General Relativity Research Articles

Observational tests of 4D double field theory

Although General Relativity (GR) is a very successful theory of gravity, it cannot explain every observational phenomenon. People have tried many kinds of modified gravity theory to explain these phenomena which GR cannot explain very well, such as string theory. In recent years Double Field Theory (DFT) has been an exciting research area in string theory. The most general, spherically symmetric, asymptotically flat, static vacuum solution to D=4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=4$$\\end{document} double field theory has been derived by S.M. Ko, J.H. Park and M. Suh. In this article, we calculate the minor corrections to the three predictions in GR: optical deflation, planet precession and gravitational redshift. These three predictions should be able to tested by observations and find the discrepancies between GR and DFT in the future.

Preliminary sensitivity study for a gravitational redshift measurement with China's Lunar Exploration Project

Abstract General relativity (GR) is a highly successful theory that describes gravity as a geometric phenomenon. The gravitational redshift, a classic test of GR, can potentially be violated in alternative gravity theories, and experimental tests on this effect are crucial for our understanding of gravity. In this paper, considering the space-ground clock comparisons with free-space links, we discuss a high-precision Doppler cancellation-based measurement model for testing gravitational redshift. This model can effectively reduce various sources of error and noise, reducing the influences of the first-order Doppler effect, atmospheric delay, Shapiro delay, etc. China's Lunar Exploration Project (CLEP) is proposed to equip the deep-space H maser with a daily stability of $2\times10^{-15}$, which provides an approach for testing gravitational redshift. Based on the simulation, we analyze the space-ground clock comparison experiments of the CLEP experiment, and simulation analysis demonstrates that under ideal condition of high-precision measurement of the onboard H-maser frequency offset and drift, the CLEP experiment may reach the uncertainty of $3.7\times10^{-6}$ after a measurement session of 60 days. Our results demonstrate that if the issue of frequency offset and drift is solved, CLEP missions have a potential of testing the gravitational redshift with high accuracy.

The Dirac equation as a linear tensor equation for one component

The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several components of the Dirac field. On the other hand, the author showed previously that the Dirac equation in electromagnetic field is equivalent to a fourth-order equation for one component of the Dirac spinor. The equivalency is used in this work to derive a linear tensor equivalent of the Dirac equation for just one component. This surprising result can be used in applications of the Dirac equation, for example, in general relativity or for lattice approximation of the Dirac field, and can improve our understanding of the Dirac equation.

Beyond the Quantum Membrane Paradigm: A Philosophical Analysis of the Structure of Black Holes in Full QG

This paper presents a philosophical analysis of the structure of black holes, focusing on the event horizon and its fundamental status. While black holes have been at the centre of countless paradoxes arising from the attempt to merge quantum mechanics and general relativity, recent experimental discoveries have emphasised their importance as objects for the development of Quantum Gravity. In particular, the statistical mechanical underpinning of black hole thermodynamics has been a central research topic. The Quantum Membrane Paradigm, proposed by Wallace (Stud Hist Philos Sci Part B 66:103-117, 2019), posits a real membrane made of black hole microstates at the black hole horizon to provide a statistical mechanical understanding of black hole thermodynamics from an exterior observer’s point of view. However, we argue that the Quantum Membrane Paradigm is limited to low-energy Quantum Gravity and needs to be modified to avoid reference to geometric notions, such as the event horizon, which presumably do not make sense in the non-spatiotemporal context of full Quantum Gravity. Our proposal relies on the central dogma of black hole physics. It considers recent developments, such as replica wormholes and entanglement wedge reconstruction, to provide a new framework for understanding the nature of black hole horizons in full Quantum Gravity.

Aether Scalar Tensor (AeST) theory: Quasistatic spherical solutions and their phenomenology

Abstract There have been many efforts in the last three decades to embed the empirical MOND program into a robust theoretical framework. While many such theories can explain the profile of galactic rotation curves, they usually cannot explain the evolution of the primordial fluctuations and the formation of large-scale-structures in the Universe. The Aether Scalar Tensor (AeST) theory seems to have overcome this difficulty, thereby providing the first compelling example of an extension of general relativity able to successfully challenge the particle dark matter hypothesis. Here we study the phenomenology of this theory in the quasistatic weak-field regime and specifically for the idealised case of spherical isolated sources. We find the existence of three distinct gravitational regimes, that is, Newtonian, MOND and a third regime characterised by the presence of oscillations in the gravitational potential which do not exist in the traditional MOND paradigm. We identify the transition scales between these three regimes and discuss their dependence on the boundary conditions and other parameters in the theory. Aided by analytical and numerical solutions, we explore the dependence of these solutions on the theory parameters. Our results could help in searching for interesting observable phenomena at low redshift pertaining to galaxy dynamics as well as lensing observations, however, this may warrant proper N-body simulations that go beyond the idealised case of spherical isolated sources.

