Gravitation

About: Gravitation is a research topic. Over the lifetime, 29306 publications have been published within this topic receiving 821510 citations.

Parameterized Beyond-Einstein Growth

Abstract: A single parameter, the gravitational growth index gamma, succeeds in characterizing the growth of density perturbations in the linear regime separately from the effects of the cosmic expansion. The parameter is restricted to a very narrow range for models of dark energy obeying the laws of general relativity but can take on distinctly different values in models of beyond-Einstein gravity. Motivated by the parameterized post-Newtonian (PPN) formalism for testing gravity, we analytically derive and extend the gravitational growth index, or Minimal Modified Gravity, approach to parameterizing beyond-Einstein cosmology. The analytic formalism demonstrates how to apply the growth index parameter to early dark energy, time-varying gravity, DGP braneworld gravity, and some scalar-tensor gravity.

Implications from GW170817 and I-Love-Q relations for relativistic hybrid stars

Abstract: Gravitational wave observations of GW170817 placed bounds on the tidal deformabilities of compact stars, allowing one to probe equations of state for matter at supranuclear densities. Here we design new parametrizations for hybrid hadron-quark equations of state, which give rise to low-mass twin stars, and test them against GW170817. We find that GW170817 is consistent with the coalescence of a binary hybrid star-neutron star. We also test and find that the I-Love-Q relations for hybrid stars in the third family agree with those for purely hadronic and quark stars within $\ensuremath{\sim}3%$ for both slowly and rapidly rotating configurations, implying that these relations can be used to perform equation-of-state independent tests of general relativity and to break degeneracies in gravitational waveforms for hybrid stars in the third family as well.

Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

Abstract: We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.

