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.

Regular black holes in quadratic gravity

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.

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

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

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

General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on one of the most fundamental principles of Nature, the Equivalence Principle, which represents the core of the Einstein theory of gravity. The confirmation of its validity at different scales and in different contexts represents one of the main challenges of modern physics both from the theoretical and the experimental points of view. A major issue related to this principle is the fact that we actually do not know if it is valid at quantum level. Furthermore, recent progress on relativistic theories of gravity have to take into account new issues like Dark Matter and Dark Energy, as well as the validity of fundamental principles like local Lorentz and position invariance. Experiments allow to set stringent constraints on well established symmetry laws, on the physics beyond the Standard Model of particles and interactions, and on General Relativity and its possible extensions. In this review, we discuss precision tests of gravity in General Relativity and alternative theories and their relation with the Equivalence Principle. In the first part, we discuss the Einstein Equivalence Principle according to its weak and strong formulation. We recall some basic topics of General Relativity and the necessity of its extension. Some models of modified gravity are presented in some details. The second part of the paper is devoted to the experimental tests of the Equivalence Principle in its weak formulation. We present the results and methods used in high-precision experiments, and discuss the potential and prospects for future experimental tests.

Precision Gravity Tests and the Einstein Equivalence Principle

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.

A unified approach to variational derivatives of modified gravitational actions

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

Rainer Schimming

Papers

On the history of fourth order metric theories of gravitation 1