Perturbations of spinning black holes in dynamical Chern-Simons gravity: Slow rotation equations

The detection of gravitational waves resulting from the coalescence of binary black holes by the LIGO-Virgo-Kagra Collaboration has inaugurated a new era in gravitational physics. These gravitational waves provide a unique opportunity to test Einstein’s general relativity and its modifications in the regime of extreme gravity. A significant aspect of such tests involves the study of the ringdown phase of gravitational waves from binary black hole coalescence, which can be decomposed into a superposition of various quasinormal modes. In general relativity, the spectra of quasinormal modes depend on the mass, spin, and charge of the final black hole, but they can also be influenced by additional properties of the black hole spacetime, as well as corrections to the general theory of relativity. In this work, we focus on a specific modified theory known as dynamical Chern-Simons gravity. We employ the modified Teukolsky formalism developed in a previous study and lay down the foundations to investigate perturbations of slowly rotating black holes admitted by the theory. Specifically, we derive the master equations for the Ψ0 and Ψ4 Weyl scalar perturbations that characterize the radiative part of gravitational perturbations, as well as the master equation for the scalar field perturbations. We employ metric reconstruction techniques to obtain explicit expressions for all relevant quantities. Finally, by leveraging the properties of spin-weighted spheroidal harmonics to eliminate the angular dependence from the evolution equations, we derive two, radial, second-order, ordinary differential equations for Ψ0 and Ψ4, respectively. These two equations are coupled to another radial, second-order, ordinary differential equation for the scalar field perturbations. This work is the first attempt to derive a master equation for black holes in dynamical Chern-Simons gravity using curvature perturbations. The master equations we obtain can then be numerically integrated to obtain the quasinormal mode spectrum of slowly rotating black holes in this theory, making progress in the study of ringdown in dynamical Chern-Simons gravity. Published by the American Physical Society 2024

Scalar radiation with a quartic Galileon

The class of Galileon scalar fields theories encapsulate the Vainshtein screening mechanism, which is characteristic of a large range of infrared modified theories of gravity. Such theories can lead to testable departures from general relativity through fifth forces and new scalar modes of gravitational radiation. However, the inherent nonlinearity of the Vainshtein mechanism has limited analytic attempts to describe Galileon theories with both cubic and quartic interactions. To improve on this, we perform direct numerical simulations of the quartic Galileon model for a rotating binary source and infer the power spectrum of given multipoles. To tame numerical instabilities we utilize a low-pass filter, extending previous work on the cubic Galileon. Our findings show that the multipole expansion is well defined and under control. Moreover, our results confirm that despite being a nonlinear scalar, the dominant Galileon radiation is quadrupole, and we find a new scaling behavior deep inside the Vainshtein region. Published by the American Physical Society 2024

Cosmologies in $f(R,\mathcal{L}_{m})$ theory with non-minimal coupling between geometry and matter

Abstract Among the recent extensions to standard General Relativity, $f(R,\mathcal{L}_{m})$ gravity has risen an interest given the possibility of coupling between geometry and matter.
We examine the simplest model with non-minimal coupling in the context
of cosmology. We pay special attention to the question of how far this
model could reproduce the observational fact of our universe.

Setting the connection free in the Galilei and Carroll expansions of gravity

We obtain a Palatini-type formulation for the Galilei and Carroll expansions of general relativity, where the connection is promoted to a variable. Known versions of these large and small speed of light expansions are derived from the Einstein-Hilbert action and involve dynamical Newton-Cartan or Carroll geometry, along with additional gauge fields at subleading orders. The corresponding Palatini actions that we obtain in this paper are derived from an appropriate expansion of the Einstein-Palatini action, and the connection variable reduces to the Galilei- or Carroll-adapted connection on shell. In particular, we present the Palatini form for the next-to-leading-order Galilean action and recover the known equations of motion. We also compute the leading-order Palatini-type action for the Carrollian case and show that, while it depends on the connection variable, it reduces on shell to the known action of electric Carroll gravity, which only depends on extrinsic curvature. Published by the American Physical Society 2024

Sudden breakdown of effective field theory near cool Kerr-Newman black holes

It was recently shown that (near-)extremal Kerr black holes are sensitive probes of small higher-derivative corrections to general relativity. In particular, these corrections produce diverging tidal forces on the horizon in the extremal limit. We show that adding a black hole charge makes this effect qualitatively stronger. Higher-derivative corrections to the Kerr-Newman solution produce tidal forces that scale inversely in the black hole temperature. We find that, unlike the Kerr case, for realistic values of the black hole charge large tidal forces can arise before quantum corrections due to the Schwarzian mode become important, so that the near-horizon behavior of the black hole is dictated by higher-derivative terms in the effective theory.

