Bang singularity provides little or no evidence for creation in the finite past and hence for theism Whether one dismisses singularities or takes them seriously, physics licenses no first moment of (space-)time A physical theory might lack a metric or any other notion of finite length for curves, so a general notion of "beginning" must involve a first moment The analogy between the Big Bang singularity and stellar gravitational collapse suggests that a Creator is required in the first case only if a Destroyer is needed in the second The need for and progress in quantum gravity and the underdetermination of theories by data make it difficult to take singularities seriously

A unified approach to variational derivatives of modified gravitational actions

Abstract: Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modified gravitational Lagrangian densities in spacetime dimensions n ≥ 3. We study the well-known gravitational actions such as those involving the Gauss–Bonnet and Ricci-squared, Kretchmann scalar, Weyl-squared terms and their algebraic generalizations similar to generic f(R) theories and the algebraic generalization of sixth order gravitational Lagrangians. We put forth a new model involving the gravitational Chern–Simons term and also give three-dimensional new massive gravity equations in a new form in terms of the Cotton 2-form.