Dynamics of Charged Particles and their Radiation Field

Abstract: The motion of a charged particle interacting with its own electromagnetic field is an area of research that has a long history; this problem has never ceased to fascinate its investigators. On the one hand the theory ought to be straightforward to formulate: one has Maxwell's equations that tell the field how to behave (given the motion of the particle), and one has the Lorentz-force law that tells the particle how to move (given the field). On the other hand the theory is fundamentally ambiguous because of the field singularities that necessarily come with a point particle. While each separate sub-problem can easily be solved, to couple the field to the particle in a self-consistent treatment turns out to be tricky. I believe it is this dilemma (the theory is straightforward but tricky) that has been the main source of the endless fascination. For readers of Classical and Quantum Gravity, the fascination does not end there. For them it is also rooted in the fact that the electromagnetic self-force problem is deeply analogous to the gravitational self-force problem, which is of direct relevance to future gravitational wave observations. The motion of point particles in curved spacetime has been the topic of a recent Topical Review [1], and it was the focus of a recent Special Issue [2]. It is surprising to me that radiation reaction is a subject that continues to be poorly covered in the standard textbooks, including Jackson's bible [3]. Exceptions are Rohrlich's excellent text [4], which makes a very useful introduction to radiation reaction, and the Landau and Lifshitz classic [5], which contains what is probably the most perfect summary of the foundational ideas (presented in characteristic terseness). It is therefore with some trepidation that I received Herbert Spohn's book, which covers both the classical and quantum theories of a charged particle coupled to its own field (the presentation is limited to flat spacetime). Is this the text that graduate students and researchers should turn to in order to get a complete and accessible education in radiation reaction? My answer is that while the book does indeed contain a lot of useful material, it is not a very accessible source of information, and it is certainly not a student-friendly textbook. Instead, the book presents a technical account of the author's personal take on the theory, and represents a culminating summary of the author's research contributions over more than a decade. The book is written in a fairly mathematical style (the author is Professor of Mathematical Physics at the Technische Universitat in Munich), and it very much emphasises mathematical rigour. This makes the book less accessible than I would wish it to be, but this is perhaps less a criticism than a statement about my taste, expectation, and attitude. The presentation of the classical theory begins with a point particle, but Spohn immediately smears the charge distribution to eliminate the vexing singularities of the retarded field. He considers both the nonrelativistic Abraham model (in which the extended particle is spherically symmetric in the laboratory frame) and the relativistic Lorentz model (in which the particle is spherical in its rest frame). In Spohn's work, the smearing of the charge distribution is entirely a mathematical procedure, and I would have wished for a more physical discussion. A physically extended body, held together against electrostatic repulsion by cohesive forces (sometimes called Poincar? stresses) would make a sound starting point for a classical theory of charged particles, and would have nicely (and physically) motivated the smearing operation adopted in the book. Spohn goes on to derive energy?momentum relations for the extended objects, and to obtain their equations of motion. A compelling aspect of his presentation is that he formally introduces the 'adiabatic limit', the idea that the external fields acting on the charged body should have length and time scales that are long compared with the particle's internal scales (respectively the electrostatic classical radius and its associated time scale). As a consequence, the equations of motion do not involve a differentiated acceleration vector (as is the case for the Abraham?Lorentz?Dirac equations) but are proper second-order differential equations for the position vector. In effect, the correct equations of motion are obtained from the Abraham?Lorentz?Dirac equations by a reduction-of-order procedure that was first proposed (as far as I know) by Landau and Lifshitz [5]. In Spohn's work this procedure is not {\it ad hoc}, but a natural consequence of the adiabatic approximation. An aspect of the classical portion of the book that got me particularly excited is Spohn's proposal for an experimental test of the predictions of the Landau?Lifshitz equations. His proposed experiment involves a Penning trap, a device that uses a uniform magnetic field and a quadrupole electric field to trap an electron for very long times. Without radiation reaction, the motion of an electron in the trap is an epicycle that consists of a rapid (and small) cyclotron orbit superposed onto a slow (and large) magnetron orbit. Spohn shows that according to the Landau?Lifshitz equations, the radiation reaction produces a damping of the cyclotron motion. For reasonable laboratory situations this damping occurs over a time scale of the order of 0.1 second. This experiment might well be within technological reach. The presentation of the quantum theory is based on the nonrelativistic Abraham model, which upon quantization leads to the well-known Pauli-Fierz Hamiltonian of nonrelativistic quantum electrodynamics. This theory, an approximation to the fully relativistic version of QED, has a wide domain of validity that includes many aspects of quantum optics and laser-matter interactions. As I am not an expert in this field, my ability to review this portion of Spohn's book is limited, and I will indeed restrict myself to a few remarks. I first admit that I found Spohn's presentation to be tough going. Unlike the pair of delightful books by Cohen-Tannoudji, Dupont-Roc, and Grynberg [6, 7], this is not a gentle introduction to the quantum theory of a charged particle coupled to its own electromagnetic field. Instead, Spohn proceeds rather quickly through the formulation of the theory (defining the Hamiltonian and the Hilbert space) and then presents some applications (for example, he constructs the ground states of the theory, he examines radiation processes, and he explores finite-temperature aspects). There is a lot of material in the eight chapters devoted to the quantum theory, but my insufficient preparation and the advanced nature of Spohn's presentation were significant obstacles; I was not able to draw much appreciation for this material. One of the most useful resources in Spohn's book are the historical notes and literature reviews that are inserted at the end of each chapter. I discovered a wealth of interesting articles by reading these, and I am grateful that the author made the effort to collect this information for the benefit of his readers. References [1] Poisson E 2004 Radiation reaction of point particles in curved spacetime Class. Quantum Grav 21 R153?R232 [2] Lousto C O 2005 Special issue: Gravitational Radiation from Binary Black Holes: Advances in the Perturbative Approach, Class. Quantum Grav22 S543?S868 [3] Jackson J D 1999 Classical Electrodynamics Third Edition (New York: Wiley) [4] Rohrlich F 1990 Classical Charged Particles (Redwood City, CA: Addison?Wesley) [5] Landau L D and Lifshitz E M 2000 The Classical Theory of Fields Fourth Edition (Oxford: Butterworth?Heinemann) [6] Cohen-Tannoudji C Dupont-Roc J and Grynberg G 1997 Photons and Atoms - Introduction to Quantum Electrodynamics (New York: Wiley-Interscience) [7] Cohen-Tannoudji C, Dupont-Roc J and G Grynberg G 1998 Atom?Photon Interactions: Basic Processes and Applications (New York: Wiley-Interscience)

Modified teleparallel theories of gravity

Abstract: We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based on the Ricci scalar are. This motivates the study of a model depending on the torsion scalar and the divergence of the torsion vector. We derive the teleparallel equivalent of $f(R)$ gravity as a particular subset of these models and also show that this is the unique theory in this class that is invariant under local Lorentz transformation. Furthermore one can show that $f(T)$ gravity is the unique theory admitting second-order field equations.