Charge asymmetric fall under gravity of a plate in general relativity

Charged test particle geodesics determine the fall toward a regular plate whose metric is expressed in plane-symmetric form depending only on the z-direction. Falling conditions are obtained in the test electric/magnetic Maxwell fields for both anisotropic and isotropic plates. These results have implications for particle/antiparticle fall differences in the case of a general relativistic plate.

Geometric interpretation of Tensor-Vector-Scalar theory in a Kaluza-Klein reference fluid

Abstract Gravitational alternatives to dark matter require additional fields or assumptions beyond general relativity while continuing to agree with tight solar system constraints. Modified Newtonian Dynamics (MOND), for example, predicts the Tully-Fisher relation for galaxies more accurately than dark matter models while limiting to Newtonian gravity in the solar system. On the other hand, MOND does a poor job predicting larger scale observations such as the Cosmic Microwave Background and Matter Power Spectra. Tensor-Vector-Scalar (TeVeS) theory is a relativistic generalization of MOND that accounts for these observations without dark matter. In this paper, I derive a generalized TeVeS from Kaluza-Klein theory in one extra dimension as a consequence of $n=0$ Kaluza-Klein modes. In the KK theory, MOND is a special case of a slicing condition in the 5D ADM formalism enforced by a reference fluid as in the Isham-Kucha\v{r} method which may arise from a broken displacement symmetry. This has two benefits: first is means that TeVeS is compatible with Kaluza-Klein dark matter theory, which is a strong candidate for Weakly Interacting Massive Particles (WIMPs), the other is that it provides an elegant mechanism for the scalar and vector fields. It constrains most of the freedom in the definition of TeVeS which does not have a field theoretic motivation. This is important because the Kaluza-Klein theory predicts that spin-2 tensor modes must propagate at the speed of light, in agreement with observation, from theoretical constraints while TeVeS has to match this observation empirically. Furthermore, it removes need for the interpolating function in MOND and the Lorentz-violating condition on the vector field to be physical since they are analogous to a gauge condition and depend on state of motion.

Back Reaction of the Electromagnetic Radiation and the Local Inertial Frame

We discuss on the problem of the electromagnetic radiation from the accelerated charged particle and the back reaction of that. The free-falling charged particle radiates the electromagnetic wave. The charged particle on the surface of the earth does not radiate the electromagnetic wave. The existence or the non-existence of the electromagnetic radiation from the charged particle and the back reaction of that is independent of the observer, which is consistent with the energy conservation. A paradox comes from combining this phenomenon with the equivalence principle in the theory of the general relativity. We consider the Hawking effect in the context of this paradox. We give our resolution on this paradox.

Isotropic compact stars admitting Heintzmann solution in Rastall gravity

This paper is devoted to observe the physical attributes of static spherically symmetric isotropic compact stellar candidates in the context of Rastall theory of gravity. In order to inspect the structural composition of compact objects, the Heintzmann ansatz is taken into account. The unknown parameters associated with Heintzmann ansatz are evaluated through matching conditions with derived values of radii and masses of some specific star models. The consistency of the adopted ansatz is analyzed via graphical interpretation of matter variables, equation of state parameter, mass components, energy constraints, causality condition, stellar equation and adiabatic index for several choices of Rastall parameter. It is observed that the stars under consideration manifest stable structures corresponding to Heintzmann ansatz in this framework. Moreover, it is shown that for vanishing Rastall coupling parameter, the standard outcomes of general relativity can be retrieved.

Distinguishability of binary extreme-mass-ratio inspirals in low frequency band

The inspiral of compact stellar objects into massive black holes are one of the main astrophysical sources for the Laser Interferometer Space Antenna (LISA) and Taiji. These extreme-mass-ratio inspirals (EMRIs) have great potential for cosmology and fundamental physics. A binary extreme-mass-ratio inspiral (b-EMRI) describes the case where binary black holes (BBHs) are captured by a supermassive black hole. The b-EMRIs serve as multi-band gravitational wave sources and provide insights into the dynamics of nuclei and tests of general relativity. However, if the b-EMRIs can be distinguished from the normal EMRIs or not is still not clear. In this work, with a few of assumptions, and using the Teukolsky equation, we calculate the approximate gravitational waves of b-EMRIs and assess their detectability by space-based detectors. We also decouple the secondary object information from the Teukolsky equation, enabling us to calculate the energy fluxes and generate the waveforms more conveniently. Variations in the quadrupole of the binary result in small but non-negligible changes in energy fluxes and waveforms, making it possible to distinguish b-EMRI signals with data analysis. This opens up the potential of using b-EMRIs to test gravity theories and for further astrophysical studies.

Can nonlocal gravity really explain dark energy?

In view to scrutinize the idea that nonlocal modifications of General Relativity could dynamically address the dark energy problem, we investigate the evolution of the Universe at infrared scales as an Infinite Derivative Gravity model of the Ricci scalar, without introducing the cosmological constant Λ or any scalar field. The accelerated expansion of the late Universe is shown to be compatible with the emergence of nonlocal gravitational effects at sufficiently low energies. A technique for circumventing the mathematical complexity of the nonlocal cosmological equations is developed and, after drawing a connection with the Starobinsky gravity, verifiable predictions are considered, like a possible decreasing in the strength of the effective gravitational constant. In conclusion, the emergence of nonlocal gravity corrections at given scales could be an efficient mechanism to address the dark energy problem.

Non-Local Cosmology: From Theory to Observations

We examine the key aspects of gravitational theories that incorporate non-local terms, particularly in the context of cosmology and spherical symmetry. We thus explore various extensions of General Relativity, including non-local effects in the action through the function F(R,□−1R), where R denotes the Ricci curvature scalar and the operator □−1 introduces non-locality. By selecting the functional forms using Noether Symmetries, we identify exact solutions within a cosmological framework. We can thus reduce the dynamics of these chosen models and obtain analytical solutions for the equations of motion. Therefore, we study the capability of the selected models in matching cosmological observations by evaluating the phase space and the fixed points; this allows one to further constrain the non-local model selected by symmetry considerations. Furthermore, we also investigate gravitational non-local effects on astrophysical scales. In this context, we seek symmetries within the framework of f(R,□−1R) gravity and place constraints on the free parameters. Specifically, we analyze the impact of non-locality on the orbits of the S2 star orbiting SgrA*.

On the covariant formulation of gauge theories with boundaries

In the present article, we review the classical covariant formulation of Yang–Mills theory and general relativity in the presence of spacetime boundaries, focusing mainly on the derivation of the presymplectic forms and their properties. We further revisit the introduction of the edge modes and the conditions which justify them, in the context where only field-independent gauge transformations are considered. We particularly show that the presence of edge modes is not justified by gauge invariance of the presymplectic form, but rather by the condition that the presymplectic form is degenerate on the initial field space, which allows to relate this presymplectic form to the symplectic form on the gauge reduced field space via pullback.

Does spacetime have memories? Searching for gravitational-wave memory in the third LIGO-Virgo-KAGRA gravitational-wave transient catalogue

Gravitational-wave memory is a non-linear effect predicted by general relativity that remains undetected. We apply a Bayesian analysis framework to search for gravitational-wave memory using binary black hole mergers in LIGO-Virgo-KAGRA’s third gravitational-wave transient catalogue. We obtain a Bayes factor of ln⁡BF=0.01 , in favour of the no-memory hypothesis, which implies that we are unable to measure memory with currently available data. This is consistent with previous work, suggesting that a catalogue of O(2000) binary black hole mergers is needed to detect memory. We look for new physics by allowing the memory amplitude to deviate from the prediction of general relativity by a multiplicative factor A. We obtain an upper limit of A < 23 (95% credibility).

A geometric framework for interstellar discourse on fundamental physical structures

This paper considers the possibility that abstract thinking and advanced synthesis skills might encourage extraterrestrial civilizations to accept communication with mankind on Earth. For this purpose, a notation not relying upon the use of alphabet and numbers is proposed, in order to denote just some basic geometric structures of current physical theories: vector fields, [Formula: see text]-form fields, and tensor fields of arbitrary order. An advanced civilization might appreciate the way here proposed to achieve a concise description of electromagnetism and general relativity, and hence it might accept the challenge of responding to our signals. The abstract symbols introduced in this paper to describe the basic structures of physical theories are encoded into black and white bitmap images that can be easily converted into short bit sequences and modulated on a carrier wave for radio transmission.